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2012

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Articles 721 - 750 of 841

Full-Text Articles in Mathematics

Enhancements Of Rack Counting Invariants Via Dynamical Cocycles, Alissa S. Crans, Sam Nelson, Aparna Sarkar Jan 2012

Enhancements Of Rack Counting Invariants Via Dynamical Cocycles, Alissa S. Crans, Sam Nelson, Aparna Sarkar

Mathematics, Statistics and Data Science Faculty Works

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

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Convergence Of A Steepest Descent Algorithm For Ratio Cut Clustering, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht Jan 2012

Convergence Of A Steepest Descent Algorithm For Ratio Cut Clustering, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht

Mathematics, Statistics and Data Science Faculty Works

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In this paper, we present an explicit-implicit gradient flow scheme for the relaxed ratio cut problem, and prove that the algorithm converges to a critical point of the energy. We also show the efficiency of the proposed algorithm on the two moons dataset.

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How Well Do The Nsf Funded Elementary Mathematics Curricula Align With The Gaise Report Recommendations?, Anna E. Bargagliotti Jan 2012

How Well Do The Nsf Funded Elementary Mathematics Curricula Align With The Gaise Report Recommendations?, Anna E. Bargagliotti

Mathematics, Statistics and Data Science Faculty Works

Statistics and probability have become an integral part of mathematics education. Therefore it is important to understand whether curricular materials adequately represent statistical ideas. The Guidelines for Assessment and Instruction in Statistics Education (GAISE) report (Franklin, Kader, Mewborn, Moreno, Peck, Perry, & Scheaffer, 2007), endorsed by the American Statistical Association, provides a two-dimensional (process and level) framework for statistical learning. This paper examines whether the statistics content contained in the NSF funded elementary curricula Investigations in Number, Data, and Space, Math Trailblazers, and Everyday Mathematics aligns with the GAISE recommendations. Results indicate that there are differences in the approaches used …

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Characterizing Conflict In Wikipedia, Nathaniel Miller Jan 2012

Characterizing Conflict In Wikipedia, Nathaniel Miller

Mathematics, Statistics, and Computer Science Honors Projects

Wikipedia serves as the Internet's most widely viewed reference. In order to ensure its success, editors who create and maintain articles must resolve conflicts over appropriate article content. Previous research has measured Wikipedia conflict at two levels: single articles and categories of pages. I observe conflicts within small groups of articles, identifying their frequency, size, and intensity. Additionally, I identify individual conflicts spanning multiple articles and effects of conflict upon users' editing habits. I analyze cross-article conflict in three stages. First, I cluster a group of 1.4 million Wikipedia articles. Next, I find individual user conflicts within each article cluster …

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The Best Mixing Time For Trees, Jeanmarie Youngblood Jan 2012

The Best Mixing Time For Trees, Jeanmarie Youngblood

Mathematics, Statistics, and Computer Science Honors Projects

A graph G consists of a set of vertices connected in pairs by edges. Two vertices connected by an edge are called neighbors. A random walk on G is a sequence of vertices, where the next vertex is chosen randomly from the neighbors of the current vertex. Under mild assumptions, the distribution of a walk's current location converges to the stationary distribution. In this distribution, the probability of being at a given vertex is proportional to the size of its neighbor set. The expected time to convergence is called a mixing measure of G. There are a variety …

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Geometry Of Partial Differential Equations, Paul Bracken Jan 2012

Geometry Of Partial Differential Equations, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The study of partial differential equations has been the object of much investigation and seen a great many advances recently. This is primarily due to the fact that certain classes of these equations fall under the category of being integrable. These kinds of equations have many useful properties such as the existence of Lax pairs, Backlund transformations, explicit solutions and the existence of a correspondence with geometric manifolds. There have also been many applications of solutions to these equations in the study of solitons and other objects which have seen applications in physics. It is the objective here to study …

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Characterizations Of Logistic Distribution Through Order Statistics With Independent Exponential Shifts, M. Ahsanullah, George Yanev, Constantin Onica Jan 2012

Characterizations Of Logistic Distribution Through Order Statistics With Independent Exponential Shifts, M. Ahsanullah, George Yanev, Constantin Onica

School of Mathematical & Statistical Sciences Faculty Publications

Distributional properties of logistic order statistics subject to independent exponential one-sided and two-sided shifts are established. Utilizing these properties, we extend several known results and obtain new characterizations of the logistic distribution.

