2024-03-28T10:35:32Z
http://surface.syr.edu/do/oai/
oai:surface.syr.edu:mat_etd-1001
2010-08-31T17:02:01Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Fast multiscale integral equation methods for image restoration
Lu, Yao
Discrete models are consistently used as practical models for image restoration. They are piecewise constant approximations of the true physical (continuous) model, and hence, inevitably impose bottleneck model errors. We propose to work directly with the continuous model for image restoration aiming at suppressing the model errors caused by the discrete models. A systematic study is conducted in the dissertation for the continuous out-of-focus image models which can be formulated as an integral equation of the first kind. The resultant integral equation is regularized by the Lavrentiev method and the Tikhonov method. We develop fast wavelet Galerkin method and fast multiscale collocation method having high accuracy to solve the regularized integral equations of the second kind with Gaussian kernels. A new adaptive numerical quadrature with exponential order of accuracy is derived for computing the integrals of Gaussian integrand. We apply the proposed adaptive numerical quadrature for generating the coefficient matrix. Numerical experiments show that the methods based on continuous model perform much better than those based on discrete model in terms of PSNR values and visual quality of the reconstructed images.
2009-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/3
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Mathematics - Dissertations
SURFACE at Syracuse University
Integral equation
Image restoration
Wavelet
Tikhonov
Physical Sciences and Mathematics
oai:surface.syr.edu:eecs_etd-1004
2010-08-31T16:45:17Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:eecs_etd
publication:lcsmith
publication:cas
publication:deecs
Approximation of kernel matrices in machine learning
Song, Guohui
Kernels are popular in a variety of fields such as approximation, interpolation, meshless methods, neural networks and machine learning. A common problem of these kernel-based methods is to calculate the inverses of the matrices generated by a kernel function and a set of points. This work focuses on developing fast algorithms for calculating the inverses by approximating the kernel matrices with related multilevel circulant matrices so that the fast Fourier transform can apply to reduce the computational cost. In the first part of this thesis, we introduce two classes of matrices that contain the kernel matrices under different assumptions of the kernel function and the data points. Some properties of these two classes of matrices such as the approximation behavior of the elements and some functions of the inverses are presented. Moreover, we give the convergence analysis of approximating the kernel matrices with related multilevel circulant matrices based on properties of these two classes of matrices. The second part of this thesis talks about the applications of this approximation technique in machine learning. After introducing the formulation of two common problems in machine learning, we present some fast algorithms for these two problems and give the convergence analysis based on the results obtained in Part I.
2009-01-01T08:00:00Z
text
https://surface.syr.edu/eecs_etd/5
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Electrical Engineering and Computer Science - Dissertations
SURFACE at Syracuse University
Kernel
Machine learning
Hilbert space
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1002
2010-08-31T17:05:09Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Growth of tessellations
Graves, Stephen James
A tessellation is understood to be a 1-ended, locally finite, locally cofinite, 3-connected planar map. A definition for the rate of exponential growth of a tessellation of the hyperbolic plane is established, and existing methods for computing growth are refined. Growth rates of both face- and edge-homogeneous tessellations are considered, and two major results are proven: first, that tessellations exist for any arbitrary growth rate greater than or equal to 1, and second, that the least rate of growth for a face-homogeneous tessellation is (1 + [Special characters omitted.] )/2.
2009-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/2
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Mathematics - Dissertations
SURFACE at Syracuse University
Tessellations
Growth rate
Hyperbolic plane
Homogeneous
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1005
2010-08-31T17:15:23Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
On the structure of reliability polynomials
Graves, Christina Marie
This dissertation explores a new way to look at reliability polynomials by use of a convex basis. The shape of reliability polynomials has been studied by numerous people including Moore, Shannon, Birnbaum, Esary, Saunders, and Colbourn. Colbourn posed the question, "Is it true that a reliability polynomial has at most one point of inflection in the range p ∈ (0; 1)?" This newly created convex basis allows us to consider the inflection point problem from a new viewpoint. In fact, it is used to deduce that reliability polynomials can have more than one inflection point.
2009-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/8
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Mathematics - Dissertations
SURFACE at Syracuse University
Reliability polynomials
Convex basis
Inflection point
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1006
2010-08-31T17:17:58Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Sampling with reproducing kernels
Zhang, Haizhang
The theme of sampling is the reconstruction of a function from its values at a set of points in its domain. It is arguable that the functions to be reconstructed should be from a reproducing kernel Hilbert space (RKHS), where point evaluations are continuous linear functionals. Under this setting, we prove that the minimal norm interpolation always provides the optimal reconstruction operator. It is also shown that the approximation error converges to zero as the number of samplings tends to infinity if and only if the sampling set is a uniqueness set for the RKHS. Uniqueness sets in various RKHS are investigated. We then turn to perfect reconstruction formulas like the Shannon sampling theorem for the Paley-Wiener space. By the frame theory, such formulas exist if the RKHS has a Riesz sampling set. Consequences, properties, and existence of Riesz sampling sets in RKHS are explored. In particular, it is shown that the RKHS of the widely used Gaussian kernels do not possess a Riesz sampling set. The last part of the thesis centers around optimal reconstruction of a function in the Paley-Wiener spaces from its localized samples. Several equivalent formulations for the approximation error of the optimal algorithm are established, followed by favorable upper and lower bound estimates. The estimates show that the approximation error decays exponentially (but not faster) as the number of localized samplings increases. We also provide an explicit and practical reconstruction formula whose approximation error satisfies the upper bound estimate.
2009-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/7
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Mathematics - Dissertations
SURFACE at Syracuse University
Kernels
Sampling theory
Optimal reconstruction
Band-limited signals
Hilbertspaces
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1009
2010-08-31T17:29:47Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Biological time series classification via reproducing kernels and sample entropy
Mao, Dong
In this thesis, we study classification of biological time series and its related theoretical issues. We focus on two issues: fast algorithms for computing the sample entropy of a time series which describes the "complexity" of the time series and reproducing kernels used in the support vector machine for classification. To compute the sample entropy of a time series, we introduce a randomized k-d tree and a fast algorithm based on the randomized k-d tree to compute the sample entropy. We systematically analyze the randomized k-d tree and estimate the time complexity of the fast algorithm. For reproducing kernels, we conduct foundational research, such as giving reproducing kernels of some commonly used function spaces like harmonic function spaces and Sobolev spaces, creating reproducing kernels from integral operators, and clarifying the inner product of reproducing kernel Hilbert spaces associated with reproducing kernels.
2008-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/11
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Mathematics - Dissertations
SURFACE at Syracuse University
Reproducing kernels
Sample entropy
k-d trees
RKHS
Support vector machines
Randomized k-d trees
Biological time series classification
Entropy
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1017
2010-09-16T18:53:17Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Structure of infinitely-ended, edge-transitive planar maps and their petrie walks
McCaffery, Adam James
A construction is described that yields a complete characterization of a class of infinitely-ended, locally finite, edge-transitive, 3-connected planar graphs. As a result, the members of a second such class are characterized and a complete presentation is given of the members of a third.
A Petrie walk in a plane graph is a walk with the property that every two consecutive edges are incident with a common face but no three consecutive edges have this property. J.E. Graver and M.E.Watkins have classified [Special characters omitted.] , consisting of all locally finite, edge-transitive, 3-connected planar graphs, in terms of the kinds of Petrie walks that occur, the number of ends of the graph, and the edge-, vertex-, face- and Petrie walk-stabilizers in the automorphism group of the graph. All ordinary members of [Special characters omitted.] , i.e., graphs admitting all vertex-face reflections, have been characterized. The existence of extraordinary members of each of four distinct subclasses has already been established.
In this work, members of two of the four subclasses of extraordinary graph are characterized, and a third subclass is completely presented. The construction used is an amalgamation construction of B. Mohar, which is a generalization of the interleaving construction used by Graver and Watkins to produce ordinary members of [Special characters omitted.] . Results about Petrie walks in these extraordinary graphs lead to a result about Petrie walks in members of [Special characters omitted.] crossing each other multiple times, and answer an open question of Graver and Watkins.
2009-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/16
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Mathematics - Dissertations
SURFACE at Syracuse University
Infinitely-ended
Edge-transitive
Planar maps
Petrie walks
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1019
2010-09-20T14:33:13Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
A new approach to test for interactions in two-way ANOVA models
Ning, Wei
The F-test has been used to detect interactions in Two-way ANOVA models. However, the F-test for the interaction is not as powerful as the F-test for the main effects, and its power is often very low if there are only a few disturbances in data under the typical restrictions. Daniel (1978) and Terbeck and Davies (1998) reparameterized the model and proposed new statistics to detect the interactions under unconditionally identifiable patterns. They showed that their tests are better than the classical F-test and also can identify the locations of the non-zero disturbances. However, their methods do not work well for the model with non-unconditionally identifiable patterns.
In this thesis, we use the parameterization, the same as the one used in Daniel (1978) and Terbeck and Davies (1998), and propose new test statistics to detect non-zero interactions. We show that our test is more powerful than the classical F-test and can handle both situations: unconditionally identifiable pattern (UIP) and non-unconditionally identifiable pattern. For a special 3 × 3 case, we also propose a selection procedure that leads us to choose the best configuration with the highest power under a UIP. Under a non-UIP condition, simulations illustrate that the selection procedure still works. In order to find critical values at a given significance level, we suggest using a numerical integration or a polynomial approximation or Worsley's approximation (1982).
For a general I × J case, simulations indicate that our test statistic still has a higher power than the classical F-test, and we can still apply the selection procedure for the best configuration to the general case. Due to high dimensional integrations involved, the numerical integration and the polynomial approximation are not feasible in finding the critical values. We suggest using Worsley's approximation (1982) to obtain reasonable accuracies.
2006-08-01T07:00:00Z
text
https://surface.syr.edu/mat_etd/20
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Mathematics - Dissertations
SURFACE at Syracuse University
Power
F-test
Two-way ANOVA
ANOVA
Biostatistics
Mathematics
oai:surface.syr.edu:mat_etd-1020
2010-09-20T18:23:01Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
On the geometry of p-harmonic mappings
Adamowicz, Tomasz
The main subject of this dissertation is the geometry of p -harmonic mappings and related topics. The class of quasiradial mappings in the plane is introduced and their basic properties are investigated. We discuss generating p -harmonic functions and mappings via compositions and observe that in several cases only composition with an affine function produces new p -harmonic functions or mappings. This illustrates the rigidity of p -harmonic mappings.
The variational interpretation of p -harmonics leads to several problems and generalizations. We present radial p -harmonics on ring domains and show solvability of the Dirichlet problem. Existence of four fundamental solutions is proven and their geometric properties are presented. We generalize the p -Dirichlet energy to the weighted case, free-Lagrangians are discussed as well. Next we investigate homeomorphisms with finite distortion and relate them to p -harmonic mappings. The planar Grötzsch problem is extended to higher dimensions and exposed in connections with polyconvex, quasiconvex and rank-one convex functionals. We define the Grötzsch property for energy functionals and show that it holds for a wide class of polyconvex energy functionals.
To every p -harmonic mapping in the plane with p ≥ 2 there corresponds a quasilinear system of first order PDE's which couples the complex gradients of the coordinate functions of the mapping. The ellipticity of such system is proved. A relation between planar quasiregular mappings and p -harmonic mappings is discussed. The p -harmonic conjugate problem is stated.
We finish the exposition with some open problems in the geometry of nonlinear systems.
2008-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/21
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Mathematics - Dissertations
SURFACE at Syracuse University
p-harmonic
Calculus of variations
Nonlinear PDEs
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1021
2010-09-22T12:23:18Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Continuity of plurisubharmonic envelopes
Gogus, Nihat Gokhan
Let D be a domain in [Special characters omitted.] . The plurisubharmonic envelope of a function [varphi] [is an element of] C(D¯) is the supremum of all plurisubharmonic functions which are not greater than [varphi] on D . A bounded domain D is called c-regular if the envelope of every function [varphi] [is an element of] C(D¯) is continuous on D and extends continuously to D¯ . The purpose of this thesis is to give a complete characterization of c -regular domains in terms of Jensen measures . We show using Gauthier's Fusion Lemma that a domain is locally c -regular if and only if it is c -regular.
2006-08-01T07:00:00Z
text
https://surface.syr.edu/mat_etd/23
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Mathematics - Dissertations
SURFACE at Syracuse University
Continuity
Plurisubharmonic envelopes
Jensen measures
Mathematics
oai:surface.syr.edu:mat_etd-1022
2010-09-22T12:29:18Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Deformations of plane curve singularities of constant class
Lynn, Philip Joseph
This dissertation considers the geometry of the locus of constant class in the deformation spaces of plane curve singularities. In [DH], Diaz and Harris discuss the geometry of the equisingular ( ES ), equigeneric ( EG ), and equiclassical ( EC ) loci in the same deformation spaces. We define the locus of constant class EK as the locus which parametrizes deformations of constant class. By definition, EK contains EC . We investigate and answer the question: Is EK equal to EC ?
We define conditions for EK to be different from EC and then explore the singularities where this might be possible. For y 2 + x n = 0, we are able to show where EK is different from EC . We also compute the tangent cones for the different pieces of EK and hence for EK itself, in many cases. Investigating the y 3 + x n = 0 singularities in search of the extra pieces of EK leads to the definition of the pre-EK loci , each of which possibly contains a piece of EK and other loci. We explore the possibilities for these other loci, finally leading up to the double triple point locus in one of the pre-EK loci for y 3 + x 6 = 0.
2006-12-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/22
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Mathematics - Dissertations
SURFACE at Syracuse University
Plane curve
Singularities
Constant class
Mathematics
oai:surface.syr.edu:mat_etd-1023
2010-09-23T18:55:11Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Representations of a valued quiver, the lattice of admissible sequences, and the Weyl group of a Kac-Moody algebra
Pelley, Allen Neil
This dissertation studies connections between the preprojective representations of a finite connected valued quiver without oriented cycles, the (+)-admissible sequences of vertices, and the Weyl group. For each preprojective representation, a shortest (+)-admissible sequence annihilating the representation is unique up to a certain equivalence. A (+)-admissible sequence is the shortest sequence annihilating some preprojective representation if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group. These statements have the following application that strengthens known results of Howlett and Fomin-Zelevinsky. For any fixed Coxeter element of the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix, the group is infinite if and only if the powers of the element are reduced words. These results also extend Gabriel's Theorem by providing a one-to-one correspondence between indecomposable preprojective representations and elements in the Weyl group that have a reduced expression whose associated sequence of vertices is a principal (+)-admissible sequence.
