Mathematics Commons^™

Uniform Gaussian Bounds For Subelliptic Heat Kernels And An Application To The Total Variation Flow Of Graphs Over Carnot Groups, Luca Capogna, Giovanna Citti, Maria Manfredini

Mathematics Sciences: Faculty Publications

In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σϵ which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ϵ rarr; 0. The main new contribution are Gaussian-Type bounds on the heat kernel for the σϵ metrics which are stable as ϵ rarr; 0 and extend the previous time-independent estimates in [16]. As an application we study well posedness of the total variation flow of graph surfaces over a bounded domain in a step two Carnot group (G; σϵ ). We establish …

Strong Solution For A High Order Boundary Value Problem With Integral Condition, Ahcene Merad, Ahmed Lakhdar Marhoune

Turkish Journal of Mathematics

The present paper is devoted to a proof of the existence and uniqueness of strong solution for a high order boundary value problem with integral condition. The proof is based by a priori estimate and on the density of the range of the operator generated by the studied problem.

On Integrability Of Golden Riemannian Structures, Aydin Gezer, Nejmi̇ Cengi̇z, Arif Salimov

Turkish Journal of Mathematics

The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. We discuss the problem of integrability for Golden Riemannian structures by using a \phi-operator which is applied to pure tensor fields. Also, the curvature properties for Golden Riemannian metrics and some properties of twin Golden Riemannian metrics are investigated. Finally, some examples are presented.

On Q-Analogs Of Wostenholme Type Congruences For Multiple Harmonic Sums, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

Multiple harmonic sums are iterated generalizations of harmonic sums. Recently Dilcher has considered congruences involving q-analogs of these sums in depth one. In this paper we shall study the homogeneous case for arbitrary depth by using generating functions and shuffle relations of the q-analog of multiple harmonic sums. At the end, we also consider some non-homogeneous cases.

Extension Properties Of Pluricomplex Green Functions, Sidika Zeynep Ozal

Mathematics - Dissertations

In 1985, Klimek introduced an extremal plurisubharmonic function on bounded domains in Cn that generalizes the Green's function of one variable. This function is called the pluricomplex Green function of Ω with logarithmic pole at a and is denoted by g_Ω(.,a). The aim of this thesis was to investigate the extension properties of g_Ω(.,a). Let Ω0 be a bounded domain of Cn and E be a compact subset of Ω0 such that Ω : = Ω0 E is connected. In general, g_Ω(.,a) cannot be extended as a pluricomplex Green function to any subdomain of …

Shimura Images Of A Family Of Half-Integral Weight Modular Forms, Kenneth Allan Brown

Theses and Dissertations

In 1973, Shimura introduced a family of maps between modular forms of half-integral weight and modular forms of even integral weight. We will give explicit formulas for the images of two different classes of modular forms under these maps. In contrast to Shimura's difficult analytic construction, our formulas will fall out of relatively simple combinatorial derivations. Using the Shimura correspondence, we will prove congruences for the eigenvalues of a family of eigenforms introduced by Garvan. Using deep results of Eichler and Shimura, we state these congruences in terms of the number of points on associated elliptic curves, and we provide …

Software Development For A 3d Gravity Inversion And Application To Study Of The Border Ranges Fault System, South-Central Alaska, Rolando Cardenas

Open Access Theses & Dissertations

The Border Ranges Fault System (BRFS) bounds the Cook Inlet and Susitna Basins, and is an important petroleum province within south-central Alaska. A primary goal of our research is to test several plausible models of structure along the BRFS using a novel three-dimensional inversion technique utilizing gravity data, constrained with other geophysical, borehole and surface geological information. This research involves the development of 3D inversion modeling software using C++ Builder from Embarcadero's XE2 Suite. The novel inversion approach directly models known geology with a priori uncertainties assigned to the geologic model to allow researchers to compare alternative interpretations. This technique …

Set Theoretic Approach To Algebraic Structures In Mathematics - A Revelation, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors bring out how sets in algebraic structure can be used to construct most generalized algebraic structures, like set linear algebra/vector space, set ideals in rings and semigroups. This sort of study is not only innovative but infact very helpful in cases instead of working with a large data we can work with a considerably small data. Thus instead of working with a vector space or a linear algebra V over a field F we can work with a subset in V and a needed subset in F, this can save both time and economy. The concept …

Control, Stability, And Qualitative Theory Of Dynamical Systems, Nazim Idrisoglu Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren

Mathematics Faculty Publications

No abstract provided.

Modified Pal Interpolation And Sampling Bilevel Signals With Finite Rate Of Innovation, Gayatri Ramesh

Electronic Theses and Dissertations

Sampling and interpolation are two important topics in signal processing. Signal processing is a vast field of study that deals with analysis and operations of signals such as sounds, images, sensor data, telecommunications and so on. It also utilizes many mathematical theories such as approximation theory, analysis and wavelets. This dissertation is divided into two chapters: Modified Pal´ Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation. In the first chapter, we introduce a new interpolation process, the modified Pal interpolation, based on papers by P ´ al, J ´ oo´ and Szabo, and we establish the existence and …

Partially Integrable Pt-Symmetric Hierarchies Of Some Canonical Nonlinear Partial Differential Equations, Keri Pecora

Electronic Theses and Dissertations

In this dissertation, we generalize the work of Bender and co-workers to derive new partially-integrable hierarchies of various PT -symmetric, nonlinear partial differential equations. The possible integrable members are identified employing the Painlev´e Test, a necessary but not sufficient integrability condition, and are indexed by the integer n, corresponding to the negative of the order of the dominant pole in the singular part of the Painlev´e expansion for the solution. For the PT -symmetric Korteweg-de Vries (KdV) equation, as with some other hierarchies, the first or n = 1 equation fails the test, the n = 2 member corresponds to …