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The Distribution Of Individual Stock Returns In A Modified Black-Scholes Option Pricing Model, Daniel Lee Richey Jan 2012

The Distribution Of Individual Stock Returns In A Modified Black-Scholes Option Pricing Model, Daniel Lee Richey

College of Graduate Studies: Theses & Dissertations

Author's abstract: There have been many attempts to find a model that can accurately price options. These models are built on many assumptions, including which probability distribution stock returns follow. In this paper, we test several distributions to see which best fit the log returns of 20 different companies over a period between November 1, 2006 to October 31, 2011. If a "best" distribution is found, a modified Black-Scholes model will be defined by modifying the Weiner process. We use Monte Carlo simulations to generate estimated prices under specified parameters, and compare these prices to those simulated by the model …

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Berry-Esseen Bounds For Nonlinear Statistics, And Asymptotic Relative Efficiency Between Correlation Statistics, Raymond E. Molzon Jan 2012

Berry-Esseen Bounds For Nonlinear Statistics, And Asymptotic Relative Efficiency Between Correlation Statistics, Raymond E. Molzon

Dissertations, Master's Theses and Master's Reports - Open

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall …

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Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert Jan 2012

Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert

Masters Theses

"In this work, we study Abel dynamic equations of the first and the second kind. After a brief introduction to time scales, we introduce the Abel differential equations of the first and the second kind, as well as the canonical Abel form in the continuous case. Using the existing information, we derive novel results for time scales. We provide formulas for the Abel dynamic equations of the second kind and present a solution method. We furthermore achieve a special class of Abel equations of the first kind and discuss the canonical Abel equation. We get relations between common dynamic equations …

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Groupoids, Imaginaries And Internal Covers, Ehud Hrushovski Jan 2012

Groupoids, Imaginaries And Internal Covers, Ehud Hrushovski

Turkish Journal of Mathematics

Let T be a first-order theory. A correspondence is established between internal covers of models of T and definable groupoids within T. We also consider amalgamations of independent diagrams of algebraically closed substructures, and find strong relation between covers, uniqueness for 3-amalgamation, existence of 4-amalgamation, imaginaries of T^\si, and definable groupoids. As a corollary, we describe the imaginary elements of families of finite-dimensional vector spaces over pseudo-finite fields.

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On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values, Youming Wang Jan 2012

On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values, Youming Wang

Turkish Journal of Mathematics

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain D \subseteq C and n be a positive integer. Let a, b be two finite complex constants such that a \neq 0. If n \geq 3 and f + a(f')^n and g + a(g')^n share b in D for every pair of functions f, g \in F, then F is normal in D. And some examples are provided to show the result is sharp.

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Invariant Subspaces Of Weakly Compact-Friendly Operators, Mert Çağlar, Remzi̇ Tunç Misirlioğlu Jan 2012

Invariant Subspaces Of Weakly Compact-Friendly Operators, Mert Çağlar, Remzi̇ Tunç Misirlioğlu

Turkish Journal of Mathematics

We prove that if a non-zero weakly compact-friendly operator B on a Banach lattice with topologically full center is locally quasi-nilpotent, then the super right-commutant [B\rangle of B has a non-trivial closed invariant ideal. An example of a weakly compact-friendly operator which is not compact-friendly is also provided.

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Extended Cross Product In A 3-Dimensional Almost Contact Metric Manifold With Applications To Curve Theory, Çeti̇n Camci Jan 2012

Extended Cross Product In A 3-Dimensional Almost Contact Metric Manifold With Applications To Curve Theory, Çeti̇n Camci

Turkish Journal of Mathematics

In this work, we define a new cross product in 3-dimensional almost contact metric manifold and we study the theory of curves using this new cross product in this manifold. Besides, in the works of Baikousis, Blair [1] and Cho et al. [4], we observe that some theorems are incomplete and excessively generalized are thus their alternative proofs presented.

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Invariants Of Symmetric Algebras Associated To Graphs, Maurizio Imbesi, Monica La Barbiera Jan 2012

Invariants Of Symmetric Algebras Associated To Graphs, Maurizio Imbesi, Monica La Barbiera

Turkish Journal of Mathematics

In this work we deal with the symmetric algebra of monomial ideals that arise from graphs, the edge ideals. The notion of s-sequence is explored for such ideals in order to compute standard algebraic invariants of their symmetric algebra in terms of the corresponding invariants of special quotients of the polynomial ring related to the graphs.