2007-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/24
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Mathematics - Dissertations
SURFACE at Syracuse University
Admissible sequences
Weyl group
Kac-Moody algebra
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat-1001
2012-09-19T15:37:59Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Elliptic Complexes and Generalized Poincaré Inequalities
Gustafson, Derek
We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincar\'e inequality holds. We show that the constant rank condition is sufficient. The concept of the Moore-Penrose generalized inverse of a matrix comes into play.
2008-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/2
https://surface.syr.edu/context/mat/article/1001/viewcontent/derek.pdf
http://creativecommons.org/licenses/by/3.0/
Mathematics - All Scholarship
English
SURFACE at Syracuse University
Analysis of PDEs
Classical Analysis and ODEs
Mathematics
oai:surface.syr.edu:mat_etd-1024
2010-09-24T18:49:36Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Wavelets on manifolds and multiscale reproducing kernel Hilbert spaces
Struble, Dale William
This research focuses on wavelets adapted to compact domains with further application to manifolds and reproducing kernel Hilbert spaces. In the setting of manifolds, technical requirements allowing the explicit construction of these wavelets are addressed. Wavelet decomposition and reconstruction formulas are given for the class of square integrable functions. Following these results is a demonstration of the theory to several different domains of interest, such as a curved surface and a simplex in dimension two. The constructions are explicit and include several possible initial wavelet spaces.
The application of these wavelets to reproducing kernel Hilbert spaces is discussed. Results include a decomposition/reconstruction algorithm and a new fully wavelet multiscale reproducing kernel. Convergence analysis of approximations using these kernels is given.
The results of this research are motivated in part by their applicability to modeling flutter. More specifically, modeling flutter for high performance aircraft traveling in high speed flight regimes, a research question sponsored by NASA. The setting and expected benefits for this application are discussed in detail.
2007-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/25
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Mathematics - Dissertations
SURFACE at Syracuse University
Wavelets
Manifolds
Reproducing kernel
Hilbert spaces
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1025
2010-09-27T14:59:35Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Multi-category support vector machines
Gao, Yunchuan
In this dissertation, we study the multi-category support vector machines (k-SVM). The design of the model and the analysis of consistency are fully discussed. The application to an NIOSH (National Institution for Occupational Safety and Health) project is also discussed.
In order to design the k-SVM model, the concepts of hyperplane separation are introduced. The points in the original space and input space are mapped into high dimensional space which is called feature space. Here we suppose that the feature space is the reproducing kernel Hilbert space of functions. The hyperplanes are searched in feature space. Firstly it is assumed that classes of points are separable, which leads to general k-SVM model. For the cases when classes of points are not separable, the 2-norm soft margin k-SVM is constructed. In both cases, the purpose is to find the hyperplanes in feature space which divides the classes with maximum margins. The search of the maximum margins leads to optimization problems. By the aid of Lagrangian multipliers, the optimization problems are transformed to constrained quadratic optimization problems. The decision functions are generated.
To analyze the performance of the model, we define the weak consistency and consistency of the algorithm. The decision function with minimum risk is constructed. We show that the risk of our decision function approaches to the minimum risk as the sample size goes to infinity. The approach is in the sense of probability measure.
As a testing of the performance of our model, we apply the algorithm to the NIOSH project. In NIOSH project, 200 scans of human body surfaces are provided. The scans contain large number of triangulated points. The k-SVM model is applied to classify the data according to the existing classes. Part of the samples are used as training data to generate the decision function. The rest of samples are used to test the prediction accuracy of the decision function. By choosing the appropriate kernel functions, our model obtains the accuracy of 92%.
2006-05-01T07:00:00Z
text
https://surface.syr.edu/mat_etd/26
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Mathematics - Dissertations
SURFACE at Syracuse University
Support vector machines
Machine learning
Classification
Multicategory
Mathematics
oai:surface.syr.edu:mat-1002
2012-09-19T15:37:27Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Polynomial Estimates, Exponential Curves and Diophantine Approximation
Coman, Dan
Poletsky, Evgeny A.
Abstract. Let [alpha] [is an element of] (0, 1) \ [the rationals] and K = {(ez, eaz) : |z| [less than or equal to] 1} [is a subset of] [the complex numbers]2.If P is a polynomial of degree n in [the complex numbers]2, normalized by ||P||K = 1, we obtain sharp estimates for ||P||[delta]2 in terms of n, where [delta]2 is the closed unit bidisk. For most [alpha], we show that supp ||P||[subdelta]2[is less than or equal to] exp (Cn2log n). However, for [alpha] in subset S of the Liouville numbers, supp ||P||[subdelta]2 has bigger order of growth. We give a precise characterization of the set S and study its properties.
2010-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/3
http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.4408v1.pdf
http://creativecommons.org/licenses/by/3.0/
Mathematics - All Scholarship
English
SURFACE at Syracuse University
Complex variables
Mathematics
oai:surface.syr.edu:mat_etd-1026
2010-09-28T18:10:21Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
A homological approach to differentiation algorithms and dimensions of finite type for representations of partially ordered sets
Reitenbach, Markus
The category of representations of a partially ordered set is studied from a homological point of view. This approach is used to generalize the differentiation algorithms for representations of partially ordered sets with respect to maximal respectively minimal elements. Homological methods and the differentiation procedure are further explored to study dimensions of finite type for representations of partially ordered sets.
2005-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/27
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Mathematics - Dissertations
SURFACE at Syracuse University
Homological
Partially ordered sets
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1027
2010-09-29T12:47:43Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Selection procedures for binomial populations
Buzaianu, Elena Mihaela
In this thesis we consider the problem of selecting the best among several experimental treatments in comparison to a control treatment, under the binomial setting. The goal is to select the experimental treatment that produces the largest value of the probability of getting a success in a single trial, when this probability is better than the one corresponding to the control population. Otherwise, we select the control treatment.
We propose selection procedures based on the single-stage procedure defined by Dunnett (1984) and the hybrid selection and testing procedure defined by Thall et al.(1988). Our procedures are exact. That is, they are based on the binomial distribution only, as opposed to most of the original procedures that involve the normal approximation to the binomial. We evaluate the probability of a correct selection P(CS) for our procedures exactly and then derive the least favorable configurations (LFC). With our results on the LFC, the redefined procedures can be applied to any sample size.
Based on the fixed sample size procedure proposed by Sobel and Hyuett (1957), with the desire of minimizing the number of observations taken from the poorer populations, Bechoffer and Kulkarni (1982) proposed a sequential procedure which achieves the same probability of a correct selection as does the Sobel-Hyuett procedure, but requires fewer observations. Along the same lines, but based on Dunnett's fixed-sample-size procedure (1984) where a control is involved, we have used strong curtailment to define a procedure which requires fewer observations from the experimental treatments and from the control, but achieves the same probability of a correct selection as does Dunnett's procedure. Then, based on Thall et al.'s two-stage design (1988), we use strong curtailment again to define a hybrid selecting and testing design which reaches the same probability of a correct selection as the original design, but requires fewer observations.
2006-08-01T07:00:00Z
text
https://surface.syr.edu/mat_etd/28
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Mathematics - Dissertations
SURFACE at Syracuse University
Binomial
Ranking
Curtailment
Least-favorable configuration
Mathematics
oai:surface.syr.edu:mat_etd-1028
2010-09-30T19:34:29Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Representations of semisimple Hopf algebras
Burciu, Sebastian
Let H be a cosemisimple Hopf algebra over an algebraically closed field. In the first chapter of the thesis, it is shown that if H has a simple subcoalgebra of dimension 9 and has no simple subcoalgebras of even dimension, then H contains either a grouplike element of order 2 or 3, or a family of simple subcoalgebras whose dimensions are the squares of each positive odd integer. In particular, if H is odd dimensional, then its dimension is divisible by 3.
In the second chapter, the induced representations from H and H * to the Drinfel'd double D ( H ) are studied. The product of two such representations is a sum of copies of the regular representation of D ( H ). The action of certain irreducible central characters of H * on the simple modules of H is considered. The modules that receive trivial action from each such irreducible central character are precisely the constituents of the tensor powers of the adjoint representation of H .
2005-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/29
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Mathematics - Dissertations
SURFACE at Syracuse University
Hopf algebras
Drinfeld double
Semisimple
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1030
2010-10-01T20:41:10Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Selection procedures for lognormal populations
John, Thomas T.
For the selection of the best from k lognormal (μ i , [Special characters omitted.] ) populations, statistical selection procedures are introduced considering the applicability of lognormal models in lifetime and quality control analysis. The major focus is given to selection based on any linear combination of μ i and [Special characters omitted.] . The starting point of the present monograph is the case of the complete samples, without the restrictions imposed in previous literature. Some existing selection rules are generalized so that a certain probability requirement is satisfied under the much more general conditions. The parametric selection based on the α-quantiles is also discussed and is compared to an existing nonparametric procedure using simulation.
Since censored data commonly appears in lifetime and quality control experiments, selection procedures are needed for those situations. For doubly type-II censored data, the case of lognormal populations with known [Special characters omitted.] can be generalized to log-location scale distributions with known scale parameters, satisfying certain conditions. The [Special characters omitted.] limit of trimmed sums of order statistics is developed and asymptotic procedures are proposed based on this result. The special cases of a few specific log-location-scale distributions, that are commonly used in lifetime data, are illustrated.
For the case of type-II censored lognormal samples with unknown [Special characters omitted.] , two-stage procedures are proposed; one for the equal case and the other for the unequal case. A modified procedure for the equal case, when there is no censoring, is compared to an existing procedure.
2004-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/30
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Mathematics - Dissertations
SURFACE at Syracuse University
Lognormal
Trimmed sums
Censored data
Log-location-scale
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1031
2010-10-04T14:56:09Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
(+)-Admissible sequences and the preprojective component
Tyler, Helene Renee
For a finite quiver without oriented cycles, we study the set of (+)-admissible sequences as introduced in [BGP]. We show how the nonisomorphic indecomposable preprojective modules can be characterized in terms of (+)-admissible sequences and establish a connection with the classical characterization presented, for example, in [ARS].
2002-08-01T07:00:00Z
text
https://surface.syr.edu/mat_etd/34
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Mathematics - Dissertations
SURFACE at Syracuse University
Preprojective component
Admissible sequences
Finite-dimensional algebras
Quiver
Mathematics
oai:surface.syr.edu:mat_etd-1032
2010-10-05T13:56:40Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Bilinski diagrams and geodesics in 1-ended planar maps
Bruce, Jennifer Antoinette
A Bilinski diagram is a labeling of a planar map with respect to a central vertex and the regional distance of other vertices of the map from that vertex. The class G a,b [Special characters omitted.] consists of all 1-ended, 3-connected planar graphs with the property that every valence is finite and at least a and every covalence is finite and at least b . A map in the class G a,b+[Special characters omitted.] contains no adjacent b-covalent faces, and dually a map in the class G a+,b[Special characters omitted.] contains no adjacent a-valent vertices. It is shown that Bilinski diagrams of maps in G6,3 , G4,4 , G3,6, G5,3+ and G3+,5[Special characters omitted.] are uniformly concentric, i.e., the set of vertices at regional distance k from the central vertex induce a circuit for each k ≥ 1. Using this property, an algorithm is developed for constructing geodetic double rays (or geodesics) containing any given edge of a map in G6,3, G4,4, or G5,3+[Special characters omitted.] . A slightly modified algorithm accomplishes the same for maps in G3,6[Special characters omitted.] . It follows that all Petrie walks in maps in G3,6[Special characters omitted.] are geodesics. These results contribute to the known classes of maps satisfying a conjecture of Bonnington, Imrich, and Seifter, without the assumption of vertex-transitivity. In addition, any path in a map in G6,3 ,G4,4 or G3,6[Special characters omitted.] that contains at most [1/2 (p*(h) - 2) ] edges incident with any face or superface (a union of two faces, at least one of which is 3-covalent, with their common incident edge removed) and at most one edge incident with any 3-covalent face is shown to be the unique geodetic path joining its end-vertices. Bilinski diagrams are further utilized to show that the distance sequence of any map in G6,3 , G4,4 or G5,3+[Special characters omitted.] is unimodal.
2002-05-01T07:00:00Z
text
https://surface.syr.edu/mat_etd/33
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Mathematics - Dissertations
SURFACE at Syracuse University
Graph theory
Unimodality
Bilinski diagrams
Geodesics
Planar maps
Mathematics
oai:surface.syr.edu:mat-1003
2013-01-29T17:25:38Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Universal Kernels
Micchelli, Charles A.
Xu, Yuesheng
Zhang, Haizhang
In this paper we investigate conditions on the features of a continuous kernel so that it may approximate an arbitrary continuous target function uniformly on any compact subset of the input space. A number of concrete examples are given of kernels with this universal approximating property.
2006-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/4
https://surface.syr.edu/context/mat/article/1003/viewcontent/download.pdf
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Mathematics - All Scholarship
English
SURFACE at Syracuse University
density
translation invariant kernels
radial kernels
Mathematics
oai:surface.syr.edu:mat-1004
2012-09-17T14:51:52Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Super-Brownian Limits of Voter Model Clusters
Bramzon, Maury
Cox, J. Theodore
Le Gall, Jean-Francois
The voter model is one of the standard interacting particle systems. Two related problems for this process are to analyze its behavior, after large times t, for the sets of sites (a) sharing the same opinion as the site 0, and (b) having the opinion that was originally at 0. Results on the sizes of these sets were given in [Sa79] and [BG80]. Here, we investigate the spatial structure of these sets in d ≥ 2, which we show converge to quantities associated with super-Brownian motion, after suitable normalization. The main theorem from [CDP98] serves as an important tool for these results.
2000-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/5
https://surface.syr.edu/context/mat/article/1004/viewcontent/download.pdf
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Mathematics - All Scholarship
English
SURFACE at Syracuse University
voter model cluster
Super-Brownian limits
interacting particle systems
Mathematics
oai:surface.syr.edu:mat-1005
2012-09-17T14:54:07Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Recurrence and Ergodicity of Interacting Particle Systems
Cox, J. Theodore
Klenke, Achim
Many interacting particle systems with short range interactions are not ergodic, but converge weakly towards a mixture of their ergodic invariant measures. The question arises whether a.s. the process eventually stays close to one of these ergodic states, or if it changes between the attainable ergodic states infinitely often ("recurrence"). Under the assumption that there exists a convergence--determining class of distributions that is (strongly) preserved under the dynamics, we show that the system is in fact recurrent in the above sense. We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we answer a question raised by Ed Perkins concerning the change of the locally predominant type in a model of mutually catalytic branching.
