Analysis Commons^™

Construction Of The Paths Of Brownian Motions On Star Graphs Ii, Vadim Kostrykin, Jürgen Potthoff, Robert Schrader

Communications on Stochastic Analysis

No abstract provided.

Asymptotic Spectral Analysis Of A Distance K-Graph Of N-Fold Direct Product Of A Graph, Jun Kurihara

Communications on Stochastic Analysis

No abstract provided.

Exact Solutions Of The Generalized Benjamin Equation And (3 + 1)- Dimensional Gkp Equation By The Extended Tanh Method, N. Taghizadeh, M. Mirzazadeh, S. R. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the extended tanh method is used to construct exact solutions of the generalized Benjamin and (3 + 1)-dimensional gKP equation. This method is shown to be an efficient method for obtaining exact solutions of nonlinear partial differential equations. It can be applied to nonintegrable equations as well as to integrable ones.

Interactive Concept To Aid In Understanding Dimensional Analysis, Alicia Hicks

Symposium 2012

Many students struggle with learning how to utilize dimensional analysis. This confusion is due to not understanding the concept of dose per volume, leading to difficulty when starting the sequencing. This could be one of the contributing causes to medication errors in clinical practice. Does using models, such as Play-doh and pebbles, help students learn the concept of milligrams per milliliters when calculating dosages using dimensional analysis method? A series of pre- and post-tests are used to measure learning growth in each of the treatment groups. Three treatment groups were utilized: Control: one group had no intervention between the pre …

Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard

Articles

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.

Using Predictive Analytics To Detect Major Problems In Department Of Defense Acquisition Programs, Austin W. Dowling

Theses and Dissertations

This research provides program analysts and Department of Defense (DoD) leadership with an approach to identify problems in real-time for acquisition contracts. Specifically, we develop optimization algorithms to detect unusual changes in acquisition programs’ Earned Value data streams. The research is focused on three questions. First, can we predict the contractor provided estimate at complete (EAC)? Second, can we use those predictions to develop an algorithm to determine if a problem will occur in an acquisition program or subprogram? Lastly, can we provide the probability of a problem occurring within a given timeframe? We find three of our models establish …

A Women-Only Comparision Of The U.S. Air Force Fitness Test And The Marine Combat Fitness Test, Tarah D. Mitchell

Theses and Dissertations

In 2009, Captain Thomas Worden determined the Air Force Physical Fitness Test (AFPFT) poorly predicted combat capability for his 86 study participants. With only 5 of these 86 volunteers being women, this limited Worden's findings to primarily men. This follow-on research investigated whether these results carried over to women. We recruited 61 female volunteers and compared their performance on the AFPFT to the Marine Combat Fitness Test, the proxy for combat capability. Like Worden's research, we discovered little association between the two (R² of 0.161). However, this association significantly increased (adj R² of 0.572) when utilizing the raw …

A Multidimensional Ruin Problem, S Ramasubramanian

Communications on Stochastic Analysis

No abstract provided.

Roots Of States, B V Rajarama Bhat

Communications on Stochastic Analysis

No abstract provided.

Lévy Processes Through Time Shift On Oscillator Weyl Algebra, Luigi Accardi, Habib Ouerdiane, Habib Rebei

Communications on Stochastic Analysis

No abstract provided.

A Vacuum-Adapted Approach To Quantum Feynman-Kac Formulae, Alexander C R Belton, J Martin Lindsay, Adam G Skalski

Communications on Stochastic Analysis

No abstract provided.

Multiple Q-Adapted Integrals And Itô Formula Of Noncommutative Stochastic Calculus In Fock Space, V P Belavkin, M F Brown

Communications on Stochastic Analysis

No abstract provided.

The Early Years Of Quantum Stochastic Calculus, R L Hudson

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For Random Matrices, Sourav Chatterjee, S R S Varadhan

Communications on Stochastic Analysis

No abstract provided.

Some Problems Involving Airy Functions, V S Varadarajan

Communications on Stochastic Analysis

No abstract provided.

An Interpolating Family Of Means, Rajendra Bhatia, Ren-Cang Li

Communications on Stochastic Analysis

No abstract provided.

Hilbert Von Neumann Modules, Panchugopal Bikram, Kunal Mukherjee, R. Srinivasan, V S Sunder

Communications on Stochastic Analysis

No abstract provided.

Bell's Inequality Violations: Relation With De Finetti's Coherence Principle And Inferential Analysis Of Experimental Data, Franco Fagnola, Matteo Gregoratti

Communications on Stochastic Analysis

No abstract provided.

The Kolmogorov And Stechkin Problems For Classes Of Functions Whose Second Derivative Belongs To The Orlicz Space, Yuliya Babenko, Dmitry Skorokhodov

Faculty Articles

For any t ∈ [0, 1], we obtain the exact value of the modulus of continuity , where L* is the dual Orlicz space with Luxemburg norm and D is the operator of differentition at the point t. As an application, we state necessary and sufficient conditions in the Kolmogorov problem for three numbers. Also we solve the Stechkin problem, i.e., the problem of approximating an unbounded operator of differentition D by bounded linear operators for the class of functions x such that $\left\| {x''} \right\|_{L_N^* [0,1]} \leqslant 1$

Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, Stephan Ramon Garcia, Daniel E. Poore '11, William T. Ross

Pomona Faculty Publications and Research

Unlike Toeplitz operators on H², truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this paper we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive, and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension ≤ 3 is unitarily equivalent to a direct sum of truncated Toeplitz operators.