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Value Distribution Of Meromorphic Functions And Their Differences, Ranran Zhang, Zongxuan Chen Jan 2012

Value Distribution Of Meromorphic Functions And Their Differences, Ranran Zhang, Zongxuan Chen

Turkish Journal of Mathematics

Let f(z) be a transcendental meromorphic function. Results are proved concerning the value distribution of the n'th forward difference \Delta^nf(z), in terms of Borel exceptional values of f(z). The results may be partly viewed as discrete analogues of a classical theorem of Hayman dealing with the possible relationships between Picard exceptional values of f(z) and its derivatives.

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On F_S-Supplemented Primary Subgroups Of Finite Groups, Lujin Zhu, Long Miao Jan 2012

On F_S-Supplemented Primary Subgroups Of Finite Groups, Lujin Zhu, Long Miao

Turkish Journal of Mathematics

Let G be a finite group and F a formation of finite groups. A subgroup H of G is called F_s-supplemented in G if there exists a subnormal subgroup T of G such that G = HT and (H \cap T)H_G/H_G is contained in the F-hypercenter Z^F_{\infty}(G/H_G) of G/H_G. In this paper, we study the structure of finite groups by using F_s-supplemented subgroups.

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On The Order Of Weighted Approximation By Positive Linear Operators, Tüli̇n Coşkun Jan 2012

On The Order Of Weighted Approximation By Positive Linear Operators, Tüli̇n Coşkun

Turkish Journal of Mathematics

An estimation of approximation of continuous functions by positive linear operators in weighted norm using the weighted modulus of continuity is established. Application of the main result to the known Gadjiyev-Ibragimov operators is given.

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C^*-Convexity And C^*-Faces In *-Rings, Ali Ebrahimi Meymand, Gholam Hossein Esslamzadeh Jan 2012

C^*-Convexity And C^*-Faces In *-Rings, Ali Ebrahimi Meymand, Gholam Hossein Esslamzadeh

Turkish Journal of Mathematics

Existence of rich algebraic, geometric and topological structures on self-adjoint operator algebras raises the general question that, for a particular theorem which of these structures have made the result work. The present paper is an effort toward the answer of this question, by investigating the role of algebraic structure in the subject of C^*-convexity. In this paper, we extend the notions of C^*-convexity, C^*-extreme point and C^*-face to *-rings and we study some of their properties. We introduce the notion of C^*-convex map on C^*-convex subsets of a *-ring. Moreover we identify optimal points of some unital *-homomorphisms on some …

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Invariant Parametrizations And Complete Systems Of Global Invariants Of Curves In The Pseudo-Euclidean Geometry, Ömer Pekşen, Djavvat Khadjiev, İdri̇s Ören Jan 2012

Invariant Parametrizations And Complete Systems Of Global Invariants Of Curves In The Pseudo-Euclidean Geometry, Ömer Pekşen, Djavvat Khadjiev, İdri̇s Ören

Turkish Journal of Mathematics

Let M(n, p) be the group of all transformations of an n-dimensional pseudo-Euclidean space E^n_p of index p generated by all pseudo-orthogonal transformations and parallel translations of E^n_p. Definitions of a pseudo-Euclidean type of a curve, an invariant parametrization of a curve and an M(n, p)-equivalence of curves are introduced. All possible invariant parametrizations of a curve with a fixed pseudo-Euclidean type are described. The problem of the M(n, p)-equivalence of curves is reduced to that of paths. Global conditions of the M(n, p)-equivalence of curves are given in terms of the pseudo-Euclidean type of a curve and the system …

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Small Covers Over Products Of A Polygon With A Simplex, Yanying Wang, Yanchang Chen Jan 2012

Small Covers Over Products Of A Polygon With A Simplex, Yanying Wang, Yanchang Chen

Turkish Journal of Mathematics

The equivariant homeomorphism class of an (orientable) small cover over a simple convex polytope P^n bijectively corresponds to the equivalence class of its (orientable) coloring under the action of automorphism group of face poset of P^n. By calculating the number of orbits of group actions we determine the number of equivariant homeomorphism classes of small covers over products of a polygon with a simplex. Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.

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Hilbert Functions And Betti Numbers Of Reverse Lexicographic Ideals In The Exterior Algebra, Marilena Crupi, Carmela Ferro' Jan 2012

Hilbert Functions And Betti Numbers Of Reverse Lexicographic Ideals In The Exterior Algebra, Marilena Crupi, Carmela Ferro'

Turkish Journal of Mathematics

Let K be a field, V a K-vector space with basis e_1,...,e_n and let E be the exterior algebra of V. We study the class of reverse lexicographic ideals in E. We analyze the behaviour of their Hilbert functions and Betti numbers.

