Existence and Uniqueness of Endemic States for the Age-structured MSEIR Epidemic Model

The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown.     

具有急慢性阶段的MSIS流行病模型阈值和稳定性结果

系统研究了具有急性和慢性两个阶段的MSIS流行病模型.由两节构成,第1节建立和研究了具有急慢性阶段的MSIS流行病模型;第2节在第1节的基础上建立和研究了具有慢性病病程的MSIS流行病模型.第1节的模型是四个常微分方程构成的方程组.第2节的模型既含有常微分方程,又含有偏微分方程.运用微分方程和积分方程中的理论和方法,得到了这两个模型再生数R0的表达式.证明了当R0<1时,无病平衡态是全局渐近稳定性,给出了各模型地方病平衡态的存在性和稳定性条件.     

Global stability and periodic solution of the viral dynamics

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.     

一类具有阶段结构和时滞的捕食系统的持续生存和稳定性

我们提出和研究一类带有阶段结构和时滞的捕食模型,得到了种群持续生存的充分条件.研究了阶段结构和时滞对系统稳定性的影响,获得了系统发生Hopf分支和稳定性的条件以及轨道渐进稳定的周期解的存在性.     

On the Rank of the Semigroup TE(X)

${\cal T}_X $ denotes the full transformation semigroup on a set $ X $. For a nontrivial equivalence $E$ on $X$, let \[ T_E (X) =\{ f\in {\cal T}_X : \forall \, (a,b)\in E,\, (af,bf)\in E \} . \] Then $T_E (X) $ is exactly the semigroup of continuous selfmaps of the topological space $X$ for which the collection of all $E$-classes is a basis. In this paper, we first discuss the rank of the homeomorphism group $G$, and then consider the rank of $T_E (X)$ for a special case that the set $X$ is finite and that each class of the equivalence $E$ has the same cardinality. Finally, the rank of the closed selfmap semigroup $\Gamma(X)$ of the space $X$ is observed. We conclude that the rank of $G$ is no more than 4, the rank of $T_E (X)$ is no more than 6 and the rank of $\Gamma(X)$ is no more than 5.     

A Mossbauer study of the magnetic coupling in iron phosphorous trisulfides

The polycrystalline sample of layered compound FePS_3 has been investigated by using M?ssbauer spectroscopy (12K to 300K), magnetic susceptibility measurements, x-ray diffraction and FTIR spectroscopy. The antiferromagnetic order exists below T_N=120.5±1K. The M?ssbauer spectra below T_N indicate that the magnetization axis is perpendicular to the layer of FePS_3, and the divalent iron cations are in their high spin configurations. By fitting the hyperfine field parameters near the Néel temperature, we obtain information on the nature of magnetic interactions in the material. The results show that the magnetic coupling can be treated by the two-dimensional Ising model, and it can be interpreted on the basis of a crystal-field effect.     

多重向量值正交小波包

本文引入多重向量值小波包的概念,提供一类多重向量值正交小波包的构造方法,并运用积分变换和算子理论,讨论了多重向量值正交小波包的性质．利用多重向量值正交小波包,构造了空间L2(R,Cs×s)的新的正交基．     

Permanence and stability of a predator–prey system with stage structure for predator

A stage-structured predator–prey system with delays for prey and predator, respectively, is proposed and analyzed. Mathematical analysis of the model equations with regard to boundedness of solutions, permanence and stability are analyzed. Some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium, respectively, are obtained.     

Highly visible-light luminescence properties of the carboxyl-functionalized short and ultrashort MWNTs

Luminescence of the short multiwalled carbon nanotubes (MWNTs) conjugated with carboxylic acid groups has been studied. The results show that the carboxyl-functionalized short MWNTs could emit luminescence and the emission peak appears at 500 nm with a corresponding optimal excitation wavelength centering at 310 nm. When the short MWNTs are filtered through 0.15 μm polytetrafluoroethylene (PTFE) membrane, the ultrashort MWNTs are obtained from the filtrate. An interesting feature for the ultrashort MWNTs is that the emission intensity is strengthened and the peak is slightly blue shifted to 460 nm. This result indicates that the luminescence properties of MWNTs are strongly affected by the tube length. After chemical oxidization cutting, defects and carboxylic acid groups at the tube end and/or sidewall can be produced; the more shorten of MWNTs, the better dispersion and carboxylic passivation of the nanotubes, and the more intense luminescence emissions. The broad emissions are logically attributed to the trapping of excitation energy by defect sites in the carboxyl-functionalized nanotube structure.     

Simultaneous and ultrasensitive detection of multiple microRNAs by single-molecule fluorescence imaging

Cell status changes are typically accompanied by the simultaneous changes of multiple microRNA (miRNA) levels. Thus, simultaneous and ultrasensitive detection of multiple miRNA biomarkers shows great promise in early cancer diagnosis. Herein, a facile single-molecule fluorescence imaging assay was proposed for the simultaneous and ultrasensitive detection of multiple miRNAs using only one capture anti-DNA/RNA antibody (S9.6 antibody). Two complementary DNAs (cDNAs) designed to hybridize with miRNA-21 and miRNA-122 were labelled with Cy3 (cDNA1) and Cy5 (cDNA2) dyes at their 5′-ends, respectively. After hybridization, both miRNA-21/cDNA1 and miRNA-122/cDNA2 complexes were captured by S9.6 antibodies pre-modified on a coverslip surface. Subsequently, the Cy3 and Cy5 dyes on the coverslip surface were imaged by the single-molecule fluorescence setup. The amount of miRNA-21 and miRNA-122 was quantified by counting the image spots from the Cy3 and Cy5 dye molecules in the green and red channels, respectively. The proposed assay displayed high specificity and sensitivity for singlet miRNA detection both with a detection limit of 5 fM and for multiple miRNA detection both with a detection limit of 20 fM. Moreover, it was also demonstrated that the assay could be used to detect multiple miRNAs simultaneously in human hepatocellular cancer cells (HepG2 cells). The proposed assay provides a novel biosensing platform for the ultrasensitive and simple detection of multiple miRNA expressions and shows great prospects for early cancer diagnosis.

A single-molecule assay for multiple microRNA detection.