Mathematics Commons^™

Spectrophotometric Characterization Of The Complexation Of Gossypol Acetic Acid With Cobalt Ion, Ugilay Abdurahmanova, Habibjon Kushiev, Maral Askarova, Dilafruz Allanazarova

Karakalpak Scientific Journal

The authors of the article suggest simple and express method of spectrophotometric determination of cobalt with the help of derivatives of gossypol. Optimal conditions of determining cobalt are found. Under optimal conditions there was created a graded graph, which is more linear in the range for cobalt concentration of 10.0 – 50.0 microgram/25 ml, contents and constants of cobalt complex with gossypol vinegar acid.

An A Posteriori Error Analysis Of Stationary Incompressible Magnetohydrodynamics, Ari E. Rappaport

Mathematics & Statistics ETDs

Adjoint based a posteriori error analysis is a technique to produce exact error repre- sentations for quantities of interests that are functions of the solution of systems of partial differential equations (PDE). The tools used in the analysis consist of duality arguments and compatible residuals. In this thesis we apply a posteriori error anal- ysis to the magnetohydrodynamics (MHD) equations . MHD provides a continuum level description of conducting fluids in the presence of electromagnetic fields. The MHD system is therefore a multi-physics system, capturing both fluid and electro- magnetic effects. Mathematically, The equations of MHD are highly nonlinear and …

A Differential-Algebraic Criterion For Obtaining A Small Maximal Cohen-Macaulay Module, Hans Schoutens

Publications and Research

We show how for a three-dimensional complete local ring in positive characteristic, the existence of an F-invariant, differentiable derivation implies Hochster’s small MCM conjecture. As an application we show that any three-dimensional pseudo-graded ring in positive characteristic satisfies Hochster’s small MCM conjecture.

Discrete-Time Control With Non-Constant Discount Factor, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau

Mathematics Faculty Research Publications

This paper deals with discrete-time Markov decision processes (MDPs) with Borel state and action spaces, and total expected discounted cost optimality criterion. We assume that the discount factor is not constant: it may depend on the state and action; moreover, it can even take the extreme values zero or one. We propose sufficient conditions on the data of the model ensuring the existence of optimal control policies and allowing the characterization of the optimal value function as a solution to the dynamic programming equation. As a particular case of these MDPs with varying discount factor, we study MDPs with stopping, …

Superposed Ornstein-Uhlenbeck Processes, Julius Esunge, Auguste Muhau

Journal of Stochastic Analysis

No abstract provided.

Bipartite Dot Product Graphs, Sean Bailey, David E. Brown

Mathematics and Statistics Faculty Publications

Given a bipartite graph G = (X, Y, E), the bipartite dot product representation of G is a function f : X ∪Y → ℝ^k and a positive threshold t such that for any x ∈ X and y ∈ Y , xy ∈ E if and only if f(x) · f(y) ≥ t. The minimum k such that a bipartite dot product representation exists for G is the bipartite dot product dimension of G, denoted bdp(G). We will show that such representations exist for all bipartite graphs as well as give an upper bound for the bipartite dot …

Studies On Polynomial Rings Through Locally Nilpotient Derivations., Nikhilesh Dasgupta Dr.

Doctoral Theses

No abstract provided.

What Is The Derivative Of Music?, Thad B. Welch, Cameron H. G. Wright, Michael G. Morrow

Electrical and Computer Engineering Faculty Publications and Presentations

In our continuing effort to prove to students that Signals & Systems is not just another mathematics course taught by the ECE Department, we ask the question, “What is the Derivative of Music?”

The first-order difference (or first-difference) is an incredibly simple algorithm that very accurately approximates the numeric derivative operator, especially for oversampled signals. Its inverse also accurately approximates the numeric integration operator, but not without numeric difficulty.

Given a real-time demonstration using winDSK8, we can now show students that these mathematical operators provide powerful signal processing filtering tools for real-world signals.

During this ASEE session, we will include …

Fuzzy Synergetic Control Nonlinear Dynamic Objects, Isomiddin Sidikov, Noilakhon Yakubova, Komil Usmanov, Saparbay Kazakhbayev

Karakalpak Scientific Journal

The article deals with the synthesis of effective algorithms for controlling a chemical reactor and developed a fuzzy synergistic controller for a class of indefinite nonlinear dynamic systems. A synergetic control scheme is proposed for solving the control problem for nonlinear systems. Non-linear systems with configurations and parameters that change over time require a completely non-linear model and adaptive control scheme for a practical operating environment. The synthesis of control laws is performed by the method of analytical design of aggregated controllers (ACAR). Fuzzy logic systems are used to evaluate the unknown nonlinear behavior of the system, and a new …

Using The Kellogg-Tsan Solution Decomposition In Numericalmethods For Singularly Perturbed Convection-Diffusion Problems, Relja Vulanović, Thái Ahn Nhan

Mathematics and Computer Science

The linear one-dimensional singularly perturbed convection-diffusion problem is solved numerically by a second-order method that is uniform in the perturbation parameter 𝜀. The method uses the Kellogg-Tsan decomposition of the continuous solution. This increases the accuracy of the numerical results and simplifies the proof of their 𝜀-uniformity

Von Neumann's Minimax Theorem For Continuous Quantum Games, Luigi Accardi, Andreas Boukas

Journal of Stochastic Analysis

No abstract provided.

