Mathematics Commons^™

Convergence Analysis Of A Proximal Point Algorithm For Minimizing Differences Of Functions, Thai An Nguyen, Mau Nam Nguyen

Mathematics and Statistics Faculty Publications and Presentations

Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A significant progress to go beyond convexity was made by considering the class of functions representable as differences of convex functions. In this paper, we introduce a generalized proximal point algorithm to minimize the difference of a nonconvex function and a convex function. We also study convergence results of this algorithm under the main assumption that the objective function satisfies the Kurdyka– ᴌojasiewicz property.

Compactness Of Isoresonant Potentials, Robert G. Wolf

Theses and Dissertations--Mathematics

Bruning considered sets of isospectral Schrodinger operators with smooth real potentials on a compact manifold of dimension three. He showed the set of potentials associated to an isospectral set is compact in the topology of smooth functions by relating the spectrum to the trace of the heat semi-group. Similarly, we can consider the resonances of Schrodinger operators with real valued potentials on Euclidean space of whose support lies inside a ball of fixed radius that generate the same resonances as some fixed Schrodinger operator, an ``isoresonant" set of potentials. This isoresonant set of potentials is also compact in the topology …

Approximation Of Solutions To The Mixed Dirichlet-Neumann Boundary Value Problem On Lipschitz Domains, Morgan F. Schreffler

Theses and Dissertations--Mathematics

We show that solutions to the mixed problem on a Lipschitz domain Ω can be approximated in the Sobolev space H¹(Ω) by solutions to a family of related mixed Dirichlet-Robin boundary value problems which converge in H¹(Ω), and we give a rate of convergence. Further, we propose a method of solving the related problem using layer potentials.

The Qq–Bit (Ii): Functional Central Limits And Monotone Representation Of The Azema Martingale, Luigi Accardi, Yun-Gang Lu

Communications on Stochastic Analysis

No abstract provided.

The Subcritical Phase For A Homopolymer Model, Iddo Ben-Ari, Hugo Panzo

Communications on Stochastic Analysis

No abstract provided.

Near-Martingale Property Of Anticipating Stochastic Integration, C R. Hwang, Hui-Hsiung Kuo, Kimiaki Saitô, Jiayu Zhai

Communications on Stochastic Analysis

No abstract provided.

An Option Pricing Model With Memory, Flavia Sancier, Salah Mohammed

Communications on Stochastic Analysis

No abstract provided.

Series Solutions Of Polarized Gowdy Universes, Doniray Brusaferro

Theses and Dissertations

Einstein's field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T³ model, and provide an explicit solution to Einstein's equations.

Curiozităţi Ale Funcţiilor Supermatematice, Florentin Smarandache, Mircea Eugen Selariu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Random Variational-Like Inclusion And Random Proximal Operator Equation For Random Fuzzy Mappings In Banach Spaces, Rais Ahmad, Iqbal Ahmad, Mijanur Rahaman

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce and study a random variational-like inclusion and its corresponding random proximal operator equation for random fuzzy mappings. It is established that the random variational-like inclusion problem for random fuzzy mappings is equivalent to a random fixed point problem. We also establish a relationship between random variational-like inclusion and random proximal operator equation for random fuzzy mappings. This equivalence is used to define an iterative algorithm for solving random proximal operator equation for random fuzzy mappings. Through an example, we show that the random Wardrop equilibrium problem is a special case of the random variational-like inclusion …

On The Convergence Of Two-Dimensional Fuzzy Volterra-Fredholm Integral Equations By Using Picard Method, Ali Ebadian, Foroozan Farahrooz, Amirahmad Khajehnasiri

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we prove convergence of the method of successive approximations used to approximate the solution of nonlinear two-dimensional Volterra-Fredholm integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration. Also we present an iterative procedure to solve such equations. Finally, the method is illustrated by solving some examples.

Weighted Inequalities For Riemann-Stieltjes Integrals, Hüseyin Budak, Mehmet Z. Sarikaya

Applications and Applied Mathematics: An International Journal (AAM)

In this paper first we define a new functional which is a weighted version of the functional defined by Dragomir and Fedotov. Then, some inequalities involving this functional are obtained. Finally, we apply this result to establish new bounds for weighted Chebysev functional.

On The Slow Growth And Approximation Of Entire Function Solutions Of Second-Order Elliptic Partial Differential Equations On Caratheodory Domains, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we consider the regular, real-valued solutions of the second-order elliptic partial differential equation. The characterization of generalized growth parameters for entire function solutions for slow growth in terms of approximation errors on more generalized domains, i.e., Caratheodory domains, has been obtained. Moreover, we studied some inequalities concerning the growth parameters of entire function solutions of above equation for slow growth which have not been studied so far.

