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Coefficients of the n-fold Theta Function and Weyl Group Multiple Dirichlet Series
Dirichlet Series Theta Function
2015/7/6
We establish a link between certain Whittaker coecients of the generalized
metaplectic theta functions, rst studied by Kazhdan and Patterson [14], and
the coecients of the stable Weyl group multi...
Integrable vs. nonintegrable geodesic soliton behavior
Geodesic motion Solitons Hamiltonian system Pulsons
2015/6/30
We study confined solutions of certain evolutionary partial differential equations (PDE) in 1 + 1 space–time. The PDE we study are Lie–Poisson Hamiltonian systems for quadratic Hamiltonians defined on...
Entropy and Renormalized Solutions for the p(x)-Kaokacuab Equation with Measure Data
Variable exponents Entropy solutions Renormalized solutions Exist- ence Uniqueness
2015/5/4
In this paper we prove the existence and uniqueness of both entropy solutions and renormalized solutions for the p(x)-Laplacian equation with variable exponents and a signed measure in L 1 (Ω) +...
First-order SODE: OU processdX+aX(t)dt= dW(t)
Three options:a >0, a= 0, a <0.
First-order SPDE:du= au
xx dt+dW(t, x)
One option:a >0(Infinite-dimensional stable OU process.)
Second-order SODE:X¨ ...
If there is a global solution Ft(x , ω), SDE is complete, also called
non-explosive, conservative.
Orthogonal Arrays Obtained By Generalized Kronecker Product
mixed-level orthogonal arrays generalized Kronecker product
2015/3/18
in this paper, we propose a new general approach to construct asymmetrical orthogonal arrays, namely generalized Kronecker product. The
operation is not usual Kronecker product in the theory of matri...
Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials
Non-square lattices, Nonlinear waves Photonic lattices
2014/12/8
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
On the Frequency of Finitely Anomalous Elliptic Curves
Elliptic Curves Galois Representations Number Theory
2014/12/8
Given an elliptic curve E over Q, we can then consider E over the finite field Fp. If Np is the number of points on the curve over Fp, then we define ap(E) = p+1-Np. We say primes p for which ap(E) = ...
Correction Methods, Approximate Biases, and Inference for Misclassified Data
Misclassified Data Approximate Biases
2014/12/8
When categorical data are misplaced into the wrong category, we say the data is affected by misclassification. This is common for data collection. It is well-known that naive estimators of category pr...
Statistical Methods for Nonlinear Dynamic Models with Measurement Error Using the Ricker Model
measurement error ricker SIMEX
2014/12/8
In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are sub...
On a fully non-linear elliptic PDE in conformal geometry
Fully nonlinear PDE generalized Yamabe problem
2014/4/3
We give an expository survey on the subject of the Yamabe-type problem and applications. With a recent technique in hand, we also present a simplified proof of the result by Chang-Gursky-Yang on...
PRINCIPAL CURVATURE ESTIMATES FOR THE CONVEX LEVEL SETS OF SEMILINEAR ELLIPTIC EQUATIONS
PRINCIPAL CURVATURE ESTIMATES THE CONVEX LEVEL SETS SEMILINEAR ELLIPTIC EQUATIONS
2014/4/3
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary...
同伦分析方法的推广及其实现
同伦分析法 Adomian分解法 Adomian多项式 aylor展开序列 非线性微分方程 同伦分析法
2014/1/11
基于Rach对Adomian多项式的新定义, 推广了同伦分析方法. 给出了三种Rm的新定义, 通过分析可知它们的展开速度优于传统同伦分析方法. 这些方法的引入为求解非线性微分方程提供了新的思路, 特别是当传统同伦分析法收敛较慢时, 可以尝试使用. 在此基础上, 基于Maple 10平台对常微分方程实现了传统同伦分析方法和推广方法的通用计算程序, 使用户可以更方便地使用.
进一步研究了基于偏微分方程的图像去噪方法。为了去除二阶偏微分方程(P-M 模型)引起的阶梯效应以及提高四阶偏微分方程(Y-K 模型)的边缘及纹理保护能力，本文将梯度矢量卷积场(GVC)引入到四阶偏微分方程Y-K模型中，提出了基于GVC的四阶各向异性扩散模型。首先，减去原始Y-K模型中的部分梯度方向扩散。然后，引入GVC场以代替图像在梯度方向的二阶导数直接计算。由于GVC场可以较准确地确定图像的边缘...