On The Extension Of Positive Definite Kernels To Topological Algebras, Daniel Alpay, Ismael L. Paiva

Mathematics, Physics, and Computer Science Faculty Articles and Research

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.

Combining Transformation Of Graphs With Solutions To Absolute Value Inequalities, Ryan D. Fox

Colorado Mathematics Teacher

I present how transformations can be applied to support students’ solving linear inequalities involving absolute value. In particular, the horizontal dilations/compressions and translations of graphical representations of distances from zero along a number line are important tools to emphasize a visual representation of the solutions to absolute value inequalities.

Burnside Chromatic Polynomials Of Group-Invariant Graphs, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We introduce the Burnside chromatic polynomial of a graph that is invariant under a group action. This is a generalization of the Q-chromatic function Zaslavsky introduced for gain graphs. Given a group G acting on a graph G and a G-set X, a proper X-coloring is a function with no monochromatic edge orbit. The set of proper colorings is a G-set which induces a polynomial function from the Burnside ring of G to itself. In this paper, we study many properties of the Burnside chromatic polynomial, answering some questions of Zaslavsky

The Structure Of Generalized Bi-Algebras And Weakening Relation Algebras, Nikolaos Galatos, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Articles and Research

Generalized bunched implication algebras (GBI-algebras) are defined as residuated lattices with a Heyting implication, and are positioned between Boolean algebras with operators and lattices with operators. We characterize congruences on GBI-algebras by filters that are closed under Gumm–Ursini terms, and for involutive GBI-algebras these terms simplify to a dual version of the congruence term for relation algebras together with two more terms. We prove that representable weakening relation algebras form a variety of cyclic involutive GBI-algebras, denoted by RWkRA, containing the variety of representable relation algebras. We describe a double-division conucleus construction on residuated lattices and on (cyclic involutive) GBI-algebras …

Vanishing Porosity Limit Of The Coupled Stokes-Brinkman System, Mingwen Fei, Dongjuan Niu, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We investigate the small porosity asymptotic behavior of the coupled Stokes-Brinkman system in the presence of a curved interface between the Stokes region and the Brinkman region. in particular, we derive a set of approximate solutions, validated via rigorous analysis, to the coupled Stokes-Brinkman system. of particular interest is that the approximate solution satisfies a generalized Beavers-Joseph-Saffman-Jones interface condition (1.9) with the constant of proportionality independent of the curvature of the interface.

Multiparty Non-Interactive Key Exchange And More From Isogenies On Elliptic Curves, Dan Boneh, Darren B. Glass, Daniel Krashen, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi, Mark Zhandry

Math Faculty Publications

We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n ≥ 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be difficult. We do not obtain a working protocol because of a missing step that is currently an open mathematical problem. What we need to complete our protocol is an efficient algorithm that takes as input an abelian variety presented as a product of isogenous elliptic curves, and outputs an isomorphism invariant of the abelian variety.

Our framework builds a cryptographic …

Taylor Expansions And Castell Estimates For Solutions Of Stochastic Differential Equations Driven By Rough Paths, Qi Feng, Xuejing Zhang

Journal of Stochastic Analysis

No abstract provided.

Origins Of Atrophy In Parkinson Linked To Early Onset And Local Transcription Patterns, Pedro D. Maia, Sneha Pandya, Benjamin Freeze, Justin Torok, Ajay Gupta, Yashar Zeighami, Ashish Raj

Mathematics Faculty Publications - Archive

There is enormous clinical value in inferring the brain regions initially atrophied in Parkinson disease for individual patients and understanding its relationship with clinical and genetic risk factors. The aim of this study is to leverage a new seed-inference algorithm demonstrated for Alzheimer’s disease to the Parkinsonian context and to cluster patients in meaningful subgroups based on these incipient atrophy patterns. Instead of testing brain regions separately as the likely initiation site for each patient, we solve an L1-penalized optimization problem that can return a more predictive heterogeneous, multi-locus seed patterns. A cluster analysis of the individual seed patterns reveals …

Solvability Of Boundary Value Problem With A Conormal Derivative For An Equation Of Mixed Elliptic-Parabolic Type, Marguba H. Akbarova, Surayyo H. Akbarova

Scientific Bulletin. Physical and Mathematical Research

This article is devoted to the formulation and study of a nonlocal boundary value problem with a conormal derivative for an equation of mixed elliptic-parabolic type. Here the existence and uniqueness of the solution of the problem is proved. Uniqueness of the solution is shown by the method of energy integrals, and existence of a solution is based on the theory of integral equations. Existence of a solution of a nonlocal boundary value problem is equivalently led to a solvability of a system of singular integral equations of normal type with zero index.