1999-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/6
https://surface.syr.edu/context/mat/article/1005/viewcontent/download.pdf
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Mathematics - All Scholarship
English
SURFACE at Syracuse University
interacting partle systems
longtime behavior
clustering
recurrence
argodicity
mutually catalytic branching
branching
Mathematics
oai:surface.syr.edu:mat-1006
2012-09-19T15:33:38Z
publication:dmat
publication:coscde
publication:mat
publication:cas
The Stepping Stone Model, II: Genealogies and the Infinite Sites Model, Submitted
Zähle, Iljana
Cox, J. Theodore
Durrett, Richard
This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman’s coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to the haplotype structure and a slower than expected decay of genetic correlation with distance revealed by recent studies of the human genome.
2005-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/7
https://surface.syr.edu/context/mat/article/1006/viewcontent/download.pdf
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Mathematics - All Scholarship
English
SURFACE at Syracuse University
Stepping stone model
Kingman's coalescent
Mutation patterns
Infinite sites model
Genetics
Geonomics
Genetics and Genomics
Mathematics
oai:surface.syr.edu:mat_etd-1033
2010-10-07T19:07:43Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Biting convergence of null-Lagrangians
Subramanian, Uma
In the calculus of variations it is essential to work with weakly sequentially compact spaces. Due to the lack of reflexivity of the space [Special characters omitted.] , given any bounded sequence { f j } ⊂ [Special characters omitted.] , we cannot guarantee the existence of a subsequence which converges weakly. Biting convergence comes to the rescue when the only available information about a sequence in [Special characters omitted.] is its boundedness. This notion of convergence has been designed mainly to deal with bounded sequences in [Special characters omitted.] that fail to be equi-integrable. We give a new proof of the theorem of K. Zhang [ Z ] on biting convergence of Jacobian determinants for mappings of Sobolev class [Special characters omitted.] . The theorem states that given a bounded sequence of functions { f j } ⊂ [Special characters omitted.] , there exists a subsequence {[Special characters omitted.] } such that [Special characters omitted.] converges in the biting sense to J ( x , f ). The novelty of our approach is in using [Special characters omitted.] -estimates with the exponents 1 [Special characters omitted.] p < n , as developed in [ IS1, IL, I1 ]. These rather strong estimates compensate for lack of equi-integrability.
We extend this result to more general wedge products of differential forms and then to null-Lagrangians. Null-Lagrangians are characterized by Euler-Lagrange equations. If the value of the energy integral [Special characters omitted.] [ f ] = [Special characters omitted.] does not change by adding to f a function that vanishes on the boundary of [Special characters omitted.] , then the function E is called a null-Lagrangian. Elliptic complexes, Hodge decomposition and non-linear commutators play a vital role in our proof.
2003-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/32
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Mathematics - Dissertations
SURFACE at Syracuse University
Biting
Convergence
Null-Lagrangians
Euler-Lagrange equations
Calculus
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1034
2010-10-11T17:52:01Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Numerical methods for smooth, detectable image perturbations
Zangor, Roxana Ioana
The area of digital watermarking, although relatively new, is well established in the field of image processing and computer engineering. It has developed rapidly over the past decade and many different watermarking algorithms, as well as sophisticated methods of testing their reliability, have been proposed.
An original watermarking method in the image domain formulated mathematically is introduced as a variational minimization problem with randomly generated boundary constraints. The properties of this method regarding detection and invariance are proved using results from calculus of variations, PDEs, as well as modern image analysis.
The method is implemented numerically using the Finite Element Method on a uniform triangulation of the unit square. Computational details are provided for the case of non-homogeneous boundary conditions. Results regarding the smoothness of the solution for convex domains and the convergence order of the method are proven.
Two classes of experiments are designed and implemented in MATLAB ® . The class supports the original claims of unobtrusiveness, detectability, and invariance of the perturbation introduced through our method. The second class compares several features of our method to those of the wavelet-projection method proposed in [16]. These features are: detection of the watermarks in both image and wavelet domain, invariance and robustness of the watermarks to blurring and resizing. Pertinent images and graphs are included, as well as the original MATLAB ® code.
2003-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/35
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Mathematics - Dissertations
SURFACE at Syracuse University
Image perturbations
Watermarking
Variational calculus
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1035
2010-10-13T12:54:04Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Selection and testing designs for selecting one among k normal populations, provided it is better than a standard
Rollin, Linda M.
We propose three separate procedures for selecting one among several normal populations, provided it is better than a specified standard. The three procedures stem from three different variance assumptions. The first procedure assumes the populations share a common known variance, the second assumes the populations share a common unknown variance, and the third assumes the population variances are unequal and unknown. Each procedure is a modification of the two-stage selection and testing procedures of Thall, Simon, and Ellenberg (1988, 1989), which were formulated to compare several binomial populations to a control population. In the first stage, ranking and selection techniques are used to screen out the one most promising population. In the second stage, hypothesis testing techniques are used to compare the chosen population to the standard. An option for terminating the procedure at stage one is offered, if none of the populations seem better than the standard.
In each of our procedures, we assume that we have k (≥2) normally distributed populations, π 1 , π 2 ,..., π k , having unknown means, μ 1 , μ 2 ,..., μ k , respectively. We also assume that we have a fixed known constant (standard) μ 0 to which the μ i are to be compared. The goal is to select one of the k populations, provided that it is better than the standard. If none of the k populations is better than the standard, then no population is to be chosen. We assume that a large population mean is desirable and hence, 'better than the standard' means that the population mean is sufficiently larger than the standard.
Tables of parameter values necessary to implement the procedures are provided, with a guarantee of appropriately defined size and power requirements. Sample size comparisons are performed between our procedures and the analogous procedures of Bechhofer and Turnbull (1978) for the case of common known and common unknown variance, and Taneja and Dudewicz (1992) for the case of unequal unknown variances. It is shown that total sample size requirements for our procedures are smaller than the corresponding procedures of Bechhofer and Turnbull. The sample size comparison with Taneja and Dudewicz's procedure indicates that our procedure is more efficient for small initial sample sizes and when none of the populations are better than the standard.
2002-08-01T07:00:00Z
text
https://surface.syr.edu/mat_etd/36
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Mathematics - Dissertations
SURFACE at Syracuse University
Testing designs
Ranking
Two-stage design
Population selection
Mathematics
Statistics and Probability
oai:surface.syr.edu:mat_etd-1036
2010-10-15T13:43:13Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
A boundedly controlled finiteness obstruction
Wiesner, Jill Heather
A CW complex X is finitely dominated if there exists a finite CW complex Y together with continuous maps [Special characters omitted.] such that [Special characters omitted.]
C.T.C. Wall asked the following question, "If X is finitely dominated, does X necessarily have the homotopy type of some finite CW complex"? He went on to discover the answer in general is, "No". In 1965 in [Wa], a now classic paper, he proved the following theorem:
Theorem: Suppose X is finitely dominated. Then there exists an invariant w ( X ) ∈ K 0 ( Z π( X )) such that X has the homotopy type of a finite CW complex if and only if w ( X ) = 0.
Here K 0 ( Z π( X )) is the reduced projective class group of the integral group ring Z π( X ) of the fundamental group of X . The invariant w ( X ) is called Wall's finiteness obstruction for X .
In the 1980's, Douglas R. Anderson and Hans J. Munkholm developed a new theory in the general area of 'topology with control' or spaces 'parametrized over a space' called boundedly controlled ( bc ) topology . The geometry and algebraic topology of be spaces was introduced in [AM 1].
In this dissertation, we review the fundamentals of boundedly controlled topology and generalize Wall's finiteness obstruction theorem to the category of boundedly controlled CW complexes.
2000-05-01T07:00:00Z
text
https://surface.syr.edu/mat_etd/37
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Mathematics - Dissertations
SURFACE at Syracuse University
Topology
Boundedly controlled
Finiteness obstruction
Geometry and Topology
Mathematics
oai:surface.syr.edu:mat_etd-1037
2010-10-18T18:53:00Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Limit laws of modulus trimmed sums
Qazi, Fozia Sanober
Let [Special characters omitted.] be a sequence of independent and identically distributed random variables. Let [Special characters omitted.] be an arrangement of [Special characters omitted.] in decreasing order of magnitude, and set [Special characters omitted.] This is known as the modulus trimmed sum. We obtain a complete characterization of the class of limit laws of the normalized modulus trimmed sum when the underlying distribution is symmetric and [Special characters omitted.] .
2001-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/38
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Mathematics - Dissertations
SURFACE at Syracuse University
Limit laws
Modulus trimmed sums
Probability theory
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat-1008
2012-09-17T14:49:42Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Rescaled Lotka-Volterra Models Converge to Super-Brownian Motion
Cox, J. Theodore
Perkins, Edwin A.
We show that a sequence of stochastic spatial Lotka–Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.
2005-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/9
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Mathematics - All Scholarship
English
SURFACE at Syracuse University
Lotka-Volterra
Voter model
Super-Brownian motion
Spatial competition
Coalescing random walk
Mathematics
oai:surface.syr.edu:mat_etd-1038
2010-10-25T17:40:52Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
A mean field model for species abundance
Pfaff, Thomas John
In this thesis, we use the multitype mean field voter model as a model of species interaction, to obtain results about species abundance. Briefly, we start with the complete graph on n vertices, K n , with each site occupied by a particle. Particles are represented by a value in (0, 1), where distinct values represent different species. Particles, then undergo mutation at rate α, and are relabeled with a value chosen uniformly from (0, 1). Particles also give birth at rate 1, and invade any of the other n sites randomly. This process has a unique stationary distribution denoted by [Special characters omitted.] , which is given by the Ewens sampling formula. For each value in (0, 1) that is present in [Special characters omitted.] , we count the number particles represented by the same value, and call that the patch size of the species. Let K n [ a, b ] denote the number of species with patch size in [ a, b ]. We study the limiting distribution of K n [ a, b ] as the mutation rate α tends to 0, which will in turn force [Special characters omitted.] . In particular, we obtain results about [Special characters omitted.] , and [Special characters omitted.] , where [Special characters omitted.] .
1999-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/42
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Mathematics - Dissertations
SURFACE at Syracuse University
Ewens sampling
Mean field
Species abundance
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1039
2010-10-25T18:55:36Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
A study of degenerate elliptic partial differential equations
Almannaei, Abdulsalam Ahmeo
In this thesis, two types of second order elliptic partial differential equations will be studied. The first type is the following equation [Special characters omitted.] for a function u of Sobolev class [Special characters omitted.] Here A, B and C are measurable functions on Ω with A > 0, C > 0 and AC - B ² > 0 a.e .
Our main result will be that u is of class C 1 (Ω) provided that [Special characters omitted.] is locally integrable on Ω.
The second equation we will study is the non-homogeneous p -harmonic equation [Special characters omitted.] for a function [Special characters omitted.] where [Special characters omitted.] with [Special characters omitted.] Our main result is the following:
THEOREM. Let u be a non-homogeneous p -harmonic function on [Special characters omitted.] of class [Special characters omitted.] where 1 < p ≤ 2. If [Special characters omitted.] then [Special characters omitted.] and the following uniform estimate holds [Special characters omitted.]
Among other applications, this theorem will be used to establish higher integrability of ∇ u .
1998-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/41
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Mathematics - Dissertations
SURFACE at Syracuse University
Degenerate
Elliptic
Partial differential
Partial differential equations
Mathematics
oai:surface.syr.edu:mat_etd-1041
2010-10-25T19:45:37Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Finite element spectral approximations
Tran, Max Minh
In this dissertation we study the convergence properties of a finite element approximation to a fourth order differential eigenvalue problem under the presence of numerical integration. In broad terms, a finite element method, FEM for short, is a Ritz-Galerkin approximation using special basis functions. When used to approximate the solution of a PDE or a variational problem, a FEM reduces the differential or variational problem to a large matrix problem. Our fourth order differential eigenvalue problem is put into variational form using a mixed method formulation. We give a brief overview of the results obtained when exact integration is used in the FEM. We then develop related theories where numerical quadrature is taken into account. We will show that the eigenvalues and eigenfunctions obtained by using a suitable quadrature scheme, without requiring the numerical scheme to be exact, converges to the actual values at the same rates as those obtained by using exact integration. The standard approach to obtaining error estimate of variational eigenvalue problems is based on the error estimate of the solution operators of the source problems. The important issues are the rate of convergence of the solution operators and the conditions required for convergence. These source problems have been extensively studied by many researchers, using a wide variety of approaches. Babuska, Osborn and Pikäranta used mesh dependent norms in their 1980 paper. Paralleling their work, we will use mesh dependent norms to obtain error estimates between the solutions operators. We then use these estimates to get errors estimates between the approximate and the actual eigenvalues and eigenvectors.
1999-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/39
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Mathematics - Dissertations
SURFACE at Syracuse University
Spectral
Finite element
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1040
2010-10-25T19:27:04Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Extending the Beltrami equation into higher dimensions
DeCampo, Raymond Kenneth
The Beltrami equation of complex analysis enjoys a rich and fascinating theory. This theory has many implications for the study of quasiconformal mappings. The main goal of this paper is to create a foundation for a similar theory for quasiregular mappings of [Special characters omitted.] to itself for dimensions higher than 2.
Straightforward attempts to accomplish this goal in the past have not borne much fruit. Thus, we have taken a different approach. The complex Beltrami theory owes much to the algebraic setting in which it resides. We have looked for extensions of this theory which will be able to take advantage of a well-chosen algebraic setting.
Two approaches have resulted. The most natural approach is to set the theory in a Clifford analysis context. This approach yields a pleasing theory which reflects in many ways the complex setting. The second approach arises from considering quasiregular mappings as solutions of a partial differential equation and then lifting that equation to the exterior algebra level. This approach is desirable because of the natural relationship with quasiregular mappings and because it will hopefully be a stepping stone to the study of the conformal geometry of manifolds. Both approaches have yielded existence and uniqueness results for certain kinds of Beltrami-like equations.