Heat Source Thermoelastic Problem In A Hollow Elliptic Cylinder Under Time-Reversal Principle, Pravin Bhad, Vinod Varghese, Lalsingh Khalsa

Applications and Applied Mathematics: An International Journal (AAM)

The article investigates the time-reversal thermoelasticity of a hollow elliptical cylinder for determining the temperature distribution and its associated thermal stresses at a certain point using integral transform techniques by unifying classical orthogonal polynomials as the kernel. Furthermore, by considering a circle as a special kind of ellipse, it is seen that the temperature distribution and the comparative study of a circular cylinder can be derived as a special case from the present mathematical solution. The numerical results obtained are accurate enough for practical purposes.

Iterative Solution Of Fractional Diffusion Equation Modelling Anomalous Diffusion, A. Elsaid, S. Shamseldeen, S. Madkour

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we study the fractional diffusion equation with spatial Riesz fractional derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution is obtained based on properties of Riesz fractional derivative operator and utilizing the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameter on the solution behavior.

Solution Of A Cauchy Singular Fractional Integro-Differential Equation In Bernstein Polynomial Basis, Avipsita Chatterjee, Uma Basu, B. N. Mandal

Applications and Applied Mathematics: An International Journal (AAM)

This article proposes a simple method to obtain approximate numerical solution of a singular fractional order integro-differential equation with Cauchy kernel by using Bernstein polynomials as basis. The fractional derivative is described in Caputo sense. The properties of Bernstein polynomials are used to reduce the fractional order integro-differential equation to the solution of algebraic equations. The numerical results obtained by the present method compares favorably with those obtained earlier for the first order integro-differential equation. Also the convergence of the method is established rigorously.

Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani

Applications and Applied Mathematics: An International Journal (AAM)

In this article, modified (G'/G )-expansion method is presented to establish the exact complex solutions of the time fractional Gross-Pitaevskii (GP) equation in the sense of the conformable fractional derivative. This method is an effective method in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The present approach has the potential to be applied to other nonlinear fractional differential equations. Based on two transformations, fractional GP equation can be converted into nonlinear ordinary differential equation of integer orders. In the end, we will discuss the solutions of the fractional GP equation with external potentials.

On The Exchange Property For The Mehler-Fock Transform, Abhishek Singh

Applications and Applied Mathematics: An International Journal (AAM)

The theory of Schwartz Distributions opened up a new area of mathematical research, which in turn has provided an impetus in the development of a number of mathematical disciplines, such as ordinary and partial differential equations, operational calculus, transformation theory and functional analysis. The integral transforms and generalized functions have also shown equivalent association of Boehmians and the integral transforms. The theory of Boehmians, which is a generalization of Schwartz distributions are discussed in this paper. Further, exchange property is defined to construct Mehler-Fock transform of tempered Boehmians. We investigate exchange property for the Mehler-Fock transform by using the theory …

Introduction To Mathematical Analysis I - 2nd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

This edition has been superseded by Introduction to Mathematical Analysis I, Third Edition.

Video lectures explaining problem solving strategies are available.

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, …

Brownian Manifolds, Negative Type And Geo-Temporal Covariances, N H Bingham, Aleksandar Mijatović, Tasmin L Symons

Communications on Stochastic Analysis

No abstract provided.

Generalized Commutative Association Schemes, Hypergroups, And Positive Product Formulas, Michael Voit

Communications on Stochastic Analysis

No abstract provided.

On The Kolmogorov-Wiener-Masani Spectrum Of A Multi-Mode Weakly Stationary Quantum Process, K R Parthasarathy, Ritabrata Sengupta

Communications on Stochastic Analysis

No abstract provided.

Convolution Semigroups Of Probability Measures On Gelfand Pairs, Revisited, David Applebaum

Communications on Stochastic Analysis

No abstract provided.

Positive Definiteness On Spheres And Hyperbolic Spaces, Walter R Bloom, N J Wildberger

Communications on Stochastic Analysis

No abstract provided.

Conditions For Stationarity And Ergodicity Of Two-Factor Affine Diffusions, Beáta Bolyog, Gyula Pap

Communications on Stochastic Analysis

No abstract provided.

Preface

Communications on Stochastic Analysis

No abstract provided.

Semimartingales In Locally Compact Abelian Groups And Their Characteristic Triples, M S Bingham

Communications on Stochastic Analysis

No abstract provided.

Some Considerations On The Structure Of Transition Densities Of Symmetric Lévy Processes, Lewis J Bray, Neils Jacob

Communications on Stochastic Analysis

No abstract provided.

Strong Stationary Times And The Fundamental Matrix For Recurrent Markov Chains, P J Fitzsimmons

Communications on Stochastic Analysis

No abstract provided.

Bimodules And Hypergroups Associated With Actions Of A Pair Of Groups, Satoshi Kawakami, Tatsuya Tsurii, Shigeru Yamagami

Communications on Stochastic Analysis

No abstract provided.