Analysis Commons^™

Anticipated Backward Stochastic Differential Equations With Continuous Coefficients, Zhe Yang, Robert J Elliott

Communications on Stochastic Analysis

No abstract provided.

Asymptotic And Geometric Properties Of Compactly Perturbed Wiener Process And Self-Intersection Local Time, Andrey A Dorogovtsev, Olga L Izyumtseva

Communications on Stochastic Analysis

No abstract provided.

Nonparametric Regression With Non-Gaussian Long Memory, Mariela Sued, Soledad Torres, Ciprian A. Tudor

Communications on Stochastic Analysis

No abstract provided.

A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam

Applications and Applied Mathematics: An International Journal (AAM)

First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization.

Boundary Value Problems For Discrete Fractional Equations, Pushp R. Awasthi

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation we develop certain aspects of the theory of discrete fractional calculus. The author begins with an introduction to the discrete delta calculus together with the fractional delta calculus which is used throughout this dissertation. The Cauchy function, the Green's function and some of their important properties for a fractional boundary value problem for are developed. This dissertation is comprised of four chapters. In the first chapter we introduce the delta fractional calculus. In the second chapter we give some preliminary definitions, properties and theorems for the fractional delta calculus and derive the appropriate Green's function and give …

Analyzing And Solving Non-Linear Stochastic Dynamic Models On Non-Periodic Discrete Time Domains, Gang Cheng

Masters Theses & Specialist Projects

Stochastic dynamic programming is a recursive method for solving sequential or multistage decision problems. It helps economists and mathematicians construct and solve a huge variety of sequential decision making problems in stochastic cases. Research on stochastic dynamic programming is important and meaningful because stochastic dynamic programming reflects the behavior of the decision maker without risk aversion; i.e., decision making under uncertainty. In the solution process, it is extremely difficult to represent the existing or future state precisely since uncertainty is a state of having limited knowledge. Indeed, compared to the deterministic case, which is decision making under certainty, the stochastic …

Analysis Of Time-Dependent Integrodifference Population Models, Taylor J. Mcadam

HMC Senior Theses

The population dynamics of species with separate growth and dispersal stages can be described by a discrete-time, continuous-space integrodifference equation relating the population density at one time step to an integral expression involving the density at the previous time step. Prior research on this model has assumed that the equation governing the population dynamics remains fixed over time, however real environments are constantly in flux. We show that for time-varying models, there is a value Λ that can be computed to determine a sufficient condition for population survival. We also develop a framework for analyzing persistence of a population for …

Applied Analysis Of Ionic Polymer Metal-Composite Actuators, Siul Ruiz, Benjamin Mead, Woosoon Yim

College of Engineering: Graduate Celebration Programs

• IPMC is a type of smart material called an electroactive polymer
• Consists of an ionic polymer such as Nafion or Flemion and a conducive metal such as platinum or gold
• COMSOL multi-physics simulations accurately model the experimental displacement results
• Optimization performed using the multi-physics model to find the maximum deflection, force, and twisting
• Using the closed loop control system accurate IPMC tip location can be achieved
• This control system has been extended to function using a computer mouse as an input

Image Processing Algorithms For Improving Planetary Exploration And Understanding, Ali Pouryazdanpanah

College of Engineering: Graduate Celebration Programs

• To design a fully automated tool-set that allows to detect and extract the sky region in planetary images.

• To develop the new method for rock segmentation in planetary stereo images.
• To develop the new method for shadow detection in planetary images

Regularity For Solutions To Parabolic Systems And Nonlocal Minimization Problems, Joe Geisbauer

Department of Mathematics: Dissertations, Theses, and Student Research

The goal of this dissertation is to contribute to both the nonlocal and local settings of regularity within the calculus of variations. We provide analogues of higher differentiability results in the context of Besov spaces for minimizers of nonlocal functionals. We also establish the Holder continuity of solutions to a system of parabolic partial differential equations.

Advisor: Mikil Foss

Moments For The Parabolic Anderson Model: On A Result By Hu And Nualart, Daniel Conus

Communications on Stochastic Analysis

No abstract provided.

Differentiability Of Stochastic Reflecting Flow With Respect To Starting Point, Andrey Pilipenko

Communications on Stochastic Analysis

No abstract provided.

Proving Existence Results In Martingale Theory Using A Subsequence Principle, Alexander Sokol

Communications on Stochastic Analysis

No abstract provided.

Parallel Mutation-Reproduction Processes In Random Environments, Ying Wang

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For The Shell Model Of Turbulence Perturbed By Lévy Noise, Utpal Manna, Manil T Mohan

Communications on Stochastic Analysis

No abstract provided.

Characterization Theorems For Differential Operators On White Noise Spaces, Abdessatar Barhoumi, Alberto Lanconelli

Communications on Stochastic Analysis

No abstract provided.