1999-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/40
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Mathematics - Dissertations
SURFACE at Syracuse University
Clifford analysis
Quasiconformal
Beltrami equation
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1042
2010-10-26T18:02:22Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
On the RO(G)-graded equivariant ordinary cohomology of generalized G-cell complexes for G = Z/p
Ferland, Kevin Keith
It is well known that the cohomology of a finite CW-complex with cells only in even dimensions is free. The equivariant analog of this result for generalized G -cell complexes is, however, not obvious, since RO ( G )-graded cohomology cannot be computed using cellular chains. We consider G = [Special characters omitted.] / p and study G -spaces that can be built as cell complexes using the unit disks of finite dimensional G -representations as cells. Our main result is that, if X is a G -complex containing only even dimensional representation cells and satisfying certain finite type assumptions, then the RO ( G )-graded equivariant ordinary cohomology is free as a graded module over the cohomology of a point. This extends a result due to Gaunce Lewis about equivariant complex projective spaces with linear [Special characters omitted.] / p actions. Our new result applies more generally to equivariant complex Grassmannians with linear [Special characters omitted.] / p actions.
1999-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/43
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Mathematics - Dissertations
SURFACE at Syracuse University
G-cell complexes
Equivariant
Cohomology
Mathematics
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1043
2010-10-28T14:10:57Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
A journey through numeracy: Correlates of success in initial college mathematics
Trimboli, John Michael
This research was undertaken to identify and analyze the correlates of mathematical success at the collegiate level. Multiple regression prediction equations were developed for each of the five initial mathematical sequences that undergraduate students at Syracuse University take. Ultimately, the goal of this study was to predict the grade in students' initial two-course college mathematics sequence solely from variables derived from their high school transcripts.
Subjects in the study consisted of 213 undergraduates (103 men and 110 women) who had completed their high school education in New York State under the New York State Regents curriculum and had completed their sophomore year at Syracuse University. The variables used as predictors were derived from high school mathematics and foreign language course performances, overall high school grade point average, Scholastic Aptitude Test (verbal and quantitative) scores, and gender.
Given the fact that each initial mathematical sequence is typically made up of different "types" of students (in terms of academic interests, goals, and pursuits; mathematical track records, etc.), it was found that different high school variables contributed significantly to prediction of mathematical performance for the different sequence types. The most promising multiple regression prediction equations (in terms of the percent of variance accounted for in the dependent variable), turned out to be the no math sequence group and the financial-management calculus group (accounting for roughly 89% and 77% of the variance in sequence grade respectively). The predictor variable comprised of SAT-verbal scores was the only statistically significant variable that was common to both of these equations. Outside of SAT-verbal, math related variables turned out to significantly predict the no-sequence students' initial grades; whereas language related variables together with overall high school performance and gender, significantly predict grades in the business calculus sequence.
The high Calculus sequence group and the probability and statistics sequence group (accounting for roughly 41% and 30% of the variance in sequence grades respectively), each had standard score of tenth grade mathematics performance as their most important predictor. The low Calculus sequence group (accounting for nearly 43% of the variance in the dependent variable) had a standard score based on the sum of all grades in high school mathematics courses and depth of concentration in a single foreign language course as significant contributing predictor variables.
1996-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/46
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Mathematics - Dissertations
SURFACE at Syracuse University
performance prediction
Mathematics education
Statistics
Mathematics
oai:surface.syr.edu:mat_etd-1044
2010-10-28T14:48:58Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
An integrated approach to some ranking and selection problems
Zhang, Jun-Lue
We refer to the two classical approaches to ranking and selection problems as the indifference zone approach and the subset selection approach. In this thesis, we integrate these two approaches in selecting (1) the population with the largest mean (the best population) among k normal populations with unknown variances; (2) the population associated with the largest population proportion (the best population) among k binomial populations assuming a common large sample size. In this integrated approach, the parameter space is divided into two disjoint subsets, namely the preference zone (PZ) and the indifference zone (IZ). The concept of correct selection is defined differently in each of these zones. In the PZ, we are required to select the best population for a correct selection ($CS\sb1$). In the IZ, we define any selected subset to be correct ($CS\sb2$) if it contains the best population. A Stein-type (Stein (1945)) two-stage selection procedure is proposed for the normal case with common and unknown variance. For the normal case with uncommon and unknown variances, a Dudewicz-Dalal-type two-stage selection procedure is proposed. A selection rule is also proposed for the large sample binomial case. Lower bounds and formulas for the probability of correct selection under PZ and the probability of correct selection under IZ are developed. It is shown that the least favorable configuration (LFC) in PZ is the slippage configuration, and the worst configuration (WC) in IZ is the equal parameter configuration for the unknown and equal variance normal case. For the unknown and unequal variances normal case, it is proven that the slippage configuration is the least favorable configuration (LFC) in PZ and simulation study is conducted to investigate the worst configuration in IZ. For the binomial case, it is shown that the equal parameter configuration is the worst configuration in IZ for the case of k = 2 and the least favorable configuration (LFC) in PZ is the slippage configuration. A set of sufficient condition is also given for the monotonicity of the probability of correct selection in the indifference zone for the binomial case. It is proven that all proposed procedures guarantee that the following probability requirements are met: (1) the probability of selecting the best population in the PZ is at least $P\sbsp{1}{*}$, and (2) the probability of selecting a subset which would contain the best population is at least $P\sbsp{2}{*}$ when the true parameters are in the IZ. The expected subset sizes for all procedures are studied. Bounds for the expected sample sizes are developed for the normal cases. Tables necessary to implement these procedures are provided. Numerical examples are given. Simulation studies are also conducted.
1995-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/45
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Mathematics - Dissertations
SURFACE at Syracuse University
indifference zone
subset selection
Statistics
Mathematics
Statistics and Probability
oai:surface.syr.edu:mat_etd-1045
2010-10-28T15:40:26Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
General properties of functions of bounded lambda-variation
Prus-Wisniowski, Franciszek
This thesis is focused on general properties of functions of bounded $\lambda$-variation. Inspiration for most of this work came from problems posed by D. Waterman, and four of them have been answered here completely. It has been shown that functions of bounded ordered $\lambda$-variation always form a proper superset of the class of functions of bounded $\lambda$-variation. A useful characterization of functions continuous in $\lambda$-variation has been found, a characterization that generalizes the decomposition of ordinary variation of a function into the sum of the variation of the continuous part of the function and the variation of saltus part of the function. A necessary and sufficient condition for the equivalence of the concepts of bounded $\lambda$-variation and continuity in $\lambda$-variation has been proven. A notion of $\lambda$-absolute continuity has been introduced, and various interesting characterizations of it has been given. Finally, all the previous results interweave beautifully in an explanation of the relationship between harmonic bounded variation and the Garsia-Sawyer class.
1995-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/44
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Mathematics - Dissertations
SURFACE at Syracuse University
lambda variation
bounded lambda variation
Garsia Sawyer class
Mathematics
oai:surface.syr.edu:mat_etd-1046
2010-10-29T13:47:59Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
A uniform property for finite sets of points in projective space
Modalli, Lakshmi
In this thesis we are concerned with the uniform properties of finite sets of points in projective space. The Hilbert function of a variety V in $P\sp{n}$ gives for each degree d, the codimension in the entire family of hypersurfaces of degree d, of the subfamily of hypersurfaces of degree d that contain V. Using the value of the Hilbert function, J. Harris defined the uniform position property for finite sets of points in projective space. Extending the notion used in the Hilbert function to include varieties of arbitrary codimension, one can define an integer valued function gXf, for each given Hilbert polynomial f and an irreducible component X of the Hilbert scheme $Hilb\sbsp{P\sp{n}}{f}.$ For any finite set Y of points in $P\sp{n},\ gXf(Y)$ gives the codimension in X of $\Omega\sb{Y}$ the set of points in X corresponding to the varieties in $P\sp{n}$ that contain Y. This dissertation is based on the study of the function $gXf$ and the uniform properties resulting from it. Chapter I contains the introduction to the problem, and the necessary preliminary definitions. Chapter II starts with the generalized Hilbert function $gXf,$ and studies the properties of $gXf$ and the set $\Omega$. In chapter III, a uniform property based on $gXf$ is defined and studied, and its relation with other existing uniform properties is explored. A weaker version of the Uniform Position Lemma of J. Harris, based on the newly defined uniform Hilbert property is proved in chapter IV. Some unanswered questions and interesting problems are also identified in chapter IV.
1996-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/47
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Mathematics - Dissertations
SURFACE at Syracuse University
Mathematics
Hilbert functions
Mathematics
oai:surface.syr.edu:mat_etd-1047
2010-11-01T18:47:50Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Functions of generalized bounded variation, generalized absolute continuity and applications to Fourier series
Schembari, Nunzio Paul
This dissertation is devoted to the study of functions of generalized bounded variation, generalized absolute continuity, and the Fourier series of such functions. We begin by defining a generalized modulus of variation which we use to define a Banach space, $\Phi$V (h), of generalized bounded variation functions which encompasses many spaces previously studied. We show that this space contains only bounded functions with simple discontinuities and that it can be written as an intersection of the Schramm spaces $\Phi$BV satisfying a certain condition. We next show that $\Phi$V (h) satisfies an analogue of Helly's theorem and that if this space contains a function which is not of harmonic bounded variation, then it does not satisfy the Dirichlet - Jordan theorem. We then show that a theorem of Zygmund may be generalized to $\Phi$V (h) as well as a larger class of generalized bounded variation spaces.
We turn our attention to Fourier series by considering the sequence $\{\alpha\sb{\rm k}$(x,f)$\}$ = $\{\rm k\ b\sb k\ cos\ kx - k\ a\sb k\ sin\ kx\}$, where a$\sb{\rm k}$ and b$\sb{\rm k}$ are the Fourier coefficients of the integrable function f. We show that this sequence is not (C,1) summable for $\Phi$V (h) functions if $\Phi$V (h) contains a function which is not of harmonic bounded variation. We show, however, that the series with terms $\alpha\sb{\rm k}$(x,f), i.e., the formally differentiated Fourier series, is (C,1) summable to (1/2) (f$\sb+\sp\prime$(x) + f$\sb-\sp\prime$(x)) if the difference quotient g(t) = (1/t) (f(x+t) $-$ f(x)) is of harmonic bounded variation in a neighborhood of t = 0. We also give conditions to insure uniform (C,1) summability of this series.
Finally, we define three generalized absolute continuity spaces,$\Lambda$AC, $\Lambda$C and $\Lambda\sb2$AC, and study the relationships between them, the space of absolutely continuous functions, and the space of continuous functions of bounded variation, BVC. We show that BVC can be written as the intersection of the $\Lambda$AC spaces and that the space of continuous functions can be written as the union of the $\Lambda$AC spaces, but that this cannot be achieved by countable intersections and unions. We end by finding a bound for the Fourier coefficients of $\Lambda\sb2$AC functions.
1991-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/48
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Mathematics - Dissertations
SURFACE at Syracuse University
Generalized bounded variation
Generalized absolute continuity
Fourier series series
Mathematics
oai:surface.syr.edu:mat_etd-1048
2010-11-02T17:17:53Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Comparison of four instructional approaches and mathematics background on students' conception of limits
Hardin, William James
Limits are central to calculus. They are what separate analysis from algebra. Unfortunately, many students find limits to be a difficult and confusing topic. In this dissertation, I attempt to see how different ways of teaching the concept of limits affect students' conceptions of limits as well as their computational proficiency.
To accomplish my goals, I taught four different recitation sections, each with a different instructional approach. The treatments were conducted for a total of three weeks. The instructional approaches were: paper-and-pencil computational, graphics calculator-based, paper-and-pencil conceptual, and computer-based. All the groups except the paper-and-pencil computational group emphasized conceptual knowledge first. I found that emphasizing conceptual knowledge (except for the graphics calculator group) resulted in students that were stronger in conceptual knowledge, while emphasizing computation yielded students stronger in computation. A notable exception was the paper-and-pencil conceptual group, that was at the top of the groups on scores, on both conceptual and procedural problems. In the instructional activities, the students in the paper-and-pencil conceptual group were asked to compute parameters like slopes of tangents themselves. This may give some indication that forcing the students to process the information may cause the connections to become more explicit.
During the investigation, I developed software to help students visualize the concept of limits. This software let students dynamically control important parameters. In this way, the software acted like a virtual manipulative. I also enhanced a classification model for students' conceptions that was developed by Williams (1991). Additionally, I attempted to classify errors based on a classification model by Movshovitz-Hadar, Zaslavsky and Inbar without too much success.
Finally, I developed a set of activities for each of the instructional approaches. The activities were similar between the pencil-and-paper conceptual and the computer-based sections but different for the calculator and the paper-and-pencil computational groups. These activities rely on the development of exposing, discrepant and resolving events to bring the notion of limits to light. The activities were designed so that the computational group did not have discussions, instead they practiced computational problems. However, in the activities, the conceptual groups were asked to make conjectures and were designed as the foundation of class discussions.
1997-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/56
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Mathematics - Dissertations
SURFACE at Syracuse University
calculus
Mathematics
oai:surface.syr.edu:mat_etd-1049
2010-11-03T13:33:20Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Feed-forward neural networks: Learning algorithms, statistical properties, and applications
Lin, Yachen
In this study, we focus on feed-forward neural networks with a single hidden layer. The research touches upon several important issues in Artificial Neural Networks such as the reliability and generalization of trained networks. The convergence of the learning algorithm in the computational sense and the strong consistency of the stable states of networks in the statistical sense have been addressed as major measures of reliability and generalization, respectively. Based on the internal structure of feed-forward neural networks with a single hidden layer, Two-Stage learning is proposed. To implement Two-Stage learning, we proposed two new learning algorithms--Two-Stage(LS) and Two-Stage(Gibbs). The reliability and generalization of these two learning algorithms, i.e. the convergence in the computational sense and the strong consistency in the statistical sense, are rigorously studied. These optimal properties of proposed learning algorithms are further confirmed by intensive empirical studies such as comparisons made on the Fisher's Iris Data ((1939) The use of multiple measurements in taxonomic problems, Ann. Eugenics 7, Pt II, pp. 197-188) between the proposed learning algorithms and statistical methods (like Bayesian discriminate analysis, Kernel density methods, and K-nearest neighbors), comparisons between the proposed learning algorithms and other existing learning algorithms like Backpropagation, and simulation studies. Both theoretical and empirical studies demonstrate the potential of the proposed algorithms to the real world.
