A note on global stability for a heroin epidemic model with distributed delay

By using the direct Lyapunov method and constructing appropriate Lyapunov functional, the global stability for the heroin epidemic model with distributed delay is investigated. It is shown that the disease endemic equilibrium of the system is globally asymptotically stable whenever it exists. This improves the related results presented in [J. Liu, T. Zhang, Global behavior of a heroin epidemic model with distributed delay, Appl. Math. Lett. 24 (2011) 1685–1692].     

Stereoselective Synthesis of the Four Stereoisomers of 4-(N,N-Dibenzylamino)-2,2-dimethyl-3-hydroxypentanenitrile

The title compounds 1(a,b) and 1(c,d) were synthesized by (i) non-chelation controlled sodium borohydride reduction of their corresponding α-N,N-dibenzylaminoketones and (ii) the Aldol-type condensation of optically pure N,N-dibenzylaminoaldehydes with the lithium derivative of isobutyronitrile, respectively. Attempted inversion of configurations of these secondary alcohols using the Moriarty method yielded 4-chloro-3-N,N-dibenzylaminonitrile via an aziridinium ion intermediate instead of the expected inverted alcohols.     

Thermal denaturation produced degenerative proteins and interfered with MS for proteins dissolved in lysis buffer in proteomic analysis

In 1-DE, proteins were traditionally mixed with the standard Laemmli buffer and boiled for several minutes. Recently, proteins dissolved in lysis buffer were used to produce better-resolved 2-DE gels, but thermal denaturation procedure still remained in some proteomic analysis. To determine the detailed effects of thermal denaturation on SDS-PAGE and MS, both 1-DE and 2-DE were performed using proteins heated at 100°C for different periods of time, and 17 protein bands/spots were positively identified by MALDI TOF/TOF MS/MS. Protein profiles on both 1-DE and 2-DE gels changed obviously and more polydisperse bands/spots were observed with increased heating time for over-heated samples. Based on these observations, an alternative protein marker-producing method was designed by directly dissolving protein standards without BSA into lysis buffer. This new kind of protein marker could be stored at room temperature for a long time, thus was more convenient for using and shipping. The identification of 17 proteins via MS and comparison of their identities revealed MASCOT-searched scores, number of both matched peptides, total searched peptides and sequence coverage became progressively lower with increasing denaturation intensity, probably due to the interference of thermal denaturation on trypsin cleavage efficiency and produced redundant modified peptides. Therefore, it was concluded that thermal denaturation not only changed the protein profiles and produced more polydisperse protein bands/spots, but also heavily interfered with the subsequent MS analysis, hence not recommended in future proteomic analysis for proteins dissolved in lysis buffer.     

耦合的凝聚态Bose-Einstein方程的双周期解

本文通过引入参数假设,利用雅可比椭圆函数展开法,得到了自散焦的耦合非线性Schr(o)dinger(NLS)方程的四种双周期解(雅可比椭圆函数).     

Least-Squares Solutions of the Matrix Equation ATXA = B Over Bisymmetric Matrices and its Optimal Approximation

A real n×n symmetric matrix X=(x_(ij))_(n×n)is called a bisymmetric matrix if x_(ij)=x_(n 1-j,n 1-i).Based on the projection theorem,the canonical correlation de- composition and the generalized singular value decomposition,a method useful for finding the least-squares solutions of the matrix equation A~TXA=B over bisymmetric matrices is proposed.The expression of the least-squares solutions is given.Moreover, in the corresponding solution set,the optimal approximate solution to a given matrix is also derived.A numerical algorithm for finding the optimal approximate solution is also described.     

Investigation on the Flow Field Entropy Structure of Non-Synchronous Blade Vibration in an Axial Turbocompressor

In order to explore the inducing factors and mechanism of the non-synchronous vibration, the flow field structure and its formation mechanism in the non-synchronous vibration state of a high speed turbocompressor are discussed in this paper, based on the fluid–structure interaction method. The predicted frequencies f_BV (4.4EO), f_AR (9.6EO) in the field have a good correspondence with the experimental data, which verify the reliability and accuracy of the numerical method. The results indicate that, under a deviation in the adjustment of inlet guide vane (IGV), the disturbances of pressure in the tip diffuse upstream and downstream, and maintain the corresponding relationship with the non-synchronous vibration frequency of the blade. An instability flow that developed at the tip region of 90% span emerged due to interactions among the incoming main flow, the axial separation backflow, and the tip leakage vortices. The separation vortices in the blade passage mixed up with the tip leakage flow reverse at the trailing edge of blade tip, presenting a spiral vortex structure which flows upstream to the leading edge of the adjacent blade. The disturbances of the spiral vortexes emerge to rotate at 54.5% of the rotor speed in the same rotating direction as a modal oscillation. The blade vibration in the turbocompressor is found to be related to the unsteadiness of the tip flow. The large pressure oscillation caused by the movement of the spiral vortex is regarded as the one of the main drivers for the non-synchronous vibration for the present turbocompressor, besides the deviation in the adjustment of IGV.     

Periodic bi-directional Cohen–Grossberg neural networks with distributed delays

Some sufficient conditions are obtained for the global exponential stability of periodic solutions to periodic bi-directional Cohen–Grossberg neural networks involving distributed delays, by using the Lyapunov functional method and some analytical techniques. These results improve and generalize some previous works, and are helpful for designing a global exponential stable periodic bi-directional Cohen–Grossberg neural networks.     

OSCILLATION OF NONLINEAR HYPERBOLIC DIFFERENTIAL EQUATION WITH IMPULSES

In this paper, oscillatory properties of solutions for nonlinear impulsive hyperbolic differential equation are investigated and some new sufficient conditions are established.     

矩阵方程（AX，XB）=（C，D）的反中心对称解及其最佳逼近

本利用矩阵对的广义奇异值分解，得到了(AX，XB)=(C，D)有反中心对称解的充要条件，并给出了其通解的一般表达式，此外，还给出了此矩阵方程的解集合与给定矩阵的最佳逼近的表迭式．