An optimal perturbation bound

Cai and Zhang establish separate perturbation bounds for distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60?89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.     

Simultaneous quantification of ondansetron and tariquidar in rat and human plasma using a high performance liquid chromatography‐ultraviolet method

Ondansetron, a widely used antiemetic agent, is a P‐glycoprotein (P‐gp) substrate and therefore expression of P‐gp at the blood–brain barrier limits its distribution to the central nervous system (CNS), which was observed to be reversed by coadministration with P‐gp inhibitors. Tariquidar is a potent and selective third‐generation P‐gp inhibitor, and coadministration with ondansetron has shown improved ondansetron distribution to the CNS. There is currently no reported bioanalytical method for simultaneously quantifying ondansetron with a third‐generation P‐gp inhibitor. Therefore, we aimed to develop and validate a method for ondansetron and tariquidar in rat and human plasma samples. A full validation was performed for both ondansetron and tariquidar, and sample stability was tested under various storage conditions. To demonstrate its utility, the method was applied to a preclinical pharmacokinetic study following coadministration of ondansetron and tariquidar in rats. The presented method will be valuable in pharmacokinetic studies of ondansetron and tariquidar in which simultaneous determination may be required. In addition, this is the first report of a bioanalytical method validated for quantification of tariquidar in plasma samples.     

Multidimensional Scaling With Very Large Datasets

Multidimensional scaling has a wide range of applications when observations are not continuous but it is possible to define a distance (or dissimilarity) among them. However, standard implementations are limited when analyzing very large datasets because they rely on eigendecomposition of the full distance matrix and require very long computing times and large quantities of memory. Here, a new approach is developed based on projection of the observations in a space defined by a subset of the full dataset. The method is easily implemented. A simulation study showed that its performance are satisfactory in different situations and can be run in a short time when the standard method takes a very long time or cannot be run because of memory requirements.     

Existence theorems for boundary value problems in difference equations

In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants.     

Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.     

A class of optimal iterative methods of inverting a linear bounded operator

A family of higher-order iterative methods for inverting a linear bounded operator in a Banach space is presented. This family depending on two integer parameters can be considered as hyperpower methods of [1]. A convergence Theorem is proved and an optimal class with respect to the efficiency index is determined . Several error bounds are derived and compared with those in the literature.     

m次幂等矩阵的等价条件

利用矩阵的秩和齐次线性方程组解空间的维数,给出了m(m≥2)次幂等矩阵的一些等价条件,推广了2,3次幂等矩阵的相应结果.此外,所获结果还给推广到了m次幂等线性变换中.     

On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

基于行列式随机循环的压缩感知测量矩阵研究

压缩感知理论,从信号的自身特性出发,通过变换作用域和线性投影实现对信号的采样和压缩。测量矩阵是该理论中获得最优测量,实现精确重构的关键。本文在介绍常用测量矩阵的基础上,重点研究了结构化测量矩阵。鉴于测量矩阵设计的最重要的原则是降低矩阵元素间的相干性,本文借鉴循环矩阵和广义轮换矩阵的优点,提出了采用均匀随机数对结构化测量矩阵进行随机循环的构造方法。仿真实验表明新矩阵在信号重建上具有更好的性能。     

SPECTRAL CHARACTERISTICS OF FREE AND LINKED PYRENE-TYPE CHROMOPHORES IN SOLUTION,POLYMER MATRICES,AND INTERPENETRATING NETWORKS

Monomers, 1-pyrenylmethyl methacrylate (PyMMA), 1-pyrenylbutyl methacrylate (PyBMA), 4-(1-pyrenyl)methoxymethyl styrene (PyMMS) and allyl-(1-pyrenylmehtyl) ether (PyMAE), with pyrene as chromophore, were prepared. Their spectral properties (absorption, emission and emission decay) in solution, and doped or bonded in polymer matrices and complex polymer systems as interpenetrating polymer networks (IPN), were investigated. Spectral properties of pyrene-containing monomers doped in polystyrene (PS), polymethylmethacrylate (PMMA), polyvinylchloride (PVC), polyethylene (PE) and grafted on PE as well as copolymerized in buthylmethacrylate-co-styrene copolymer (BMA-co-S) have been compared. Absorption and emission spectra of pyrene type probes in solution and in IPN matrices exhibit typical absorption of the pyrene moiety. For IPN with grafted probes on PE, the absorption is slightly shifted to red wavelength. For monomers, PyMMA, PyBMA and PyMAE grafted to PE, the shape of the emission spectrum depends on the wavelength of excitation. The ratio of intensity of the vibrational band, I₁/I₃, (I₁ peak at 377 nm and I₃ peak at 388 nm) has been a quite useful indicator of polarity of IPN. The relative quantum yields of fluorescence in IPN matrices are lower in comparison to polymer matrices of PE, PS, PMMA for all probes under study. The fluorescence life-times for bound and free probes have been in the range 100–200 ns, which is substiantialy shorter than for the parent pyrene chromophore under the same or similar condition. Grafted probes on PE alone, or as a part of IPN, exhibit substantially shorter life-time around 10 ns and decay is rather complex.