1996-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/55
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Mathematics - Dissertations
SURFACE at Syracuse University
backpropagation
Statistics
Mathematics
Computer science
Artificial intelligence
Mathematics
oai:surface.syr.edu:mat_etd-1050
2010-11-04T18:14:38Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Fourier series on Vilenkin groups
Dezern, David Herman
The focus of this investigation is pointwise convergence of Fourier series of functions defined on a compact Vilenkin group, i.e., a compact metrizable totally disconnected abelian group. Throughout we assume that the Vilenkin group satisfies a certain boundedness condition, namely, that a sequence of primes determined by the structure of the group is a bounded sequence.
We begin with an examination of the Salem test for uniform convergence of Fourier series. We provide a new proof of an adaptation of the Salem test to Fourier series on Vilenkin groups due to C. W. Onneweer and Daniel Waterman.
Next we localize the Salem test to obtain a test for pointwise convergence of the Fourier series of f. Here it is shown that the assumption of continuity of f at x, which was required in the proof of uniform convergence, may be weakened to the existence of a suitably defined derivative of the integral of f(x-t). This localized Salem test is very closely related to a version of the Lebesgue test due to Onneweer and Waterman.
Application of similar methods to the study of functions of harmonic bounded fluctuation yields the result that the Fourier series of a function of harmonic bounded fluctuation converges everywhere the function satisfies the differentiability of the integral condition mentioned above.
Finally, we construct a Banach space of functions with everywhere-convergent Fourier series.
1988-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/54
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Mathematics - Dissertations
SURFACE at Syracuse University
Boundedness
Bounded sequence
Salem test
Mathematics
oai:surface.syr.edu:mat_etd-1051
2010-11-04T19:43:10Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Strong laws of large numbers for certain sequences and arrays of dependent random variables
Rieders, Eric Forrest
In this work, we study the almost sure convergence of the averages of certain classes of sequences and arrays of dependent random variables, and the behaviour of the associated maximal functions. We first consider sequences of identically distributed random variables that are strongly mixing. Our main interest here is to obtain some insight into how the dependence structure of such sequences affects the relationship between the moments of the random variables and the behaviour of the maximal function. We find that for strictly stationary sequences, there is a natural division between those sequences for which the existence of the first moment is necessary for the almost sure finiteness of the ergodic maximal function, and those for which this is not the case. When the condition of stationarity is relaxed, we can still obtain some partial results in this direction.
In the two parameter setting, we study arrays whose joint distributions are invariant under interchange of rows and columns. We have formulated an analog of the Marcinkiewicz strong law of large numbers for such arrays. The results extend earlier work by Smythe (1974), Gut (1978) and McConnell (1987). We have also obtained a dominated ergodic theorem for a particular subclass of this type of array. This result facilitates the proof of a two parameter strong law for degenerate U-statistics of degree two which complements some results due to McConnell (1987).
The key role that Kronecker's lemma plays in many proofs of the classical one parameter results has led us to formulate and prove an analogous two parameter result appropriate for our purposes. Although the general approach we use is classical, relatively modern methods concerning multiparameter martingales and Banach space valued random variables are heavily relied upon. We also make substantial use of symmetrization techniques. Fairly recent results concerning Rademacher quadratic forms play an important role in the successful application of these techniques.
1988-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/53
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Mathematics - Dissertations
SURFACE at Syracuse University
identically distributed random variables
dependence structure
maximal function
Mathematics
oai:surface.syr.edu:mat_etd-1052
2010-11-05T11:59:35Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Functions Of Generalized Bounded Variation And Summability Of Fourier Series
D'antonio, Lawrence Arthur
This dissertation is devoted to the study of functions of generalized bounded variation.
A definition is given for a Banach space of regulated functions in a manner analogous to that for functions of ordered (LAMDA)-bounded variation, but using intervals of equal length and requiring that the functions satisfy a generalized continuity condition.
A summability method is given which is effective on Fourier series of function in this Banach space but not on Fourier series of functions in larger such spaces. This method is defined as the convolution of a function with a kernel obtained by multiplying the Dirichlet kernel with a certain simple function, where this simple function is 2(pi)-periodic, even, and decreasing on O,(pi) . Two methods equivalent to this method are also discussed and analogues of the Dini test and the localization principles are proven.
Finally, we give necessary and sufficient conditions for everywhere convergence and for uniform convergence of the summability method under every change of variable.
1986-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/52
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Mathematics - Dissertations
SURFACE at Syracuse University
Mathematics
Mathematics
oai:surface.syr.edu:mat_etd-1053
2010-11-05T12:04:52Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Functions Of Generalized Bounded Variation And Fourier Series
Isaza, Pedro
This dissertation is devoted to the study of some properties and applications of functions of generalized bounded variation.
Estimates are obtained for the Fourier coefficients of a function f whose Fourier series has small gaps and whose restriction to a subinterval I of 0,2(pi) , f(VBAR)(,I), belongs to one of the following classes: (PHI) bounded variation, (WEDGE) bounded variation, or V h of Canturija. A condition is obtained for the absolute convergence of the Fourier series of f when f(VBAR)(,I) is in V n('(alpha)) , 0 (LESSTHEQ) (alpha) < 1/2.
Hypotheses for the existence of the Stieltjes integral of functions in Canturija classes are given and the integral is estimated.
It is proved that each space V h is the intersection of all (WEDGE)B(V) classes satisfying certain conditions, but is not the intersection of any countable subcollection of these classes.
Finally, a definition is given for a Banach space of regulated functions in a manner analogous to that for functions of ordered harmonic bounded variation, but using only intervals of equal length and requiring that the functions satisfy a generalized continuity condition. It is shown that functions in this space have everywhere convergent Fourier series.
1986-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/51
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Mathematics - Dissertations
SURFACE at Syracuse University
Mathematics
Mathematics
oai:surface.syr.edu:mat_etd-1054
2010-11-05T16:55:46Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
On the preservation of certain properties of functions under composition
Pierce, Pamela Bitler
Let $I\sb{n,m},\ m = 1,2,\...,k\sb{n}$ be disjoint closed intervals such that for each $n,\ I\sb{n,m-1}$ is to the left of $I\sb{n,m}.$ Given x, if for every $\epsilon>0$ there exists N such that $I\sb{n,m}\subset(x,x + \epsilon)$ whenever $n>N,$ then ${\cal I} = \{I\sb{n,m}:n = 1,2,\...;\ m = 1,2,\...,k\sb{n}\}$ is called a right system of intervals (at x). A left system is defined similarly. Let$$\alpha\sb{n}({\cal I}) = \sum\sbsp{i=1}{k\sb{n}}{f(I\sb{n,i})\over i}\quad{\rm where}\quad f(\lbrack a,b\rbrack) = f(b) - f(a).$$In Chapter 1 we prove the following result:
Theorem 1. If f is regulated, then $f\ \circ\ g$ has everywhere convergent Fourier series for every homeomorphism g is f and only if $\lim\limits\sb{n\to\infty}\alpha\sb{n}({\cal I}) = 0$ for every system ${\cal I}$ and for every x.
Goffman and Waterman proved an analogous theorem for the case where f is continuous.
In Chapter 2 we turn our attention to functions of bounded. $\Lambda$-variation, which we define as follows: Suppose $\Lambda = \{\lambda\sb{n}\}$ is an increasing sequence such that $\sum\limits\sbsp{n=1}{\infty}{1\over\lambda\sb{n}} = \infty.$ We say that $f\in\Lambda BV$ on an interval (a,b) if $\sum\limits\sbsp{n=1}{\infty}{\vert f(I\sb{n})\vert\over\lambda\sb{n}}<\infty$ for every collection $\{I\sb{n}\}$ of nonoverlapping intervals in (a,b). Here we show that $g\ \circ\ f\in\Lambda BV$ for every $f\in\Lambda BV$ if and only if $g\in Lip1.$ Chaika and Waterman proved an analogous result for the classes GW, UGW and HBV.
In Chapter 3 we prove an analogous theorem for the class $\Phi BV$, which we define as follows: Let $\phi$ be a convex function satisfying $\phi(0) = 0,\ \phi(x)>0$ for $x>0,\ {\phi(x)\over x}\to0$ as $x\to0,$ and ${\phi(x)\over x}\to\infty$ as $x\to\infty.$ We say $f\in\Phi BV$ on (a,b) if $\sum\limits\sbsp{n=1}{\infty}\phi(\vert f(I\sb{n})\vert)<\infty$ for every collection $\{I\sb{n}\}$ of nonoverlapping intervals in (a,b). We will make the further assumption that $\phi$ satisfy the $\Delta\sb2$ condition so that the resulting class $\Phi BV$ forms a linear space. In this chapter we prove that $g\ \circ\ f\in\Phi BV$ for every $f\in\Phi BV$ if and only if $g\in Lip1.$ We also present an interesting condition which is equivalent to the $\Delta\sb2$ condition.
1994-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/50
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Mathematics - Dissertations
SURFACE at Syracuse University
homeomorphisms
convex functions
fourier series
Number Theory
Partial Differential Equations
Physical Sciences and Mathematics
oai:surface.syr.edu:mat_etd-1055
2010-11-05T17:29:37Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Procedures for selecting the best experimental treatment with comparison to a control
Bernhofen, Laura Trasher
We consider the problem of selecting the best of k experimental treatments (populations) in comparison to a control treatment (population) when the treatments are normally distributed with unknown means and have a common, unknown variance. Our goal is to select the experimental treatment with the largest mean, when this mean is larger than the control treatment mean. Otherwise, we select the control treatment.
Three different procedures are proposed to satisfy our goal. The first procedure is a balanced, two-stage, Stein-type selection procedure, R$\sb{\rm E}$, similar to that of Bechhofer and Turnbull (1978). We define probability requirements and tabulate procedural parameters for R$\sb{\rm E}.$ The expected sample size is derived and we use it to compare procedure R$\sb{\rm E}$ with the other proposed procedures.
The second procedure extends R$\sb{\rm E}$ to an unbalanced, two-stage, Stein-type selection procedure, R$\sb{\rm U}.$ R$\sb{\rm U}$ allows for different sample sizes in a given fixed ratio, R, to be drawn from the control treatment and the experimental treatments. We define the selection procedure and probability requirements. Procedural parameters are then computed for a number of choices of R. The expected sample size is derived and we use it to compare procedure R$\sb{\rm U}$ to procedure R$\sb{\rm E}$ for different values of R.
The third procedure, ST, combines statistical selection with hypothesis testing and is similar to the method of Thall, Simon, and Ellenberg (1988). In the first phase, we use a selection procedure to determine preliminarily whether the best experimental treatment is better than the control. If no experimental treatment exhibits sufficient evidence of being an improvement over the control, the procedure is terminated. Otherwise, we proceed to the second phase and test the best experimental treatment against the control. The two-phase procedure ST is defined and definitions of power and level appropriate for our hybrid decision method are given. We calculate procedural parameters and derive the expected sample size of this procedure. A comparison of procedure ST with procedure R$\sb{\rm E}$ is discussed.
1994-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/49
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Mathematics - Dissertations
SURFACE at Syracuse University
statistical selection
Mathematics
Statistics and Probability
oai:surface.syr.edu:mat_etd-1056
2010-11-08T15:19:36Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Regularity of A-harmonic forms
Budney, Leonard Robert
In this thesis we are concerned with estimating the regularity of ${\cal A}$-harmonic differential forms in Euclidean space. The prototype of the ${\cal A}$-harmonic equation is the so-called p-Laplacian equation, div$\vert\nabla f\vert\sp{p-2}\nabla f=0,$ which arises as a nonlinear generalization of the classical Dirichlet problem. When $p=n$ it also serves to characterize quasiconformal functions. In Chapter 1 we discuss existence and uniqueness questions relating to the latter equation. It is natural to consider p-harmonic functions belonging to the Sobolev space ${\cal W}\sp{1,p}.$ Certain estimates are most easily derived in $L\sp2,$ however, so in Chapter 2 we prove that when f is a p-harmonic function, the vector field $\vert\nabla f\vert\sp{{p-1\over2}}\nabla f\in L\sp2$ actually belongs to ${\cal W}\sp{1,2}.$ This is a first step in our proof of the previously unknown fact that $\vert\nabla f\vert\sp{{p-2\over2}}\nabla f$ belongs to $L\sp{s}$ for some $s>2.$ In 2-dimensional Euclidean space, this higher integrability has as a consequence the famous result of K. Uhlenbeck and Ladyzhenskaya and Ural'tseva that p-harmonic functions have Holder continuous gradients. In Chapter 3 we introduce the Sobolev spaces of differential forms, and the general ${\cal A}$-harmonic problem. We present a characterization of ${\cal W}\sbsp{0}{1,p}$ which is naturally adapted to the study of ${\cal A}$-harmonic equations; that our characterization is equivalent to the classical definition in Euclidean space belongs to folklore, but the first recorded proof in the setting of Riemannian manifolds is due to the author and C. Scott. Chapter 4 contains an original extension of Morrey's Lemma to differential forms, which is used to estimate the Holder regularity of $L\sp{p}\ {\cal A}$-harmonic forms, where p is close to n. Some extensions to Riemannian manifolds are extant, and others are still in progress. We will introduce them in Chapter 5, and also mention some directions for future research to expand the applicability of the ideas discussed herein.
1996-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/59
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Mathematics - Dissertations
SURFACE at Syracuse University
mathematics
Mathematics
oai:surface.syr.edu:mat_etd-1057
2012-07-25T13:14:02Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Growth and Almost Periodicity of Dirichlet Series with Random Signs
Friske, Melvin John
This dissertation discusses the Dirichlet Series with random signs.
1976-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/58
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Mathematics - Dissertations
SURFACE at Syracuse University
Dirichlet series
Fourier series
Carelson
Riesz-Fischer theory
Mathematics
oai:surface.syr.edu:mat_etd-1058
2010-11-12T17:07:29Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
Structure of the Degrees of Enumeration Reducibility
Moore, Brian Barry
The material presented in this paper lies in the realm of recursive function theory. Major emphasis is upon various reducibilities and the degrees associated with them. The paper is not entirely self contained and a background in basic recursive function is required for full comprehension.
1974-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/57
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Mathematics - Dissertations
SURFACE at Syracuse University
mathematics
recursive function theory
Mathematics
oai:surface.syr.edu:mat_etd-1059
2010-11-16T19:05:35Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
On some aspects of the Arens-Hoffman extension of Banach algebras
Brown, David Theodore
In this dissertation, we will refer to any commutative algebra over the complex field which possesses an identity e simply as an algebra...
This dissertaion deals primarily with algebraic aspects of the Arens-Hoffman extension of a Banach Algebra A and thus builds upon the work of G. A. Heuer, J.A. Lindberg, and Heuer and Lidberg...