Abstract Criteria For Multiple Solutions To Nonlinear Coupled Equations Involving Magnetic Schrodinger Operators, Mattias Enstedt, Michael Melgaard

Articles

We consider a system of nonlinear coupled equations involving magnetic Schrodinger

operators and general potentials. We provide a criteria for the existence of multiple

solutions to these equations. As special cases we get the classical results on

existence of innitely many distinct solutions within Hartree and Hartree-Fock

theory of atoms and molecules subject to an external magnetic fields. We also

extend recent results within this theory, including Coulomb system with a constant

magnetic field, a decreasing magnetic field and a "physically measurable" magnetic field.

On The Closure Of The Complex Symmetric Operators: Compact Operators And Weighted Shifts, Stephan Ramon Garcia, Daniel E. Poore '11

Pomona Faculty Publications and Research

We study the closure $\bar{CSO}$ of the set $CSO$ of all complex symmetric operators on a separable, infinite-dimensional, complex Hilbert space. Among other things, we prove that every compact operator in $\bar{CSO}$ is complex symmetric. Using a construction of Kakutani as motivation, we also describe many properties of weighted shifts in $\bar{CSO} \backslash CSO$. In particular, we show that weighted shifts which demonstrate a type of approximate self-similarity belong to $\bar{CSO}\backslash CSO$. As a byproduct of our treatment of weighted shifts, we explain several ways in which our result on compact operators is optimal.

Two Remarks About Nilpotent Operators Of Order Two, Stephan Ramon Garcia, Bob Lutz '13, D. Timotin

Pomona Faculty Publications and Research

We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a complex symmetric operator. In fact, we prove that this property characterizes nilpotents of order two among all nonzero bounded operators. Second, we establish that every nilpotent of order two is unitarily equivalent to a truncated Toeplitz operator.

Spaces Of Sections Of Banach Algebra Bundles, Emmanuel Dror Farjoun, Claude Schochet

Mathematics Faculty Research Publications

Suppose that B is a G-Banach algebra over 𝔽 = ℝ or ℂ, X is a finite dimensional compact metric space, ζ : P → X is a standard principal G-bundle, and A_ζ = Γ(X,P x_G B) is the associated algebra of sections. We produce a spectral sequence which converges to π_∗(GL_oA_ζ) with

E_{_}²_p,q ≅ Ȟ^p(X ; π_q(GL_oB)).

A related spectral sequence converging to K_∗+1(A_ζ) (the real or complex topological …

Subspace Segmentation And High-Dimensional Data Analysis, Ali Safak Sekmen

Computer Science Faculty Research

This thesis developed theory and associated algorithms to solve subspace segmentation problem. Given a set of data W={w_1,...,w_N} in R^D that comes from a union of subspaces, we focused on determining a nonlinear model of the form U={S_i}_{i in I}, where S_i is a set of subspaces, that is nearest to W. The model is then used to classify W into clusters. Our first approach is based on the binary reduced row echelon form of data matrix. We prove that, in absence of noise, our approach can find the number of subspaces, their dimensions, and an orthonormal basis for each …

Semigroup As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors study the zero divisor graph and unit graph of a semigroup. The zero divisor graphs of semigroups Zn under multiplication is studied and characterized.

Non Associative Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of non associative vector spaces and non associative linear algebras over a field. We construct non associative space using loops and groupoids over fields. In general in all situations, which we come across to find solutions may not be associative; in such cases we can without any difficulty adopt these non associative vector spaces/linear algebras. Thus this research is a significant one.

This book has six chapters. First chapter is introductory in nature. The new concept of non associative semilinear algebras is introduced in chapter two. This structure is …

Dual Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Dual numbers was first introduced by W.K. Clifford in 1873. This nice concept has lots of applications; to screw systems, modeling plane joint, iterative methods for displacement analysis of spatial mechanisms, inertial force analysis of spatial mechanisms etc. In this book the authors study dual numbers in a special way. The main aim of this book is to find rich sources of new elements g such that g2 = 0. The main sources of such new elements are from Zn, n a composite number. We give algebraic structures on them. This book is organized into six chapters. The final chapter …

Exploring The Extension Of Natural Operations On Intervals, Matrices And Complex Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

This book extends the natural operations defined on intervals, finite complex numbers and matrices. The intervals [a, b] are such that a ≤ b. But the natural class of intervals [a, b] introduced by the authors are such that a ≥ b or a need not be comparable with b. This way of defining natural class of intervals enables the authors to extend all the natural operations defined on reals to these natural class of intervals without any difficulty. Thus with these natural class of intervals working with interval matrices like stiffness matrices finding eigenvalues takes the same time as …

Natural Product Xn On Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new product on matrices called the natural product. ...

Thus by introducing natural product we can find the product of column matrices and product of two rectangular matrices of same order. Further this product is more natural which is just identical with addition replaced by multiplication on these matrices. Another fact about natural product is this enables the product of any two super matrices of same order and with same type of partition. We see on supermatrices products cannot be defined easily which prevents from having any nice algebraic structure on the collection …