Stochastic Burgers Equation With Polynomial Nonlinearity Driven By Lévy Process, Erika Hausenblas, Ankik Kumar Giri

Communications on Stochastic Analysis

No abstract provided.

Two-Dimensional Magneto-Hydrodynamic System With Jump Processes: Well Posedness And Invariant Measures, Utpal Manna, Manil T Mohan

Communications on Stochastic Analysis

No abstract provided.

White Noise Representation Of Gaussian Random Fields, Zachary Gelbaum

Communications on Stochastic Analysis

No abstract provided.

On The Norm Closure Problem For Complex Symmetric Operators, Stephan Ramon Garcia, Daniel E. Poore '11

Pomona Faculty Publications and Research

We prove that the set of all complex symmetric operators on a separable, infinite-dimensional Hilbert space is not norm closed.

On A Paley-Wiener Theorem For The Zs-Akns Scattering Transform, Ryan D. Walker

Theses and Dissertations--Mathematics

In this thesis, we establish an analog of the Paley-Wiener Theorem for the ZS-AKNS scattering transform on a set of real potentials. We also demonstrate one application of our techniques to the study of an inverse spectral problem for a half-line Miura potential Schroedinger equation.

On The Persistence Properties Of The Cross-Coupled Camassa-Holm System, David Henry, Darryl Holm, Rossen Ivanov

Articles

In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the persistence of compact support for the momenta. For solutions of the system itself, the answer is more convoluted, and we determine when the compactness of the support is lost, replaced instead by an exponential decay rate.

Particle Trajectories In Extreme Stokes Waves Over Inifinte Depth, Tony Lyons

Articles

We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of the particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid being zero there.

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 …

Regularity And Uniqueness Of Some Geometric Heat Flows And It's Applications, Tao Huang

Theses and Dissertations--Mathematics

This manuscript demonstrates the regularity and uniqueness of some geometric heat flows with critical nonlinearity.

First, under the assumption of smallness of renormalized energy, several issues of the regularity and uniqueness of heat flow of harmonic maps into a unit sphere or a compact Riemannian homogeneous manifold without boundary are established.

For a class of heat flow of harmonic maps to any compact Riemannian manifold without boundary, satisfying the Serrin's condition,

the regularity and uniqueness is also established.

As an application, the hydrodynamic flow of nematic liquid crystals in Serrin's class is proved to be regular and unique.

The natural …

On Well-Posedness, Stability, And Bifurcation For The Axisymmetric Surface Diffusion Flow, Jeremy Lecrone, Gieri Simonett

Department of Math & Statistics Faculty Publications

We study the axisymmetric surface diffusion (ASD) flow, a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2+α)-little-Holder regular surfaces of revolution embedded in R3 and satisfying periodic boundary conditions. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability, and bifurcation behavior, with the radius acting as a bifurcation parameter.

Special Type Of Subset Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we construct special subset topological spaces using subsets from semigroups or groups or rings or semirings. Such study is carried out for the first time and it is both interesting and innovative. Suppose P is a semigroup and S is the collection of all subsets of P together with the empty set, then S can be given three types of topologies and all the three related topological spaces are distinct and results in more types of topological spaces. When the semigroup is finite, S gives more types of finite topological spaces. The same is true in case …

Subset Non Associative Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of non associative topological space is new and innovative. In general topological spaces are defined as union and intersection of subsets of a set X. In this book authors for the first time define non associative topological spaces using subsets of groupoids or subsets of loops or subsets of groupoid rings or subsets of loop rings. This study leads to several interesting results in this direction.

Over hundred problems on non associative topological spaces using of subsets of loops or groupoids is suggested at the end of chapter two. Also conditions for these non associative subset topological spaces …

Subset Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the new notion of constructing non associative algebraic structures using subsets of a groupoid. Thus subset groupoids are constructed using groupoids or loops. Even if we use subsets of loops still the algebraic structure we get with it is only a groupoid. However we can get a proper subset of it to be a subset loop which will be isomorphic with the loop which was used in the construction of the subset groupoid. To the best of the authors’ knowledge this is the first time non associative algebraic structures are constructed using subsets. We get …

Variance On Topics Of Plane Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book contains 21 papers of plane geometry. It deals with various topics, such as: quasi-isogonal cevians, nedians, polar of a point with respect to a circle, anti-bisector, aalsonti-symmedian, anti-height and their isogonal. A nedian is a line segment that has its origin in a triangle’s vertex and divides the opposite side in Q equal segments. The papers also study distances between remarkable points in the 2D-geometry, the circumscribed octagon and the inscribable octagon, the circles adjointly ex-inscribed associated to a triangle, and several classical results such as: Carnot circles, Euler’s line, Desargues theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s theorem, …