1965-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/61
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Mathematics - Dissertations
SURFACE at Syracuse University
Banach algebras
Arens-Hoffman
Applied Mathematics
oai:surface.syr.edu:mat_etd-1060
2010-11-17T17:22:14Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
An Experimental Comparison of Two Liberal Arts Courses in General Mathematics at Syracuse University
Smith, Roland Frederick
The problem of this thesis is to determine, if possible, which of two different sets of course materials results in better attainment of certain objective of Mathematics 7, the first semester of the general education course in mathematics at Syracuse University.
These objectives can be grouped under four main heads: 1. Ability to think critically 2. Skill in performing elementary mathematical operations 3. Understanding of the number systems 4. Understanding of abstract rational systems.
1955-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/60
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Mathematics - Dissertations
SURFACE at Syracuse University
Curriculum
Critical thinking
Mathematical operations
Number system
Abstract rational systems
Mathematics
oai:surface.syr.edu:mat_etd-1061
2011-08-31T16:38:05Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
On the convergence and superconvergence of the Generalized Finite Element Methods
Anitescu, Cosmin
In this thesis, we study the approximation properties of the Generalized Finite Element Method (GFEM), which is a Galerkin method to approximate the solutions of Partial Differential Equations (PDEs). The GFEM is an extension of the standard Finite Element Method (FEM), and it uses a partition of unity and local approximating functions. In certain situations, the partition of unity functions may have some approximation properties themselves (for example, the standard "hat" functions from the FEM). We have obtained an approximation result for the GFEM that exploits this property and yields a more accurate approximate solution of the PDE. This result could not be obtained from the classical error estimate of GFEM, which does not reflect the approximation properties of the partition of unity functions. In the second part of the thesis, the phenomenon of superconvergence has been studied in the context of GFEM. Superconvergence occurs when the error of the numerical approximation converges faster at certain points compared to the maximum error in a subdomain of the underlying domain of the PDE. We study superconvergence near the boundary of the domain, and extend previous results that only hold in the interior of the domain. In particular, we show that the dominant term of the approximation error can be decomposed into a component that is periodic throughout the domain, and a non-periodic component which decays exponentially away from the boundary. Using these two components, and also possibly their roots, a new approximation to the exact solution can be obtained, which has higher convergence rate on the entire domain (or subdomain) than the standard GFEM solution. Under certain conditions, this new approximation can be used to estimate the error between the original numerical solution (i.e. GFEM solution) and the unknown exact solution, a process known as a posteriori error estimation.
2010-01-01T08:00:00Z
text
https://surface.syr.edu/mat_etd/63
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Mathematics - Dissertations
SURFACE at Syracuse University
Convergence
Superconvergence
Generalized finite element method
Mathematics
oai:surface.syr.edu:mat_etd-1062
2011-09-15T19:24:46Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
publication:oa_etd
Complexity over Finite-Dimensional Algebras
Purin, Marju
In this thesis we study two types of complexity of modules over finite-dimensional algebras.
In the first part, we examine the Ω-complexity of a family of self-injective k-algebras where k is an algebraically closed field and Ω is the syzygy operator. More precisely, let T be the trivial extension of an iterated tilted algebra of type H. We prove that modules over the trivial extension T all have complexities either 0, 1, 2 or infinity, depending on the representation type of the hereditary algebra H. As part of the proof, we show that a stable equivalence between self-injective algebras preserves the complexity of modules.
In the second part, we study the τ-complexity of modules over cluster tilted algebras where τ is the Auslander-Reiten translate. We prove that modules over the cluster tilted algebra of type H all have complexities either 0, 1, 2 or infinity, depending on the representation type of the hereditary algebra H.
2011-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat_etd/62
https://surface.syr.edu/context/mat_etd/article/1062/viewcontent/Purin_syr_0659E_10038.pdf
Mathematics - Dissertations
SURFACE at Syracuse University
cluster tilted algebra
complexity
finite-dimensional algebra
tilting theory
trivial extension
Mathematics
oai:surface.syr.edu:mat_etd-1063
2011-09-15T20:01:48Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
publication:oa_etd
Mathematical Knowledge for Teaching Teachers: The Case of Multiplication and Division of Fractions
Olanoff, Dana E.
This study attempts to answer the question, What is the mathematical knowledge required by teachers of elementary mathematics content courses in the area of multiplication and division of fractions? Beginning in the mid-1980s, when Shulman (1986) introduced the idea of pedagogical content knowledge, researchers have been looking at the knowledge needed to teach in a variety of different content areas. One area that has garnered much of the research is that of mathematics. Researchers have developed frameworks for what they call mathematical knowledge for teaching, but there has been little work done looking at the knowledge requirements for teachers of teachers. This study attempts to fill this gap by determining some aspects of a framework for the mathematical knowledge required to teach prospective elementary teachers multiplication and division of fractions.
In order to determine aspects of a framework for mathematics teacher educator knowledge in relation to multiplication and division of fractions, I interviewed, observed, and audiotaped three experienced teacher educators in different educational settings to determine the mathematical work of teaching prospective teachers fraction multiplication and division. My analysis focused on three of major tasks that came out of the work: introducing fraction multiplication, helping students make sense of fraction division, and assessing student understanding. Each of these tasks played a major role in the work of the teacher educators, and the knowledge required to perform these tasks was evident in varying degrees in each teacher educator.
After analyzing the three mathematical tasks and the knowledge required by them, I was able to determine some components of a framework for the mathematical knowledge needed for teaching teachers multiplication and division of fractions. These aspects include: understanding multiple representations of fraction multiplication and division and how these representations relate to each other, to whole number ideas, and to the algorithms, deciding which aspects of the topics will help prospective teachers make the connections that they will need in order to teach these topics, especially since time often plays a factor in what gets taught in mathematics content classes for prospective teachers, setting specific goals of exactly what one wants one's students to know, rather than having a general goal of wanting prospective teachers to develop conceptual understanding of a topic, and being able to design and use assessments effectively to help decide if one is achieving one's goals.
While each of the aspects described above are components of a framework for the mathematical knowledge needed by teacher educators, the three teacher educators in my study all lacked or were unable to demonstrate some of the knowledge components that would have helped them to meet their goals, despite having a wealth of experience teaching and designing mathematics content courses for prospective elementary teachers. One possible reason for this is that each of the teacher educators in my study were basically alone in their departments, without opportunities to collaborate or discuss these ideas with anyone else. These results suggest a need for better professional development for teacher educators in the field of mathematics education.
2011-01-01T08:00:00Z
text
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https://surface.syr.edu/mat_etd/64
https://surface.syr.edu/context/mat_etd/article/1063/viewcontent/Olanoff_syr_0659E_10062.pdf
Mathematics - Dissertations
SURFACE at Syracuse University
fractions
mathematical knowledge
teacher educators
Mathematics
oai:surface.syr.edu:mat_etd-1064
2011-09-15T20:02:01Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
publication:oa_etd
Potential Theory on Compact Sets
Perkins, Tony
The primary goal of this work is to extend the notions of potential theory to compact sets. There are several equivalent ways to define continuous harmonic functions H(K) on a compact set K in [the set of real numbers]n. One may let H(K) be the uniform closure of all functions in C(K) which are restrictions of harmonic functions on a neighborhood of K, or take H(K) as the subspace of C(K) consisting of functions which are finely harmonic on the fine interior of K. In [9] it was shown that these definitions are equivalent.
2011-01-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat_etd/65
https://surface.syr.edu/context/mat_etd/article/1064/viewcontent/Perkins_syr_0659E_10067.pdf
Mathematics - Dissertations
SURFACE at Syracuse University
Compact sets
Harmonic functions
Jensen measures
Potential Theory
Restoring Coverings
Subharmonic functions
Mathematics
oai:surface.syr.edu:mat_etd-1065
2011-09-15T20:02:15Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
publication:oa_etd
Mixed Problems and Layer Potentials for Harmonic and Biharmonic Functions
Venouziou, Moises
The mixed problem is to find a harmonic or biharmonic function having prescribed Dirichlet data on one part of the boundary and prescribed Neumann data on the remainder. One must make a choice as to the required boundary regularity of solutions. When only weak regularity conditions are imposed, the harmonic mixed problem has been solved on smooth domains in the plane by Wendland, Stephan, and Hsiao. Significant advances were later made on Lipschitz domains by Ott and Brown. The strain of requiring a square-integrable gradient on the boundary, however, forces a strong geometric restriction on the domain. Well-known counterexamples by Brown show this restriction to be a necessary condition. This thesis proves that these harmonic counterexamples are an anomaly, in that the mixed problem can be solved for all data modulo a finite dimensional subspace. The geometric restriction now required is significantly less stringent than the one referred to above. This result is proved by representing solutions in terms of single and double layer potentials, establishing a mixed Rellich inequality, and applying functional analytic arguments to solve a two-by-two system of equations. These results are then extended to allow Robin data in place of Neumann data. This thesis also establishes counterexamples for the biharmonic mixed problem with Poisson ratio in the interval [ -1, -.5]. These counterexamples are biharmonic analogues to the harmonic ones referred to above. Their exact form is obtained by solving a four-by-four system of equations.
2011-01-01T08:00:00Z
text
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https://surface.syr.edu/mat_etd/66
https://surface.syr.edu/context/mat_etd/article/1065/viewcontent/Venouziou_syr_0659E_10075.pdf
Mathematics - Dissertations
SURFACE at Syracuse University
biharmonic
boundary value problem
harmonic
layer potential
mixed problem
partial differential equation
Mathematics
oai:surface.syr.edu:mat_etd-1066
2011-10-06T20:51:16Z
publication:etd
publication:dmat
publication:coscde
publication:mat
publication:mat_etd
publication:cas
publication:oa_etd
Excess Porteous, Coherent Porteous, and the Hyperelliptic Locus in M3
Bleier, Thomas S.
In the moduli space of curves of genus 3, the locus of hyperelliptic curves forms a divisor, that is a closed subscheme of codimension 1. J. Harris and I. Morrison compute an expression for the class of this divisor, in the Chow ring of the moduli space, using a map of vector bundles and by applying the Thom-Porteous formula to determine an expression for a certain degeneracy locus of this map. One would like to extend their idea in order to compute an expression for the divisor associated to the closure of the hyperelliptic locus, in the Chow ring of the moduli space of stable curves (of genus 3.) Recent work due to S. Diaz allows one to define the degeneracy class of a map between coherent sheaves, and gives explicit means for computing this class. Diaz uses his technique to partially extend the above mentioned computation, but he points out that in order to complete the computation one must combine his techniques with an Excess Thom-Porteous formula. This thesis completes this computation by combining the work of Diaz with this Excess Thom-Porteous formula.
2011-01-01T08:00:00Z
text
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https://surface.syr.edu/mat_etd/67
https://surface.syr.edu/context/mat_etd/article/1066/viewcontent/Bleier_syr_0659E_10116.pdf
Mathematics - Dissertations
SURFACE at Syracuse University
Algebra
Geometry
Mathematics
oai:surface.syr.edu:mat-1009
2011-11-10T20:15:44Z
publication:dmat
publication:coscde
publication:mat
publication:cas
A Comparison of Continuously Controlled and Controlled K-theory
Anderson, Douglas R.
Connollly, Francis X
Munkholm, Hans J
We define an unreduced version of the ǫ-controlled lower K -theoretic groups of Ranicki and Yamasaki, [?], and Quinn, [?]. We show that the reduced versions of our groups coincide (in the inverse limit and its first derived, lim1) with those of [?]. We also relate the controlled groups to the continuously controlled groups of [?], and to the Quinn homology groups of [?].
1994-09-16T07:00:00Z
text
https://surface.syr.edu/mat/140
Mathematics - All Scholarship
SURFACE at Syracuse University
tbd
Mathematics
oai:surface.syr.edu:mat-1011
2012-09-19T15:32:15Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Equidistribution Results for Singular Metrics on Line Bundles
Coman, Dan
Marinescu, George
Let L be a holomorphic line bundle with a positively curved singular Hermitian metric over a complex manifold X. One can define naturally the sequence of Fubini-Study currents associated to the space of square integrable holomorphic sections of the p-th tensor powers of L. Assuming that the singular set of the metric is contained in a compact analytic subset of X and that the logarithm of the Bergman kernel function associated to the p-th tensor power of L (defined outside the singular set) grows like o(p) as p tends to infinity, we prove the following: 1) the k-th power of the Fubini-Study currents converge weakly on the whole X to the k-th power of the curvature current of L. 2) the expectations of the common zeros of a random k-tuple of square integrable holomorphic sections converge weakly in the sense of currents to to the k-th power of the curvature current of L. Here k is so that the codimension of the singular set of the metric is greater or equal as k. Our weak asymptotic condition on the Bergman kernel function is known to hold in many cases, as it is a consequence of its asymptotic expansion. We also prove it here in a quite general setting. We then show that many important geometric situations (singular metrics on big line bundles, Kaehler-Einstein metrics on Zariski-open sets, artihmetic quotients) fit into our framework.
2011-08-25T07:00:00Z
text
application/pdf
https://surface.syr.edu/mat/25
https://surface.syr.edu/context/mat/article/1011/viewcontent/1.pdf
http://creativecommons.org/licenses/by/3.0/
Mathematics - All Scholarship
SURFACE at Syracuse University
Mathematics
oai:surface.syr.edu:mat-1010
2011-11-10T20:23:46Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Stable Generalized Finite Element Method (SGFEM)
Babuska, I.
Banerjee, U.
The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial shape functions with compact support. These shape functions, which are also known as the enrichments, mimic the local behavior of the unknown solution of the underlying variational problem. GFEM has been successfully used to solve a variety of problems with complicated features and microstructure. However, the stiffness matrix of GFEM is badly conditioned (much worse compared to the standard FEM) and there could be a severe loss of accuracy in the computed solution of the associated linear system. In this paper, we address this issue and propose a modification of the GFEM, referred to as the Stable GFEM (SGFEM). We show that the conditioning of the stiffness matrix of SGFEM is not worse than that of the standard FEM. Moreover, SGFEM is very robust with respect to the parameters of the enrichments. We show these features of SGFEM on several examples.