Sets Of Discontinuities Of Linearly Continuous Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

The class of linearly continuous functions f:Rⁿ-->R, that is, having continuous restrictions f|L to every straight line L, have been studied since the dawn of the twentieth century. In this paper we refine a description of the form that the sets D(f) of points of discontinuities of such functions can have. It has been proved by Slobodnik that D(f) must be a countable union of isometric copies of the graphs of Lipschitz functions h:K-->R, where K is a compact nowhere dense subset of R^n-1. Since the class Dⁿ of all …

Convex Cones Of Generalized Positive Rational Functions And Nevanlinna-Pick Interpolation, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

Scalar rational functions with a non-negative real part on the right half plane, called positive, are classical in the study of electrical networks, dissipative systems, Nevanlinna-Pick interpolation and other areas. We here study generalized positive functions, i.e with a non-negative real part on the imaginary axis. These functions form a Convex Invertible Cone, cic in short, and we explore two partitionings of this set: (i) into (infinitely many non-invertible) convex cones of functions with prescribed poles and zeroes in the right half plane and (ii) each generalized positive function can be written as a sum of even and odd parts. …

Numerical Studies Of The Generalized L₁ Greedy Algorithm For Sparse Signals, Fangjun Arroyo, Edward Arroyo, Xiezhang Li, Jiehua Zhu

Mathematical Sciences: Faculty Publications

The generalized l₁ greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l₁-minimization and l₁ greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l₁ greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l₁ greedy algorithm is superior to the reweighted l₁-minimization and l₁ greedy algorithms …

Distance-Based Graph Invariants Of Trees And The Harary Index, Stephan G. Wagner, Hua Wang, Xiao-Dong Zhang

Mathematical Sciences: Faculty Publications

Introduced in 1947, the Wiener index W(T) = ∑{u,v}⊆V(T) d(u, v) is one of the most thoroughly studied chemical indices. The extremal structures (in particular, trees with various constraints) that maximize or minimize the Wiener index have been extensively investigated. The Harary index H(T) = ∑{u,v}⊆V(T) , introduced in 1993, can be considered as the 'reciprocal analogue' of the Wiener index. From recent studies, it is known that the extremal structures of the Harary index and the Wiener index coincide in many instances, i.e., the graphs that maximize the Wiener index minimize the Harary index and vice versa. In this …

Greedy Trees, Subtrees And Antichains, Eric Ould Dadah Andriantiana, Stephan G. Wagner, Hua Wang

Mathematical Sciences: Faculty Publications

Greedy trees are constructed from a given degree sequence by a simple greedy algorithm that assigns the highest degree to the root, the second-, third-, ... highest degrees to the root's neighbors, and so on.

They have been shown to maximize or minimize a number of different graph invariants among trees with a given degree sequence. In particular, the total number of subtrees of a tree is maximized by the greedy tree. In this work, we show that in fact a much stronger statement holds true: greedy trees maximize the number of subtrees of any given order. This parallels recent …

Extremal Values Of Ratios: Distance Problems Vs. Subtree Problems In Trees, László A. Székely, Hua Wang

Mathematical Sciences: Faculty Publications

The authors discovered a dual behaviour of two tree indices, the Wiener index and the number of subtrees, for a number of extremal problems [Discrete Appl. Math. 155 (3) 2006, 374-385; Adv. Appl. Math. 34 (2005), 138-155]. Barefoot, Entringer and Székely [Discrete Appl. Math. 80 (1997), 37-56] determined extremal values of σT(w)/σT(u), σT(w)/σT(v), σ(T)/σT(v), and σ(T)/σT(w), where T is a tree on n vertices, v is in the centroid of …

The Gordon Game, Anthony Frenk

EWU Masters Thesis Collection

In 1992, about 30 years after Gordon introduced group sequencings to construct row-complete Latin squares, John Isbell introduced the idea of competitive sequencing, the Gordon Game. Isbell investigated the Gordon Game and found solutions for groups of small order. The purpose of this thesis is to analyze the Gordon Game and develop a brute force method of determining solutions to the game for all groups of order 12 (up to isomorphism) as well as for abelian groups of order less than 20. The method used will be a depth first search program written in MATLAB. Consequently, group representation using matrices …

Essays On Rethinking African Development: Contextual And Methodological Advances, Olumayokun Soremekun

2013

This research study sets out to provide analytical answers to the questions of African development and inequality. We examine various aspects of development from the issue of inequality among African countries to unravelling the synergies among the MDG goals and finally to investigating the progress if any that African countries have made towards attaining the MDG goals.

This research is broken down into three main studies: measuring inequality of opportunity, examining the synergies between the Millennium development goals at a particular point in time and lastly assessing the progress that has been made towards attaining the MDG goals in Africa. …

Effects Of Discrete Time Delays And Parameters Variation On Dynamical Systems, Ibrahim Oumar Diakite

Mathematics Dissertations - Archive

To understand the effects of discrete time delays and of parameters variation on certain biological system models, we first consider a Delay Differential Equation model of human immunodeficiency virus (HIV). We investigate the effects of the discrete time on the virulence of the HIV strain, and present sufficient and necessary condition for the virulence of the pathogen to change as the time delay changes. We also consider the same delay differential model for HIV infection, and we investigate analytically and numerically the stability of the endemically infected equilibrium. Our analysis shows that certain key parameters, such as the rate of …