Mathematics Commons^™

Duffing-Van Der Pol Type Oscillator, Guangyue Gao

Theses and Dissertations - UTB/UTPA

The nonlinear Duffing-van der Pol oscillator system is studied by means of the Lie symmetry reduction method and the Preller-Singer method. With the particular case of coefficients, this system has physical relevance as a simple model in certain flow-induced structural vibration problems. Under certain parametric conditions, we are concerned with the first integrals of the Duffing-van der Pol oscillator system. After making a series of variable transformations, we apply the Preller-Singer method and the Lie symmetry reduction method to obtain the first integrals of the simplified equations without complicated calculations.

Modeling Instabilities Of Electrically Driven Jets With Finite Conductivity Under Constant Or Variable Applied Field, Saulo I. Orizaga

Theses and Dissertations - UTB/UTPA

We investigate the problem of spatial (S), combined spatial and temporal (CST), and non-linear temporal instability (NLT) of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton‟s Method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One …

Post-Processing Techniques And Wavelet Applications For Hammerstein Integral Equations, Khomsan Neamprem

Mathematics & Statistics Theses & Dissertations

This dissertation is focused on the varieties of numerical solutions of nonlinear Hammerstein integral equations. In the first part of this dissertation, several acceleration techniques for post-processed solutions of the Hammerstein equation are discussed. The post-processing techniques are implemented based on interpolation and extrapolation. In this connection, we generalize the results in [29] and [28] to nonlinear integral equations of the Hammerstein type. Post-processed collocation solutions are shown to exhibit better accuracy. Moreover, an extrapolation technique for the Galerkin solution of Hammerstein equation is also obtained. This result appears new even in the setting of the linear Fredholm equation.

In …

Semi-Parametric Likelihood Functions For Bivariate Survival Data, S. H. Sathish Indika

Mathematics & Statistics Theses & Dissertations

Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of …

Gender Bias In Education In West Bengal., Chayanika Mitra Dr.

Doctoral Theses

There exists a vast literature with evidences of gender discrimination against females in allocation of goods and services at regional/national level in India. Evidence of gender bias on Indian data include, among many others, studies by Subramanian and Deaton (1991), Azam and Kingdon (2013), Kingdon (2005), Drèze and Kingdon (2001), Zimmerman (2012) and Lancaster, Maitra, and Ray (2008). India has a history of preference for sons over daughters for cultural and economic reasons. This is manifested through high birth sex ratios, which is possibly a result of female foeticide. The child sex ratio is within the normal natural range in …

LP Estimates For The Maximal Functions, Alexander M. Stokolos

Mathematical Sciences: Faculty Presentations (1991-2022)

This talk was given during the Jozef Marcinkiewicz Centenary Conference.

Hopf Differentials And Smoothing Sobolev Homeomorphisms, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space W^1,2 and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.

Topology Of Cyclo-Octane Energy Landscape, Evangelos A. Coutsias, Shawn Martin, Aidan Thompson, Jean-Paul Watson

Branch Mathematics and Statistics Faculty and Staff Publications

Understanding energy landscapes is a major challenge in chemistry and biology. Although a wide variety of methods have been invented and applied to this problem, very little is understood about the actual mathematical structures underlying such landscapes. Perhaps the most general assumption is the idea that energy landscapes are low-dimensional manifolds embedded in high-dimensional Euclidean space. While this is a very mild assumption, we have discovered an example of an energy landscape which is nonmanifold, demonstrating previously unknown mathematical complexity. The example occurs in the energy landscape of cyclo-octane, which was found to have the structure of a reducible algebraic …

A Characteristic Free Tilting Bundle For Grassmannians, Ragar-Olaf Buchweitz, Graham J. Leuschke, Michel Van Den Bergh

Mathematics - All Scholarship

We construct a characteristic free tilting bundle on Grassmannians.

Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa

MPP Published Research

In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new …

The Minimum Rank, Inverse Inertia, And Inverse Eigenvalue Problems For Graphs, Mark Condie Kempton

Theses and Dissertations

For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.

Approximation Of Stationary Statistical Properties Of Dissipative Dynamical Systems: Time Discretization, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We consider temporal approximation of stationary statistical properties of dissipative infinite-dimensional dynamical systems. We demonstrate that stationary statistical properties of the time discrete approximations, i.e., numerical scheme, converge to those of the underlying continuous dissipative infinite-dimensional dynamical system under three very natural assumptions as the time step approaches zero. the three conditions that are sufficient for the convergence of the stationary statistical properties are: (1) uniform dissipativity of the scheme in the sense that the union of the global attractors for the numerical approximations is pre-compact in the phase space; (2) convergence of the solutions of the numerical scheme to …

Wild Low-Dimensional Topology And Dynamics, Mark H. Meilstrup

Theses and Dissertations

In this dissertation we discuss various results for spaces that are wild, i.e. not locally simply connected. We first discuss periodic properties of maps from a given space to itself, similar to Sharkovskii's Theorem for interval maps. We study many non-locally connected spaces and show that some have periodic structure either identical or related to Sharkovskii's result, while others have essentially no restrictions on the periodic structure. We next consider embeddings of solenoids together with their complements in three space. We differentiate solenoid complements via both algebraic and geometric means, and show that every solenoid has an unknotted embedding …

Extended Second Welfare Theorem For Nonconvex Economies With Infinite Commodities And Public Goods, Aychiluhim Habte, Boris S. Mordukhovich

Mathematics Research Reports

This paper is devoted to the study of nonconvex models of welfare economics with public goods and infinite-dimensional commodity spaces. Our main attention is paid to new extensions of the fundamental second welfare theorem to the models under consideration. Based on advanced tools of variational analysis and generalized differentiation, we establish appropriate approximate and exact versions of the extended second welfare theorem for Pareto, weak Pareto, and strong Pareto optimal allocations in both marginal price and decentralized price forms.

Weakly Infinite Dimensional Subsets Of RN, Liljana Babinkostova, Marion Scheepers

Mathematics Faculty Publications and Presentations

The Continuum Hypothesis implies an Erdö-Sierpiński like duality between the ideal of first category subsets of ℝ^ℕ, and the ideal of countable dimensional subsets of ℝ^ℕ. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of ℝ^ℕ with any compactly countable dimensional subset of ℝ^ℕ has first category.

The Yao Graph Y6 Is A Spanner, Joseph O'Rourke

Computer Science: Faculty Publications

We prove that Y₆ is a spanner. Y₆ is the Yao graph on a set of planar points, which has an edge from each point x to a closest point y within each of the six angular cones of 60^◦ surrounding x .

Fast Placement And Floorplanning Methods In Modern Reconfigurable Fpgas., Pritha Baneerjee Dr.

Doctoral Theses

FPGA Field-programmable gate-arrays (FPGA) are programmable hardware platforms with pre-fabricated logic and interconnects, which are electrically programmed by the user to realize a variety of circuits frequently required in a wide range of applications. Unlike application-specific integrated-circuits (ASICs), where realization of a circuit design takes several man-hours and enormous effort, the pre-fabricated logic and interconnects can be quickly programmed according to the design specification and made functional. Thus, in contrast to the ASICs, FPGAs can be customized and reconfigured depending on the need of the user. A basic FPGA chip consists of a set of configurable logic blocks (CLB) and …

An Anticipative Stochastic Calculus Approach To Pricing In Markets Driven By Lévy Process, Bernt Øksendal, Agnès Sulem

Communications on Stochastic Analysis

No abstract provided.

Preface

Communications on Stochastic Analysis

No abstract provided.

Persistence Of Invertibility In The Wiener Space, A S Üstünel

Communications on Stochastic Analysis

No abstract provided.