Pull-in parameters of cantilever type nanomechanical switches in presence of Casimir force

In this paper, the effect of the Casimir force on pull-in parameters of cantilever type nanomechanical switches is investigated by using a distributed parameter model. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the Casimir and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. The integral equation is solved analytically by assuming an appropriate shape function for the beam deflection. The pull-in parameters of the switch are computed in three cases including nanoactuators without applied voltages, microswitches, and the general case of nanocantilevers. Nanoactuators without applied voltages are studied to determine the detachment length and the minimum initial gap of freestanding nanocantilevers, which are the basic design parameters for NEMS switches. The pull-in parameters of microswitches are investigated as a special case of our study by neglecting the Casimir effect and the results are verified through comparison with other works published in the literature. The general case of nanocantilevers is studied considering coexistence of the electrostatic and Casimir forces. The results of the distributed parameter model are compared with the lumped parameter model.     

与Selectins相关的细胞粘附及有关疾病的药物研究

本文阐述了细胞粘附分子select in s 的作用机制以及由此引起的各种疾病, 综述了近几年来有关select in s 细胞粘附抑制剂的研究进展。     

Resistance distance and the normalized Laplacian spectrum

It is well known that the resistance distance between two arbitrary vertices in an electrical network can be obtained in terms of the eigenvalues and eigenvectors of the combinatorial Laplacian matrix associated with the network. By studying this matrix, people have proved many properties of resistance distances. But in recent years, the other kind of matrix, named the normalized Laplacian, which is consistent with the matrix in spectral geometry and random walks [Chung, F.R.K., Spectral Graph Theory, American Mathematical Society: Providence, RI, 1997], has engendered people's attention. For many people think the quantities based on this matrix may more faithfully reflect the structure and properties of a graph. In this paper, we not only show the resistance distance can be naturally expressed in terms of the normalized Laplacian eigenvalues and eigenvectors of G, but also introduce a new index which is closely related to the spectrum of the normalized Laplacian. Finally we find a non-trivial relation between the well-known Kirchhoff index and the new index.     

Large time behavior of solutions to a class of doubly nonlinear parabolic equations

We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u _t = div(u ^m−1|Du| ^p−2 Du) − u ^q with an initial condition u(x, 0) = u ₀(x). Here the exponents m, p and q satisfy m + p ⩾ 3, p > 1 and q > m + p − 2. The paper was supported by NSF of China (10571144), NSF for youth of Fujian province in China (2005J037) and NSF of Jimei University in China.     

Numerical simulation of the fractional-order control system

Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractionalorder dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.     

两种多酸型酪氨酸酶抑制剂的性能研究

以H₃PW₁₂O₄₀和H₄SiW₁₂O₄₀(简写为PW₁₂和SiW₁₂)为效应物, 测定其对酪氨酸酶活力的抑制作用. 通过非变性聚丙烯凝胶(Native-PAGE)电泳确定酪氨酸酶是多家族基因编码, 其分子量为3×10⁴~3.4×10⁴, 4.2×10⁴~4.6×10⁴, 6.4×10⁴~6.8×10⁴, 且均具有活性, 测定PW₁₂和SiW₁₂对酪氨酸酶的抑制效果, 并结合酶动力学法研究其抑制机理. 结果表明, 当PW₁₂和SiW₁₂浓度分别达到13和25 mmol/L时, 酪氨酸酶的活力完全被抑制, 即PW₁₂和SiW₁₂对酪氨酸酶二酚酶具有不同程度的抑制效果. 当所加酶量为0.0173 mg/mL时, PW₁₂和SiW₁₂对酪氨酸酶二酚酶活力的半抑制率 (IC₅₀)分别为1.57和2.31 mmol/L, 它们对酪氨酸酶二酚酶的抑制均为可逆过程. 其中, PW₁₂对二酚酶的抑制类型为混合型, 其K_I及K_IS分别为0.34和0.43 mmol/L, SiW₁₂对二酚酶的抑制类型表现为竞争型, 其K_I为0.59 mmol/L. 综合考虑IC₅₀值和抑制常数等参数, PW₁₂对酪氨酸酶二酚酶的抑制能力优于SiW₁₂.     

Fixed point theorems of multivalued monotone mappings in ordered metric spaces

In this work, some new fixed point and coupled fixed point theorems for multivalued monotone mappings in ordered metric spaces are proved.     

The Tangent cones on constraint qualifications in optimization problems

This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of cones on the constraint qualifications are presented.The interrelations among the constraint qualifications,a few cones involved, and level sets of upper and lower directional derivatives are derived.     

Qualitative analysis and applications of a kind of state-dependent impulsive differential equations

This paper analyzes a certain type of impulsive differential equations (IDEs). Several useful theorems for its periodic solutions and their stabilities are given. The key idea is that a periodically time-dependent IDE can be transformed into the state-dependent IDE. As applications of our theory, the optimization problems in population dynamics are studied. That is, the maximum sustainable yields of single population models with periodically impulsive constant harvesting are discussed. Furthermore, we apply these results to the studies of the order-1 periodic solutions and their stability of a single population model with stage structure in which the mature is impulsively proportionally harvested while the immature is impulsively added with the constant.     

Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain

In this paper, we propose and study a model of a hybrid ratio-dependent three species food chain, which is constituted by a hybrid type subsystem of prey and middle-predator and a middle-top predators’ subsystem with Holling type-II functional response. We investigate the persistence and Hopf bifurcation of the system. Computer simulations are carried out to explain the mathematical conclusions. The chaotic attractor is obtained for suitable choice of parametric values.