Other Mathematics Commons^™

Ergodicity Of Burgers' System, Szymon Peszat, Krystyna Twardowska, Jerzy Zabczyk

Journal of Stochastic Analysis

No abstract provided.

Two Of Kunita's Papers On Stochastic Flows In Early 1980s, Setsuo Taniguchi

Journal of Stochastic Analysis

No abstract provided.

Error Estimates For Discrete Approximations Of Game Options With Multivariate Diffusion Asset Prices, Yuri Kifer

Journal of Stochastic Analysis

No abstract provided.

Hessian Formulas And Estimates For Parabolic Schrödinger Operators, Xue-Mei Li

Journal of Stochastic Analysis

No abstract provided.

Remembering Kunita-San, Ken-Iti Sato

Journal of Stochastic Analysis

No abstract provided.

On The Application Of Principal Component Analysis To Classification Problems, Jianwei Zheng, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

Principal Component Analysis (PCA) is a commonly used technique that uses the correlation structure of the original variables to reduce the dimensionality of the data. This reduction is achieved by considering only the first few principal components for a subsequent analysis. The usual inclusion criterion is defined by the proportion of the total variance of the principal components exceeding a predetermined threshold. We show that in certain classification problems, even extremely high inclusion threshold can negatively impact the classification accuracy. The omission of small variance principal components can severely diminish the performance of the models. We noticed this phenomenon in …

The Life And Scientific Work Of Hiroshi Kunita, Yasushi Ishikawa

Journal of Stochastic Analysis

No abstract provided.

Memories Of Professor Hiroshi Kunita, Ichiro Shigkeawa

Journal of Stochastic Analysis

No abstract provided.

On The Works Of Hiroshi Kunita In The Sixties, Masatoshi Fukushima

Journal of Stochastic Analysis

No abstract provided.

Personal Memories Of Hiroshi Kunita, David Elworthy

Journal of Stochastic Analysis

No abstract provided.

Preface, Shigeki Aida, David Applebaum, Yasushi Ishikawa, Arturo Kohatsu-Higa, Nicolas Privault

Journal of Stochastic Analysis

No abstract provided.

Elliptic Curves And Their Practical Applications, Henry H. Hayden Iv

Graduate Theses/Dissertations

Finding rational points that satisfy functions known as elliptic curves induces a finitely-generated abelian group. Such functions are powerful tools that were used to solve Fermat's Last Theorem and are used in cryptography to send private keys over public systems. Elliptic curves are also useful in factoring and determining primality.

Trilinear Smoothing Inequalities And A Variant Of The Triangular Hilbert Transform, Michael Christ, Polona Durcik, Joris Roos

Mathematics, Physics, and Computer Science Faculty Articles and Research

Lebesgue space inequalities are proved for a variant of the triangular Hilbert transform involving curvature. The analysis relies on a crucial trilinear smoothing inequality developed herein, and on bounds for an anisotropic variant of the twisted paraproduct.

The trilinear smoothing inequality also leads to Lebesgue space bounds for a corresponding maximal function and a quantitative nonlinear Roth-type theorem concerning patterns in the Euclidean plane.

Graph-Theoretic Partitioning Of Rnas And Classification Of Pseudoknots-Ii, Louis Petingi

Publications and Research

Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called blocks and determine whether each block contains a pseudoknot or not. As pseudoknots can not be contained into two different blocks, this characterization allow us to efficiently isolate smaller RNA fragments and classify them as pseudoknotted or pseudoknot-free regions, while keeping these sub-structures intact. Moreover we have extended the partitioning algorithm by classifying a pseudoknot as either recursive or non-recursive in order to continue with our research …

Computable Model Theory On Loops, Josiah Schmidt

All NMU Master's Theses

We give an introduction to the problem of computable algebras. Specifically, the algebras of loops and groups. We start by defining a loop and group, then give some of their properties. We then give an overview of comptability theory, and apply it to loops and groups. We conclude by showing that a finitely presented residually finite algebra has a solvable word problem.

Estimating Turbulence Distribution Over A Heterogeneous Path Using Time‐Lapse Imagery From Dual Cameras, Benjamin Wilson, Santasri Bose-Pillai, Jack E. Mccrae, Kevin J. Keefer, Steven T. Fiorino

Faculty Publications

Knowledge of turbulence distribution along an experimental path can help in effective turbulence compensation and mitigation. Although scintillometers are traditionally used to measure the strength of turbulence, they provide a path-integrated measurement and have limited operational ranges. A technique to profile turbulence using time-lapse imagery of a distant target from spatially separated cameras is presented here. The method uses the turbulence induced differential motion between pairs of point features on a target, sensed at a single camera and between cameras to extract turbulence distribution along the path. The method is successfully demonstrated on a 511 m almost horizontal path going …

Berry-Esseen Bounds For Approximate Maximum Likelihood Estimators In The Α-Brownian Bridge, Khalifa Es-Sebaiy, Jabrane Moustaaid, Idir Ouassou

Journal of Stochastic Analysis

No abstract provided.

On A Polyanalytic Approach To Noncommutative De Branges–Rovnyak Spaces And Schur Analysis, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we begin the study of Schur analysis and of de Branges–Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like polynomials. This approach is very efficient from various points of view, for example in operator theory, and allows us to make connections with the recently developed theory of slice polyanalytic functions. We tackle a number of problems: we describe a Hardy space, Schur multipliers and related results. We also discuss Blaschke functions, Herglotz multipliers and their associated kernels and Hilbert spaces. Finally, …

Numeric And Dynamic B-Stability, Exact-Monotone And Asymptotic Two-Point Behavior Of Theta Methods For Stochastic Differential Equations, Henri Schurz

Journal of Stochastic Analysis

No abstract provided.

A Math Without Words Puzzle, Jane H. Long, Clint Richardson

Journal of Math Circles

A visual puzzle by James Tanton forms the basis for a session that has been successfully implemented with various audiences. Designed to be presented with no directions or description, the puzzle requires participants to discover the goals themselves and to generate their own questions for investigation. Solutions, significant facilitation suggestions, and possibilities for deep mathematical extensions are discussed; extensive illustrations are included.