Mathematics Commons^™

Optimal Quantizers For Some Absolutely Continuous Probability Measures, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of n-means and the nth quantization errors are calculated for some positive integers n.

A Multi-Step Nonlinear Dimension-Reduction Approach With Applications To Bigdata, R. Krishnan, V. A. Samaranayake, Jagannathan Sarangapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, a multi-step dimension-reduction approach is proposed for addressing nonlinear relationships within attributes. In this work, the attributes in the data are first organized into groups. In each group, the dimensions are reduced via a parametric mapping that takes into account nonlinear relationships. Mapping parameters are estimated using a low rank singular value decomposition (SVD) of distance covariance. Subsequently, the attributes are reorganized into groups based on the magnitude of their respective singular values. The group-wise organization and the subsequent reduction process is performed for multiple steps until a singular value-based user-defined criterion is satisfied. Simulation analysis is …

Algorithms For Numerical Implementation Of The Shooting Method Of The Boundary Solution Problems For Ordinary Second-Order Differential Equations, A. Otarov Professor, Kh. Umarova, S. Karabekov

Karakalpak Scientific Journal

In the article algorithms of numerical realization of a shooting method decisions of marginal problems for nonlinear ordinary differential equations of the second order are under construction.

On Lattices Of Z-Ideals Of Function Rings, Themba Dube, Oghenetega Ighedo

Mathematics, Physics, and Computer Science Faculty Articles and Research

An ideal I of a ring A is a z-ideal if whenever a, b ∈ A belong to the same maximal ideals of A and a ∈ I, then b ∈ I as well. On the other hand, an ideal J of A is a d-ideal if Ann²(a) ⊆ J for every a ∈ J. It is known that the lattices Z(L) and D(L) of the ring 𝓡L of continuous real-valued functions on a frame L, consisting of z-ideals and d-ideals of 𝓡 …

Rook Placements And Jordan Forms Of Upper-Triangular Nilpotent Matrices, Martha Yip

Mathematics Faculty Publications

The set of n by n upper-triangular nilpotent matrices with entries in a finite field 𝔽_q has Jordan canonical forms indexed by partitions λ ⊢ n. We present a combinatorial formula for computing the number F_λ(q) of matrices of Jordan type λ as a weighted sum over standard Young tableaux. We construct a bijection between paths in a modified version of Young's lattice and non-attacking rook placements, which leads to a refinement of the formula for F_λ(q).

Lozenge Tilings Of A Halved Hexagon With An Array Of Triangles Removed From The Boundary, Tri Lai

Department of Mathematics: Faculty Publications

Proctor's work on staircase plane partitions yields an enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi recently extended this tiling enumeration to a halved hexagon with a triangle removed from the boundary. In this paper, we prove a generalization of the results of Proctor and Rohatgi by enumerating lozenge tilings of a halved hexagon in which an array of an arbitrary number of adjacent triangles has been removed from the boundary.

A Variation On The Theme Of Nicomachus, Florian Luca, Geremías Polanco, Wadim Zudilin

Mathematics Sciences: Faculty Publications

In this paper, we prove some conjectures of K. Stolarsky concerning the first and third moments of the Beatty sequences with the golden section and its square.

A Review On Entanglement And Maxwell-Dirac Isomorphism, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In RG forum, one senior professor of physics posted a project called: “Future science and technology.” As a response, one of us (VC) wrote in reply: “I think one of future science's tasks is to discover the link between entanglement and classical electromagnetic theory. This is to fulfill Einstein's position that present QM theory is incomplete, a new one must be found. We are on a way to that goal.” Therefore, in this paper we will discuss how entanglement can be explained in terms of Maxwell-Dirac isomorphism. This short review may be considered as Einstein’s dream of completing QM in …

Using An A Priori Estimate For Constructing Difference Schemes For Quasi-Linear Hyperbolic Systems, Rakhmatillo Aloev, Mirzoali Khudayberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.

Some Cardinal And Topological Properties Of The $N$-Permutation Degree Of A Topological Spaces And Locally $\Tau$-Density Of Hyperspaces, Farkhod Mukhamadiev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the paper we investigate some cardinal and topological properties of the $n$-permutation degree of a topological spaces and locally $\tau$-density of hyperspaces. It is proved that the functors $\exp_n$ and $SP^n$ preserves locally $\tau$-density of any infinite $T_1$-spaces.

Using An A Priori Estimate For Constructing Difference Schemes For Quasi-Linear Hyperbolic Systems, Rakhmatillo Aloev, Mirzoali Khudayberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.

Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng

Theses and Dissertations

Solutions to the one-dimensional and two-dimensional nonlinear Schrodinger (NLS) equation are obtained numerically using methods based on radial basis functions (RBFs). Periodic boundary conditions are enforced with a non-periodic initial condition over varying domain sizes. The spatial structure of the solutions is represented using RBFs while several explicit and implicit iterative methods for solving ordinary differential equations (ODEs) are used in temporal discretization for the approximate solutions to the NLS equation. Splitting schemes, integration factors and hyperviscosity are used to stabilize the time-stepping schemes and are compared with one another in terms of computational efficiency and accuracy. This thesis shows …

Text Classification Of Installation Support Contract Topic Models For Category Management, William C. Sevier

Theses and Dissertations

Air Force Installation Contracting Agency manages nearly 18 percent of total Air Force spend, equating to approximately 57 billion dollars. To improve strategic sourcing, the organization is beginning to categorize installation-support spend and assign accountable portfolio managers to respective spend categories. A critical task in this new strategic environment includes the appropriate categorization of Air Force contracts into newly created, manageable spend categories. It has been recognized that current composite categories have the opportunity to be further distinguished into sub-categories leveraging text analytics on the contract descriptions. Furthermore, upon establishing newly constructed categories, future contracts must be classified into these …

Shortest Path Across Stochastic Network With Correlated Random Arcs, Stephanie M. Boone

Theses and Dissertations

This paper introduces a new approach to identify the shortest path across a stochastic network with correlated random arcs utilizing nonparametric samples of arc lengths. This approach is applied to find optimal aircraft routes that minimize expected fuel consumption for a given airspeed utilizing predicted wind output from NWP ensemble models. Results from this new methodology are then compared to the current fuel minimization route planning method that utilizes deterministic NWP wind data for arc lengths. Comparisons are also made to other previously proposed alternative fuel minimization methodologies that utilize mean and median wind data calculated from NWP ensemble wind …

Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

Let S be a Riemann surface and G a large subgroup of Aut(S) (Aut(S) may be unknown). We are particularly interested in regular n-gonal surfaces, i.e., the quotient surface S/G (and hence S/Aut(S)) has genus zero. For various H the ramification information of the branched coverings S/K -> S/H may be captured in a matrix. The ramification information, in particular strong branching, may be then be used in analyzing the structure of Aut(S). The ramification information is conjugation invariant so the matrix's rows and columns may be indexed by conjugacy classes of subgroups. The only required …

Lie Sphere Geometry And Dupin Hypersurfaces, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

These notes were originally written for a short course held at the Institute of Mathematics and Statistics, University of São Paulo, S.P. Brazil, January 9–20, 2012. The notes are based on the author’s book [17], Lie Sphere Geometry With Applications to Submanifolds, Second Edition, published in 2008, and many passages are taken directly from that book. The notes have been updated from their original version to include some recent developments in the field.

A hypersurface Mⁿ⁻¹ in Euclidean space Rⁿ is proper Dupin if the number of distinct principal curvatures is constant on M^{n−1 …}

Preface Of 2nd Annual Meeting Of Siam Central States Section, Xiaoming He, Stephen Pankavich, Erik Van Vleck, Zhu Wang, Xiu Ye

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Modeling Of First-Order Photobleaching Kinetics Using Krylov Subspace Spectral Methods, Somayyeh Sheikholeslami, James V. Lambers

Faculty Publications

We solve the first order 2-D reaction–diffusion equations which describe binding-diffusion kinetics using the photobleaching scanning profile of a confocal laser scanning microscope, approximated by a Gaussian laser profile. We show how to solve the first-order photobleaching kinetics partial differential equations (PDEs) using a time-stepping method known as a Krylov subspace spectral (KSS) method. KSS methods are explicit methods for solving time-dependent variable-coefficient partial differential equations. They approximate Fourier coefficients of the solution using Gaussian quadrature rules in the spectral domain. In this paper, we show how a KSS method can be used to obtain not only an approximate numerical …

A Weak Galerkin Method For Second Order Elliptic Equations With Polynomial Reductions, Nolisa Malluwawadu

Theses and Dissertations

The second order elliptic equation, which is also known as the diffusion-convection equation, is of great interest in many branches of physics and industry. In this dissertation, we use the weak Galerkin finite element method to study the general elliptic equation with Dirichlet boundary condition and the elliptic equation with mixed boundary conditions. Weak Galerkin finite element schemes are proposed and analyzed. These schemes feature piecewise polynomials of degree k ≥ 1 on each element and piecewise polynomials of degree k − 1 ≥ 0 on each edge or face of the element. Error estimates of optimal order are established …

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …