一阶变系数滞后型微分方程解的振动性积分条件与渐近性

本文给出了一阶变系数滞后型微分方程振动解存在的积分条件,同时利用Banach不动点定理讨论了该类方程解的渐近性。     

Cholera toxin-induced modulation of gene expression: elucidation via cDNA microarray for rational cell-based sensor design

Cell-based biosensors utilize functional changes in cellular response to identify the biological threats in a physiological relevant manner. Cell-based sensors have been used for a wide array of applications including toxicological assessment and drug-screening. In this paper, we utilize DNA arrays to identify differential gene expression events induced by toxin exposure for the purpose of developing a reporter gene assay system compatible with insertion into a cell-based sensor platform. HT29, an intestine epithelial cell line, was used as a cell model to study the cholera toxin (CT)-induced host cell modulation using DNA array analysis. A false positive model was generated from analysis of housekeeping genes in untreated control experiments to characterize our system and to minimize the number of false positives in the data. Threshold probability scores (−3.72), which gives <0.02% false positives for up/down regulation from the false positive model, were used to identify 73 and 25 known genes/expression tag sequences (ESTs) that were up- and down-regulated, respectively, in cells exposed 23 nM of CT. Using quantitative multiplex PCR assay, the gene expression levels for several genes shown to be modulated according to the microarray experiments, such as apolipoprotein D (Apol D), E-cadherin, and cyclin A2, were confirmed. The differential expression of genes encoding cytochrome P450, glutathione transferase (GST), and MGAT2 were noteworthy and consistent with previous studies. Our study provides an approach to analyze cDNA microarray data with defined false positive rates. The utility of cDNA microarray information for the design of cell-based sensor using a reporter gene approach is discussed.     

Norm Inequalities for Commutators of Self-adjoint Operators

Let A, B, and X be bounded linear operators on a complex separable Hilbert space. It is shown that if A and B are self-adjoint with and for some real numbers a ₁, a ₂, b ₁, and b ₂, then for every unitarily invariant norm|||·|||,

EXISTENCE OF POSITIVE MULTIPLE SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR

In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point theorem on the cone.     

对称广义中心对称半正定矩阵模型修正的矩阵逼近法及其应用

设X,B分别是实测的位移矩阵和载荷矩阵, C是有限元模型估计,找对称广义中心对称半正定矩阵(A)使‖C-(A)‖F=min(A:AX=B)‖C-A‖F.我们证明这样的(A)存在唯一,并应用它来修正动力模型.数值结果证明方法是行之有效的.     

Riemann-Stieltjes积分边值问题正解的存在唯一性

利用解的先验估计和极值原理,研究了一类具有Riemann-Stieltjes积分边值问题正解的存在唯一性．     

四阶微分方程三点边值问题三个正解的存在性

在四阶微分方程非线性项f中含有未知函数“的二阶导数u”的情况下,运用Avery-Peterson不动点定理,研究了一类四阶微分方程三点边值问题三个正解的存在性,得到了该类边值问题存在三个正解的充分条件．     

The DJL Conjecture for CP Matrices over Special Inclines

Drew, Johnson, and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n²/4]. While this conjecture has recently been disproved for completely positive real matrices, we show that this conjecture is true for n × n completely positive matrices over certain special types of inclines. In addition, we prove an incline version of Markham's theorems which gives sufficient conditions for completely positive matrices over special inclines to have triangular factorizations.     

On a second-order nonlinear discrete multi-point eigenvalue problem

We study the existence and non-existence of positive solutions of a system of nonlinear second-order difference equations with eigenvalues subject to multi-point boundary conditions.