Well-posedness of an evolution problem with nonlocal diffusion

We prove the well-posedness of a general evolution reaction–nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continuity of the range kernel and the bounded variation of the spatial kernel and the initial datum. In the second set of assumptions, we relax the Lipschitz continuity of the range kernel to Hölder continuity, and assume monotonic behavior. In this case, the spatial kernel and the initial data can be just integrable functions. The main applications of this model are related to the fields of Image Processing and Population Dynamics.     

A Multidimensional Generalization of Shukla's 8ψ8 Summation

   Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised ₈ ψ ₈ summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A _r-1 or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A _r-1 nonterminating very-well-poised ₆ φ ₅ summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.     

An effusion-evaporation model for image edge detection

A novel quasi-physical edge detection model is presented. The model, referred to as the effusion-evaporation model (EEM), is inspired by the natural phenomenon that the water effusing from the ground evaporates in the sunshine and leaves a wire like water stain on the ground surface, which reflects the physiognomy of the terrain. Based on the simulation of water effusing and evaporating, an EEM regards the complement of gradient magnitude image as a three-dimensional terrain, and the concave regions, which contain the residual water in the evolution final state, are used to determine the edges. Subjective and objective comparisons are performed on the proposed algorithm and two conventional edge detectors, namely Canny and LoG. The comparison results show that the proposed method outperforms Canny and LoG detectors for the real images and the standard test images with Gaussian noise.     

The t-coefficient method II: A new series expansion formula of theta function products and its implications

By means of Jacobi?s triple product identity and the t  -coefficient method, we establish a general series expansion formula with five free parameters for the product of arbitrary two Jacobi theta functions. It embodies the triple, quintuple, sextuple and septuple theta function product identities and the generalized Schröter formula. As further applications, we also set up a series expansion formula for the product of three theta functions. It not only generalizes Ewell?s and Chen–Chen–Huang?s octuple product identities, but also contains three cubic theta function identities due to Farkas–Kra and Ramanujan respectively and the Macdonald identity for the root system _A2$A_2$ as special cases. In the meantime, many other new identities including a new short expression of the triple theta series of Andrews are also presented.     

The Method of Integrodifferential Relations for Linear Elasticity Problems

Some possible modifications of the governing equations of the linear theory of elasticity are considered. The stress–strain relation is specified by an integral equality instead of the local Hooke’s law. The modified integrodifferential boundary value problem is reduced to the minimization of a nonnegative functional under differential constraints. A numerical algorithm based on polynomial approximations of unknown functions (stresses and displacements) is developed and applied to linear elasticity problems. The bilateral estimation criteria of solution errors are proposed in order to analyze the algorithm convergence rate. The numerical results obtained by applying the integrodifferential relation method and the conventional variational method are compared and discussed.     

双向Poission点过程与反应时测试

本文研究一类应用于反应时测试的随机数学模型——双向Poission点过程及其拓广。首先考察双向Poission点过程及其点间间距的统计特性,并拓广之为齐次双向点过程;最后讨论这一模型在反应时测试中的应用。     

Semi-finite forms of bilateral basic hypergeometric series

We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan's summation, Bailey's transformations, and Bailey's summation.

     

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.     

结合多尺度空间滤波和层级网络的基于结构保持的高光谱特征选择

为了充分利用高光谱图像蕴含的丰富的光谱信息和空间信息,提出了结合多尺度空间滤波和层级网络的基于结构保持的高光谱特征选择算法.算法利用基于l2,1范数的数学模型,选出同时保存全局相似性结构和局部流形结构的特征子集;在多个尺度的窗口中使用双边滤波,自适应计算滤波核,自动在光谱数据中融入空间信息,增强了类内相似性和类间相异性,避免了参量选择;引入层级结构实现空间信息和光谱信息的深入融合,提高了分类准确度;讨论了层级数目和窗口尺度个数对分类准确度的影响.在Indian Pines和PaviaU两个数据集的实验表明,该算法在大部分地物种类上的分类准确度都有较大幅度的提升,总体分类准确度分别达到90.98%和94.20%,相比其他方法明显提高了地物分类准确度.