2011-04-05T07:00:00Z
text
application/pdf
https://surface.syr.edu/mat/139
https://surface.syr.edu/context/mat/article/1010/viewcontent/1.pdf
Mathematics - All Scholarship
SURFACE at Syracuse University
tbd
Mathematics
oai:surface.syr.edu:mat-1012
2012-09-19T15:31:25Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Pade Interpolation by F-Polynomials and Transfinite Diameter
Coman, Dan
Poletsky, Evgeny A
We define F-polynomials as linear combinations of dilations by some frequencies of an entire function F. In this paper we use Pade interpolation of holomorphic functions in the unit disk by F-polynomials to obtain explicitly approximating F-polynomials with sharp estimates on their coefficients. We show that when frequencies lie in a compact set K C C then optimal choices for the frequencies of interpolating polynomials are similar to Fekete points. Moreover, the minimal norms of the interpolating operators form a sequence whose rate of growth is determined by the transfinite diameter of K. In case of the Laplace transforms of measures on K, we show that the coefficients of interpolating polynomials stay bounded provided that the frequencies are Fekete points. Finally, we give a sufficient condition for measures on the unit circle which ensures that the sums of the absolute values of the coefficients of interpolating polynomials stay bounded.
2011-05-03T07:00:00Z
text
https://surface.syr.edu/mat/24
http://creativecommons.org/licenses/by/3.0/
Mathematics - All Scholarship
SURFACE at Syracuse University
Mathematics
oai:surface.syr.edu:mat-1014
2012-11-28T15:51:49Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Extension of Plurisubharmonic Functions with Growth Control
Coman, Dan
Guedj, Vincent
Zeriahi, Ahmed
Suppose that X is an analytic subvariety of a Stein manifold M and that varphi is a plurisubharmonic (psh) function on X which is dominated by a continuous psh exhaustion function u of M. Given any number c > 1, we show that varphi admits a psh extension to M which is dominated by cu on M. We use this result to prove that any omega-psh function on a subvariety of the complex projective space is the restriction of a global omega-psh function, where omega is the Fubini-Study Kahler form.
2010-07-01T07:00:00Z
text
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https://surface.syr.edu/mat/22
https://surface.syr.edu/context/mat/article/1014/viewcontent/4.pdf
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oai:surface.syr.edu:mat-1015
2012-11-28T15:52:00Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Quasiplurisubharmonic Green Functions
Coman, Dan
Guedj, Vincent
Given a compact Kahler manifold X, a quasiplurisubharmonic function is called a Green function with pole at p in X if its Monge-Ampere measure is supported at p. We study in this paper the existence and properties of such functions, in connection to their singularity at p. A full characterization is obtainedin concrete cases, such as (multi)projective spaces.
2009-07-25T07:00:00Z
text
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https://surface.syr.edu/mat/21
https://surface.syr.edu/context/mat/article/1015/viewcontent/5.pdf
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oai:surface.syr.edu:mat-1016
2012-11-28T15:52:25Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Domains of Definition of Monge-Ampère Operators on Compact Kähler Manifolds
Coman, Dan
Guedj, Vincent
Zeriahi, Ahmed
Let (X, w) be a compact Kahler manifold. We introduce and study the largest set DMA(X, w) of w-plurisubharmonic (psh) functions on which the complex Monge-Ampere operator is well defined. It is much larger than the corresponding local domain of definition, though still a proper subset of the set PSH(X, w) of all w-psh functions. We prove that certain twisted Monge-Ampere operators are well defined for all w-psh functions. As a consequence, any w-psh function with slightly attenuated singularities has finite weighted Monge-Ampere energy.
2007-05-31T07:00:00Z
text
application/pdf
https://surface.syr.edu/mat/20
https://surface.syr.edu/context/mat/article/1016/viewcontent/6.pdf
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oai:surface.syr.edu:mat-1018
2011-11-29T18:49:42Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Overinterpolation
Coman, Dan
Poletsky, Evgeny A.
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such a function has specific forms.
2006-11-29T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/18
https://surface.syr.edu/context/mat/article/1018/viewcontent/7.pdf
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oai:surface.syr.edu:mat-1017
2012-09-19T15:28:50Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Stable Algebras of Entire Functions
Coman, Dan
Poletsky, Evgeny A.
Suppose that h and g belong to the algebra B generated by the rational functions and an entire function f of finite order on Cn and that h/g has algebraic polar variety. We show that either h/g in B or f = q1ep +q2, where p is a polynomial and q1, q2 are rational functions. In the latter case, h/g belongs to the algebra generated by the rational functions, ep and e−p.
2007-04-09T07:00:00Z
text
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https://surface.syr.edu/mat/19
https://surface.syr.edu/context/mat/article/1017/viewcontent/6.pdf
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oai:surface.syr.edu:mat-1019
2012-09-19T15:27:47Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Entire Pluricomplex Green Functions and Lelong Numbers of Projective Currents
Coman, Dan
Let T be a positive closed current of bidimension (1,1) and unit masson the complex projective space Pn. We prove that the set Valpa(T) of points where T has Lelong number larger than alpha is contained in a complex line if alpha ≥ 2/3, and |V alpa(T ) \ L| ≤ 1 for some complex line L if 1/2 ≤ alpha < 2/3. We also prove that in dimension 2 and if 2/5 ≤ alpha < 1/2, then |V alpha (T ) \ C| ≤ 1 for some conic C.
2004-09-13T07:00:00Z
text
application/pdf
https://surface.syr.edu/mat/17
https://surface.syr.edu/context/mat/article/1019/viewcontent/8.pdf
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oai:surface.syr.edu:mat-1020
2012-09-19T15:26:47Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Transcendence Measures and Algebraic Growth of Entire Functions
Coman, Dan
Poletsky, Evgeny A.
In this paper we obtain estimates for certain transcendence measures of an entire function f. Using these estimates, we prove Bernstein, doubling and Markov inequalities for a polynomial P(z,w) in C2 along the graph of f. These inequalities provide, in turn, estimates for the number of zeros of the function P(z, f(z)) in the disk of radius r, in terms of the degree of P and of r. Our estimates hold for arbitrary entire functions f of finite order, and for a subsequence {nj} of degrees of polynomials. But for special classes of functions, including the Riemann zeta-function, they hold for all degrees and are asymptotically best possible. From this theory we derive lower estimates for a certain algebraic measure ofa set of values f(E), in terms of the size of the set E.
2004-03-24T08:00:00Z
text
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https://surface.syr.edu/mat/16
https://surface.syr.edu/context/mat/article/1020/viewcontent/9.pdf
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oai:surface.syr.edu:mat-1021
2012-09-19T15:25:17Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Quasianalyticity and Pluripolarity
Coman, Dan
Levenberg, Norman
Poletsky, Evgeny A
We show that the graph gamma f = {(z, f(z)) in C2 : z in S} in C2 of a function f on the unit circle S which is either continuous and quasianalytic in the sense of Bernstein or C1 and quasianalytic in the sense of Denjoy is pluripolar.
2004-02-23T08:00:00Z
text
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https://surface.syr.edu/mat/15
https://surface.syr.edu/context/mat/article/1021/viewcontent/10.pdf
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oai:surface.syr.edu:mat-1022
2012-09-19T15:24:41Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Smooth Submanifolds Intersecting any Analytic Curve in a Discrete Set
Coman, Dan
Levenberg, Norman
Poletsky, Evgeny A.
We construct examples of Cinifinity smooth submanifolds in Cn and Rn of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact tori or as properly imbedded Euclidean spaces, and are the graphs of quasianalytic functions. In the complex case, these submanifolds contain real n-dimensional tori or Euclidean spaces that are not pluripolar while the intersection with any complex analytic disk is polar.
2004-02-23T08:00:00Z
text
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https://surface.syr.edu/mat/14
https://surface.syr.edu/context/mat/article/1022/viewcontent/11.pdf
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oai:surface.syr.edu:mat-1023
2012-11-28T15:52:37Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Invariant Currents and Dynamical Lelong Numbers
Coman, Dan
Guedj, Vincent
Let f be a polynomial automorphism of Ck of degree lamda, whose rational extension to Pk maps the hyperplane at infinity to a single point. Given any positive closed current S on Pk of bidegree (1,1), we show that the sequence lamda−n(fn)*S converges in the sense of currents on Pk to a linear combination of the Green current T+ of f and the current of integration along the hyperplane at infinity. We give an interpretation of the coefficients in terms of generalized Lelong numbers with respect to an invariant dynamical current for f−1.
2004-01-06T08:00:00Z
text
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https://surface.syr.edu/mat/13
https://surface.syr.edu/context/mat/article/1023/viewcontent/12.pdf
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oai:surface.syr.edu:mat-1024
2012-09-17T14:46:04Z
publication:dmat
publication:coscde
publication:mat
publication:cas
A Branching Process for Virus Survival
Cox, J. Theodore
Schinazi, Rinaldo B
Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to replicate the best adapted genotype, leading to a population composed of low replicating mutants that is eventually doomed. We propose a new branching model that shows that this is not necessarily so. That is, a population composed of ever changing mutants may survive.
2011-09-23T07:00:00Z
text
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https://surface.syr.edu/mat/46
https://surface.syr.edu/context/mat/article/1024/viewcontent/13.pdf
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oai:surface.syr.edu:mat-1028
2011-11-11T17:11:06Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Resolutions of Subsets of Finite Sets of Points in Projective Space
Diaz, Steven P
Geramita, Anthony V
Migliore, Juan C
Given a finite set, X, of points in projective space for which the Hilbert function is known, a standard result says that there exists a subset of this finite set whose Hilbert function is "as big as possible" inside X. Given a finite set of points in projective space for which the minimal free resolution of its homogeneous ideal is known, what can be said about possible resolutions of ideals of subsets of this finite set? We first give a maximal rank type description of the most generic possible resolution of a subset. Then we show that this generic resolution is not always achieved, by incorporating an example of Eisenbud and Popescu. However, we show that it is achieved for sets of points in projective two space: given any finite set of points in projective two space for which the minimal free resolution is known, there must exist a subset having the predicted resolution.
1999-06-29T07:00:00Z
text
https://surface.syr.edu/mat/138
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oai:surface.syr.edu:mat-1031
2011-12-09T18:12:09Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Path Decomposition of Ruinous Behaviour for a General Lévy Insurance Risk Process
Griffin, Philip S
Maller, Ross A
We analyse the general Levy insurance risk process for Levy measures in the convolution equivalence class
S(alpha), alpha> 0, via a new kind of path decomposition. This yields a very general functional limit theorem as the initial reserve level u → ∞, and a host of new results for functionals of interest in insurance risk. Particular emphasis is placed on the time to ruin, which is shown to have a proper limiting distribution, as u → ∞, conditional on ruin occurring, under our assumptions. Existing asymptotic results under the S(alpha)
assumption are synthesised and extended, and proofs are much simplified, by comparison with previous methods specific to the convolution equivalence analyses. Additionally, limiting expressions for penalty functions of the type introduced into actuarial mathematics by Gerber and Shiu, are derived as straightforward applications of our main results.
2011-06-30T07:00:00Z
text
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https://surface.syr.edu/mat/100
https://surface.syr.edu/context/mat/article/1031/viewcontent/20.pdf
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oai:surface.syr.edu:mat-1032
2011-12-09T18:10:58Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Asymptotic Distributions of the Overshoot and Undershoots for the Lévy Insurance Risk Process in the Cramér and Convolution Equivalent Cases
Griffin, Philip S
Maller, Ross A
van Schaik, Kees
Recent models of the insurance risk process use a Levy process to generalise the traditional Cramer-Lundberg compound Poisson model. This paper is concerned with the behaviour of the distributions of the overshoot and undershoots of a high level, for a Levy process which drifts to -infinity and satisfies a Cramer or a convolution equivalent condition. We derive these asymptotics under minimal conditions in the Cramer case, and compare them with known results for the convolution equivalent case, drawing attention to the striking and unexpected fact that they become identical when certain parameters tend to equality. Thus, at least regarding these quantities, the "medium-heavy" tailed convolution equivalent model segues into the "light-tailed" Cramer model in a natural way. This suggests a usefully expanded exibility for modelling the insurance risk process. We illustrate this relationship by comparing the asymptotic distributions obtained for the overshoot and undershoots, assuming the Levy process belongs to the "GTSC" class.
2011-06-16T07:00:00Z
text
https://surface.syr.edu/mat/99
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oai:surface.syr.edu:mat-1029
2012-09-19T15:22:38Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Small and Large Time Stability of the Time Taken for a Lévy Process to Cross Curved Boundaries
Griffin, Philip S
Maller, Ross A
This paper is concerned with the small time behaviour of a Levy process X. In particular, we investigate the stabilities of the times, Tb(r) and Tb*(r), at which X, started with X0 = 0, first leaves the space-time regions {(t, y) ∈ R2 : y ≤ rtb, t ≥ 0} (one-sided exit), or {(t, y) in R2 :|y| ≤ rtb, t ≥ 0} (two-sided exit), 0 ≤ b < 1, as r -> 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence in probability, almost surely and in Lp. In many instances these are seen to be equivalent to relative stability of the process X itself. The analogous large time problem is also discussed.
2011-10-13T07:00:00Z
text
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https://surface.syr.edu/mat/102
https://surface.syr.edu/context/mat/article/1029/viewcontent/18.pdf
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oai:surface.syr.edu:mat-1030
2012-09-19T15:21:37Z
publication:dmat
publication:coscde
publication:mat
publication:cas
The Time at Which a Lévy Process Creeps
Griffin, Philip S
Maller, Ross A
We show that if a Levy process creeps then, as a function of u, the renewal function V (t, u) of the bivariate ascending ladder process (L−1,H) is absolutely continuous on [0,∞) and left differentiable on (0,∞), and the left derivative at u is proportional to the (improper) distribution function of the time at which the process creeps over level u, where the constant of proportionality is d−1H, the reciprocal of the (positive) drift of H. This yields the (missing) term due to creeping in the recent quintuple law of Doney and Kyprianou (2006). As an application, we derive a Laplace transform identity which generalises the second factorization identity. We also relate Doney and Kyprianou’s extension of Vigon’s equation amicale inversee to creeping. Some results concerning the ladder process of X, including the second factorization identity, continue to hold for a general bivariate subordinator, and are given in this generality.
2011-06-30T07:00:00Z
text
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https://surface.syr.edu/mat/101
https://surface.syr.edu/context/mat/article/1030/viewcontent/19.pdf
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oai:surface.syr.edu:mat-1033
2011-12-09T18:09:06Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Pruitt's Estimates in Banach Space
Griffin, Philip S
Pruitt's estimates on the expectation and the distribution of the time taken by a random walk to exit a ball of radius r are extended to the infinite dimensional setting. It is shown that they separate into two pairs of estimates depending on whether the space is type 2 or cotype 2. It is further shown that these estimates characterize type 2 and cotype 2 spaces.
