Completely normal matrices

Normal matrices in which all submatrices are normal are said to be completely normal. We characterize this class of matrices, determine the possible inertias of a particular completely normal matrix, and show that real matrices in this class are closed under (general) Schur complementation. We provide explicit formulas for the Moore–Penrose inverse of a completely normal matrix of size at least four. A result on irreducible principally normal matrices is derived as well.     

拟正规与Hayman 选择

本文证明了亚纯函数族的一个拟正规定则, 推广了Xu-Fang, Chang 与Nevo-Pang-Zalcman 的相应结果; 并应用此拟正规定则得到了一个值分布结果, 推广与改进了著名的Hayman 选择, 以及Wang-Fang, Chang 和Nevo-Pang-Zalcman 的相关结论.     

Necessary conditions for constrained optimal control problems via mathematical programming

Necessary conditions for optimal control problems with state-control variable inequality constraints are obtained via mathematical programming formulation and functional analysis in Banach space. These conditions are general ones that hold without any constraint qualifications but differentiability. Furthermore, these conditions are shown to be equivalent to the classical result in the presence of the linear independence constraint qualification.     

Using Complex Integration to Compute Multivariate Normal Probabilities

Abstract

The execution of most multiple comparison methods involves, at least in part, the computation of the probability that a multivariate normal or multivarite t random vector is in a hyper-rectangle. In multiple comparison with a control as well as multiple comparison with the best (of normal populations or multinomial cell probabilities), the correlation matrix R of the random vector is nonsingular and of the form , where D is a diagonal matrix and is a known vector. It is well known that, in this case, the multivariate normal rectangular probability can be expressed as a one-dimensional integral and successfully computed using Gaussian quadrature techniques. However, in multiple comparison with the mean (sometimes called analysis of means) of normal distributions, all-pairwise comparisons of three normal distributions, as well as simultaneous inference on multinomial cell probabilities themselves, the correlation matrix is singular and of the form . It is not well known that, in this latter case, the multivariate normal rectangular probability can still be expressed as a single integral, albeit one with complex variables in its integrand. Previously published proofs of the validity of this expression either contained a gap or relied on a numerical demonstration, and this article will provide an analytic proof. Furthermore, we explain how this complex integral can be computed accurately, using Romberg integration of complex variables when the dimension is low, and using ?idák's inequality as an approximation when the dimension is at least moderate.     

Groups with Certain Normality Conditions

We classify two types of finite groups with certain normality conditions, namely SSN groups and groups with all noncyclic subgroups normal. These conditions are key ingredients in the study of the multiplicative Jordan decomposition problem for group rings.     

Personalized Metabolic Profile by Synergic Use of NMR and HRMS

A new strategy that takes advantage of the synergism between NMR and UHPLC–HRMS yields accurate concentrations of a high number of compounds in biofluids to delineate a personalized metabolic profile (SYNHMET). Metabolite identification and quantification by this method result in a higher accuracy compared to the use of the two techniques separately, even in urine, one of the most challenging biofluids to characterize due to its complexity and variability. We quantified a total of 165 metabolites in the urine of healthy subjects, patients with chronic cystitis, and patients with bladder cancer, with a minimum number of missing values. This result was achieved without the use of analytical standards and calibration curves. A patient’s personalized profile can be mapped out from the final dataset’s concentrations by comparing them with known normal ranges. This detailed picture has potential applications in clinical practice to monitor a patient’s health status and disease progression.     

非线性模型中VaR估测的正态性改进

VaR风险测度技术已经被学界和业界广泛使用,但其局限性也是显而易见的,国内外学者对其进行了一系列的改进.由线性模型扩展为非线性模型以及由正态假定转换到非正态性均源于风险测度的精确化.探讨依数据特征改进和扩展VaR估测方法,使用Johnson转换方法与Cornish-Fisher扩展方法这两种正态性改进方法改善VaR估值,一方面利用正态假定成熟理论结果简化VaR估测方法的推演,另一方面从实证分析角度论证了正态性改进方法在VaR估测中的准确性与有效性.