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L^P Regularity Of Some Weighted Bergman Projections On The Unit Disc, Yunus Ergi̇n Zeytuncu Jan 2012

L^P Regularity Of Some Weighted Bergman Projections On The Unit Disc, Yunus Ergi̇n Zeytuncu

Turkish Journal of Mathematics

We show that weighted Bergman projections, corresponding to weights of the form M(z)(1- z ^2)^\alpha, where \alpha > -1 and M(z) is a radially symmetric, strictly positive and at least C^2 function on \overline{D}, are L^p regular.

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Superinjective Simplicial Maps Of The Complexes Of Curves On Nonorientable Surfaces, Elmas Irmak Jan 2012

Superinjective Simplicial Maps Of The Complexes Of Curves On Nonorientable Surfaces, Elmas Irmak

Turkish Journal of Mathematics

We prove that each superinjective simplicial map of the complex of curves of a compact, connected, nonorientable surface is induced by a homeomorphism of the surface, if (g, n) \in {(1, 0), (1, 1), (2, 0), (2, 1), (3, 0)} or g + n \geq 5, where g is the genus of the surface and n is the number of the boundary components.

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On The Biharmonic Vector Fields, Mustapha Djaa, Hichem Elhendi, Seddik Ouakkas Jan 2012

On The Biharmonic Vector Fields, Mustapha Djaa, Hichem Elhendi, Seddik Ouakkas

Turkish Journal of Mathematics

The problem studied in this paper is related to the biharmonicity of a vector field from a Riemannian manifold (M,g) to its tangent bundle TM equipped with the Sasaki metric g^s. We show that a vector field on a compact manifold is biharmonic if and only if is harmonic. We also investigate the biharmonicity of vector field of M, as a map from (M,g) to (TM,g^s).

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Generalized Berwald Metrics, Esmaeil Peyghan, Akbar Tayebi Jan 2012

Generalized Berwald Metrics, Esmaeil Peyghan, Akbar Tayebi

Turkish Journal of Mathematics

In this paper, we consider a class of Finsler metrics called generalized Berwald metrics which contains the class of Berwald metrics as a special case. We prove that every generalized Berwald metrics with non-zero scalar flag curvature or isotropic Berwald curvature is a Randers metric. Then we prove that on generalized Berwald metrics, the notions of generalized Landsberg and Landsberg curvatures are equivalent.

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Weight And Nonlinearity Of Boolean Functions, Lavinia Corina Ciungu Jan 2012

Weight And Nonlinearity Of Boolean Functions, Lavinia Corina Ciungu

Turkish Journal of Mathematics

In this paper we analyze the weight and the nonlinearity of various types of Boolean functions. We give some general results related to rotation symmetric Boolean functions, and in particular, we prove partially a conjecture stated by Cusick and Stanica in [3].

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Results Of Generalized Local Cohomology Modules Of A-Minimax Modules, Hero Saremi Jan 2012

Results Of Generalized Local Cohomology Modules Of A-Minimax Modules, Hero Saremi

Turkish Journal of Mathematics

Let R be a commutative Noetherian ring, M a finitely generated R-module, and N a minimax R-module. It is shown that if a is an ideal of R, such that cd(a)=1, where cd is the cohomological dimension of a in R, then H_a^j(M, N) and Ext_R^i(M,H_a^j(N)) are a-cominimax for all i,j. Furthermore, if t is a non-negative integer such that H_a^j(M, N) is a-minimax for all j

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Essential Normality For Certain Weighted Composition Operators On The Hardy Space H^2, Mahsa Fatehi, Bahram Khani Robati Jan 2012

Essential Normality For Certain Weighted Composition Operators On The Hardy Space H^2, Mahsa Fatehi, Bahram Khani Robati

Turkish Journal of Mathematics

We characterize the essentially normal weighted composition operators C_{\psi,\varphi} on the Hardy space H^2, whenever \varphi is a linear-fractional transformation and \psi \in A(D). Also we investigate the essential normality problem for some other weighted composition operators on H^2.

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P-Rank And P-Groups In Algebraic Groups, Adrien Deloro Jan 2012

P-Rank And P-Groups In Algebraic Groups, Adrien Deloro

Turkish Journal of Mathematics

A few remarks on the measures of the p-rank of a group equipped with a dimension, including the refutation of a result of Burdges and Cherlin.

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