2011-05-11T07:00:00Z
text
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https://surface.syr.edu/mat/98
https://surface.syr.edu/context/mat/article/1033/viewcontent/22.pdf
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oai:surface.syr.edu:mat-1034
2012-09-19T15:19:41Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Why Probability Appears in Quantum Mechaincs
Blackman, Jerome
Hsiang, Wu Teh
Early in the development of quantum theory Bohr introduced what came to be called the Copenhagen interpretation. Specifically, the square of the absolute value of the wave function was to be used as a probability density. There followed lengthy arguments about this ranging from alternative universes to Schrodinger's cat. Einstein famously remarked "I am convinced that He (God) does not play dice." The purpose of this paper is to present a mathematical model of the measuring process that shows that the Copenhagen interpretation can actually follow from the fact that the time development of quantum systems is governed by the usual one parameter group of unitary transformations exp-iHt and that probability enters into the theory in the way it usually does in physics, namely, by having a large number of deterministic equations that can only be handled probabilistically.
2011-10-18T07:00:00Z
text
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https://surface.syr.edu/mat/92
https://surface.syr.edu/context/mat/article/1034/viewcontent/23.pdf
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oai:surface.syr.edu:mat-1037
2011-11-29T20:05:26Z
publication:dmat
publication:coscde
publication:mat
publication:cas
n-Harmonic Mappings Between Annuli
Iwaniec, Tadeusz
Onninen, Jani
The central theme of this paper is the variational analysis of homeomorphisms h: X onto −→ Y between two given domains X,Y ⊂ Rn. We look for the extremal mappings in the Sobolev space W1,n(X,Y) which minimize the energy integral Eh =ZX ||Dh(x) ||n dx Because of the natural connections with quasiconformal mappings this n harmonic alternative to the classical Dirichlet integral (for planar domains) has drawn the attention of researchers in Geometric Function Theory. Explicit analysis is made here for a pair of concentric spherical annuli where many unexpected phenomena about minimal n -harmonic mappings are observed. The underlying integration of nonlinear differential forms, called free Lagrangians, becomes truly a work of art.
2011-02-04T08:00:00Z
text
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https://surface.syr.edu/mat/83
https://surface.syr.edu/context/mat/article/1037/viewcontent/26.pdf
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oai:surface.syr.edu:mat-1038
2011-11-29T20:03:59Z
publication:dmat
publication:coscde
publication:mat
publication:cas
An Essay on the Interpolation Theorem of Józef Marcinkiewicz - Polish Patriot
Iwaniec, Tadeusz
In memory of Polish mathematicians murdured by the Soviets and the Nazis. The total record of accomplishments of Marcinkiewicz in his short life, his talent, perceptions rich in concepts, and technical novelties, go far beyond my ability to give full play within the confines of one article. The importance of Marcinkiewicz's short paper is reflected in the myriad applications and generalizations which earns the right to be called Marcinkiewicz Interpolation Theory Marcinkiewicz interpolation theorem came after the celebrated convexity theorem of M. Riesz and his student G.O. Thorin. These fundamental works by M. Riesz, G.O. Thorin and J. Marcinkiewicz deal with estimates of the Lp-norms of an operator, knowing its behavior at the end-points of the interval of the exponents p, where the operator is still defined. There are, however, some subtle differences between the Riesz-Thorin and the Marcinkiewicz ideas. Marcinkiewicz approach can be adapted to nonlinear operators, this is what we demonstrate in the present paper.
2011-02-01T08:00:00Z
text
application/pdf
https://surface.syr.edu/mat/82
https://surface.syr.edu/context/mat/article/1038/viewcontent/27.pdf
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oai:surface.syr.edu:mat-1039
2012-09-19T15:18:39Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Burkholder Integrals, Morrey's Problem and Quasiconformal Mappings
Astala, Kari
Iwaniec, Tadeusz
Prause, Istvan
Saksman, Eero
Inspired by Morrey's Problem (on rank-one convex functionals) and the Burkholder integrals (of his martingale theory) we find that the Burkholder functionals Bp, p > 2, are quasiconcave, when tested on deformations of identity f in Id+Coinifinty (omega) with Bp (Df(x)) > 0 pointwise, or equivalently, deformations such that abs[Df]2 < (p/(p-2))Jf. In particular, this holds in explicit neighbourhoods of the identity map. Among the many immediate consequences, this gives the strongest possible Lp-estimates for the gradient of a principal solution to the Beltrami equation fz = mu(z)fz , for any p in the critical interval 2 < 1+1/ abs[mu f]infinity. Examples of local maxima lacking symmetry manifest the intricate nature of the problem.
2010-12-02T08:00:00Z
text
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https://surface.syr.edu/mat/81
https://surface.syr.edu/context/mat/article/1039/viewcontent/28.pdf
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oai:surface.syr.edu:mat-1043
2012-09-19T15:17:43Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Hopf Differentials and Smoothing Sobolev Homeomorphisms
Iwaniec, Tadeusz
Kovalev, Leonid V
Onninen, Jani
We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space W1,2 and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.
2010-06-27T07:00:00Z
text
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https://surface.syr.edu/mat/64
https://surface.syr.edu/context/mat/article/1043/viewcontent/32.pdf
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oai:surface.syr.edu:mat-1044
2012-09-19T15:17:09Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Harmonic Mapping Problem and Affine Capacity
Iwaniec, Tadeusz
Kovalev, Leonid V
Onninen, Jani
The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this problem for doubly connected domains in the plane, where it already presents considerable challenge and leads to several interesting open questions.
2010-01-13T08:00:00Z
text
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https://surface.syr.edu/mat/63
https://surface.syr.edu/context/mat/article/1044/viewcontent/33.pdf
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oai:surface.syr.edu:mat-1049
2012-09-19T15:12:41Z
publication:dmat
publication:coscde
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publication:cas
On Injectivity of Quasiregular Mappings
Iwaniec, Tadeusz
Kovalev, Leonid V
Onninen, Jani
We give sufficient conditions for a planar quasiregular mapping to be injective in terms of the range of the differential matrix.
2008-10-22T07:00:00Z
text
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https://surface.syr.edu/mat/58
https://surface.syr.edu/context/mat/article/1049/viewcontent/38.pdf
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oai:surface.syr.edu:mat-1045
2012-09-19T15:16:18Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Doubly Connected Minimal Surfaces and Extremal Harmonic Mappings
Iwaniec, Tadeusz
Kovalev, Leonid V
Onninen, Jani
The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.
2010-02-15T08:00:00Z
text
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https://surface.syr.edu/mat/62
https://surface.syr.edu/context/mat/article/1045/viewcontent/34.pdf
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oai:surface.syr.edu:mat-1047
2012-09-19T15:14:25Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Harmonic Mappings of an Annulus, Nitsche Conjecture and its Generalizations
Iwaniec, Tadeusz
Kovalev, Leonid V
Onninen, Jani
As long ago as 1962 Nitsche conjectured that a harmonic homeomorphism h: A(r,R) onto-> A(r*, R*) between planar annuli exists if and only if R*/r* > 1/2 ((R/r) + (r/R)). We prove this conjecture when the domain annulus is not too wide; explicitly, when log(R/r) < 3/2. For general A(r,R) the conjecture is proved under additional assumption that either h or its normal derivative have vanishing average on the inner boundary circle. This is the case for the critical Nitsche mapping which yields equality in the above inequality. The Nitsche mapping represents so-called free evolution of circles of the annulus A(r,R). It will be shown on the other hand that forced harmonic evolution results in greater ratio R*/r*. To this end, we introduce the underlying differential operators for the circular means of the forced evolution and use them to obtain sharp lower bounds of R*/r*.
2009-03-16T07:00:00Z
text
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https://surface.syr.edu/mat/60
https://surface.syr.edu/context/mat/article/1047/viewcontent/36.pdf
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Mathematics
oai:surface.syr.edu:mat-1048
2012-12-11T17:48:27Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Dynamics of Quasiconformal Fields
Iwaniec, Tadeusz
Kovalev, Leonid V
Onninen, Jani
A uniqueness theorem is established for autonomous systems of ODEs, x= f(x), where f is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every non-critical point of f there passes a unique integral curve.
2008-11-26T08:00:00Z
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https://surface.syr.edu/mat/59
https://surface.syr.edu/context/mat/article/1048/viewcontent/37.pdf
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Mathematics
oai:surface.syr.edu:mat-1046
2012-09-19T15:15:02Z
publication:dmat
publication:coscde
publication:mat
publication:cas
The Nitsche Conjecture
Iwaniec, Tadeusz
Kovalev, Leonid V
Onninen, Jani
The conjecture in question concerns the existence of a harmonic homeomorphism between circular annuli A(r,R) and A(r*,R*), and is motivated in part by the existence problem for doubly-connected minimal surfaces with prescribed boundary. In 1962 J.C.C. Nitsche observed that the image annulus cannot be too thin, but it can be arbitrarily thick (even a punctured disk). Then he conjectured that for such a mapping to exist we must have the following inequality, now known as the Nitsche bound: R*/r* is greater than or equal to (R/r+r/R)/2. In this paper we give an affirmative answer to his conjecture. As a corollary, we find that among all minimal graphs over given annulus the upper slab of catenoid has the greatest conformal modulus.
2009-11-01T07:00:00Z
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https://surface.syr.edu/mat/61
https://surface.syr.edu/context/mat/article/1046/viewcontent/35.pdf
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Mathematics
oai:surface.syr.edu:mat-1050
2011-11-29T19:58:50Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Adjoint Functors, Projectivization, and Differentiation Algorithms for Representations of Partially Ordered Sets
Kleiner, Mark
Reitenbach, Markus
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial construction of the derived set and for the differentiation functor.
2011-09-19T07:00:00Z
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https://surface.syr.edu/mat/79
https://surface.syr.edu/context/mat/article/1050/viewcontent/39.pdf
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oai:surface.syr.edu:mat-1051
2012-09-19T15:11:50Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Preprojective Representations of Valued Quivers and Reduced Words in the Weyl Group of a Kac-Moody Algebra
Kleiner, Mark
Pelley, Allen
This paper studies connections between the preprojective representations of a valued quiver, the (+)-admissible sequences of vertices, and the Weyl group by associating to each preprojective representation a canonical (+)-admissible sequence. A (+)-admissible sequence is the canonical sequence of some preprojective representation if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group. As a consequence, for any Coxeter element of the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix, the group is infinite if and only if the powers of the element are reduced words. The latter strengthens known results of Howlett, Fomin-Zelevinsky, and the authors.
2006-08-24T07:00:00Z
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https://surface.syr.edu/mat/78
https://surface.syr.edu/context/mat/article/1051/viewcontent/40.pdf
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oai:surface.syr.edu:mat-1052
2012-09-19T15:09:34Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Sequences of Reflection Functors and the Preprojective Component of a Valued Quiver
Kleiner, Mark
Tyler, Helene R
This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander-Reiten quiver. The results apply to the study of reduced words in the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix.
2006-08-07T07:00:00Z
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https://surface.syr.edu/mat/77
https://surface.syr.edu/context/mat/article/1052/viewcontent/41.pdf
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Mathematics
oai:surface.syr.edu:mat-1059
2011-11-29T19:28:55Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Strong Approximation of Homeomorphisms of Finite Dirichlet Energy
Iwaniec, Tadeusz
Kovalev, Leonid V
Onninen, Jani
Let X and Y be planar Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h:X->Y in the Sobolev space W1,2 extends to a continuous map between closed domains. We prove that there exist homeomorphisms between closed domains which converge to h uniformly and in W1,2. The problem of approximation of Sobolev homeomorphisms, raised by J. M. Ball and L. C. Evans, is deeply rooted in a study of energy-minimal deformations in nonlinear elasticity. The new feature of our main result is that approximation takes place also on the boundary, where the original map need not be a homeomorphism.
2011-07-31T07:00:00Z
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https://surface.syr.edu/mat/56
https://surface.syr.edu/context/mat/article/1059/viewcontent/48.pdf
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oai:surface.syr.edu:mat-1055
2011-11-29T19:52:51Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank
Diaz, Steven P
Kleiner, Mark
With a grading previously introduced by the second-named author, the multiplication maps in the preprojective algebra satisfy a maximal rank property that is similar to the maximal rank property proven by Hochster and Laksov for the multiplication maps in the commutative polynomial ring. The result follows from a more general theorem about the maximal rank property of a minimal almost split morphism, which also yields a quadratic inequality for the dimensions of indecomposable modules involved.
2005-12-30T08:00:00Z
text
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https://surface.syr.edu/mat/75
https://surface.syr.edu/context/mat/article/1055/viewcontent/44.pdf
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oai:surface.syr.edu:mat-1057
2012-09-19T15:06:19Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Local Theory of Almost Split Sequences for Comodules
Chin, William
Kleiner, Mark
Quinn, Declan
We show that almost split sequences in the category of comodules over a coalgebra with finite-dimensional right-hand term are direct limits of almost split sequences over finite dimensional subcoalgebras. In previous work we showed that such almost split sequences exist if the right hand term has a quasifinitely copresented linear dual. Conversely, taking limits of almost split sequences over finte-dimensional comodule categories, we then show that, for countable-dimensional coalgebras, certain exact sequences exist which satisfy a condition weaker than being almost split, which we call ``finitely almost split''. Under additional assumptions, these sequences are shown to be almost split in the appropriate category.
2005-04-05T07:00:00Z
text
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https://surface.syr.edu/mat/73
https://surface.syr.edu/context/mat/article/1057/viewcontent/46.pdf
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SURFACE at Syracuse University
Mathematics
oai:surface.syr.edu:mat-1056
2012-09-19T15:07:02Z
publication:dmat
publication:coscde
publication:mat
publication:cas
Finite-Dimensional Algebras with Smallest Resolutions of Simple Modules
Jagadeeshan, Shashidhar
Kleiner, Mark
Let lamda be an associative ring with identity and with the Jacobson radical r, let mod lamda be the category of finitely generated left lamda-modules, and let lamdaop be the opposite ring of lamda. All modules are left unital modules, and if X is a module then pd X is the projective dimension of X. If lamda is left artinian and M in mod labmda, we denote by P(M) a projective cover of M.
2005-12-30T08:00:00Z
text
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https://surface.syr.edu/mat/74
https://surface.syr.edu/context/mat/article/1056/viewcontent/45.pdf
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