On cohomological dimension and depth under linkage

Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.     

基本养老保险缴费心理活动维度的实证研究:个人心理账户视角

本文从心理账户理论视角,通过问卷调查,运用非集计模型,对个人基本养老保险缴费心理活动维度进行了实证研究。研究结果表明,受教育程度、非常规的额外收入、经营性收入、安全型保障账户和风险型存储账户是影响缴费的关键性因素,进而提出引导设立特定缴费心理账户、增强缴费制度弹性,改变缴费者的选择框架, 提升缴费遵从度。     

Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.     

A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation $$u_t+i{u}_{xx}+i|u{|}^{2}u+\gamma u=f,f\in {\mathrm{??}}^2(?).$$ “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?”     

Gorenstein平坦模与Frobenius扩张

设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的.     

Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.     

High‐throughput data dimension reduction via seeded canonical correlation analysis

Canonical correlation analysis (CCA) is one of popular statistical methodologies in multivariate analysis, especially, in studying relation of two sets of variables. However, if sample sizes are smaller than the maximum of the dimensions of two sets of variables, it is not plausible to construct canonical coefficient matrices due to failure of inverting sample covariance matrices. In this article, we develop a two step procedure of CCA implemented in such situation. For this, seeded dimension reduction is adapted into CCA. Numerical studies confirm the approach, and two real data analyses are presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Adsorption in columns packed with porous adsorbent particles having partially fractal structures

A mathematical model is constructed and solved that could describe the dynamic behavior of the adsorption of a solute of interest in single and stratified columns packed with partially fractal porous adsorbent particles. The results show that a stratified column bed whose length is the same as that of a single column bed, provides larger breakthrough times and a higher dynamic utilization of the adsorptive capacity of the particles than those obtained from the single column bed, and the superior performance of the stratified bed becomes especially more important when the superficial velocity of the flowing fluid stream in the column is increased to accommodate increases in the system throughput. This occurs because the stratified column bed provides larger average external and intraparticle mass transfer and adsorption rates per unit length of packed column. It is also shown that increases in the total number of recursions of the fractal and the ratio of the radii between larger and smaller microspheres that make up the partially fractal particles, increase the intraparticle mass transfer and adsorption rates and lead to larger breakthrough times and dynamic utilization of the adsorptive capacity of the particles. The results of this work indicate that highly efficient adsorption separations could be realized through the use of a stratified column comprised from a practically reasonable number of sections packed with partially fractal porous adsorbent particles having reasonably large (i) total number of recursions of the fractal and (ii) ratio of the radii between larger and smaller microspheres from which the partially fractal particles are made from. It is important to mention here that the physical concepts and modeling approaches presented in this work could be, after a few modifications of the model, applied in studying the dynamic behavior of chemical catalysis and biocatalysis in reactor beds packed with partially fractal porous catalyst particles.