胶原矿化与仿生修复

脊椎动物硬组织（牙和骨）是通过生命系统的矿化过程形成的,其中矿化胶原是这些生物材料的基本结构单元。矿化胶原是由胶原分子与纳米磷酸钙矿物形成的有机-无机复合材料,其所特有的纳米有序多级结构赋予了生物硬组织材料优异的机械性能（如硬度和韧性）。该结构特性和矿化过程可为新型硬组织修复材料制备提供有益的启示。其中,胶原纤维内有序矿化是仿生重构的难点,也是开展硬组织修复的关键。本文综述了骨的分层结构特征、胶原分子的组装和矿化胶原的多级结构特点,胶原分子和非胶原蛋白与磷酸钙材料的相互作用,功能调控分子对胶原和矿物的界面修饰,以及胶原矿化技术在硬组织修复中的应用;指出了目前胶原矿化亟须解决的一些关键问题,如调控无定形矿物进入胶原纤维、胶原矿化速度和程度,大规模有序胶原纤维制备等。     

Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation

This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitude-frequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.     

An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems

In this paper, an online algorithm is proposed for the identification of unknown time-varying input delay in the case of discrete non-linear systems described by decoupled multimodel. This method relies on the minimization of a performance index based on the error between the real system and the partial internal models outputs. In addition, a decoupled internal multimodel control is proposed for the compensation of discrete non-linear systems with time-varying delay. This control scheme incorporates partial internal model controls. Each partial controller is associated to a specified operating zone of the non-linear system. The switching between these controllers is ensured by a supervisor that contains a set of local predictors. A simulation example is carried out to illustrate the significance of the proposed time-varying delay identification algorithm and the proposed internal multimodel control scheme.     

A short survey on delay differential systems with periodic coefficients

In this survey, we collect a few results scatted in the literature covering advances in systems of periodic delay differential equations including both modeling and theory. We will present the (almost) most oldest and (almost) most recent contributions made for this subject.     

Global analysis in delayed ratio-dependent Gause-type predator-prey models

A class of three-dimensional delayed Gause-type predator-prey model with ratio-dependent is considered. Firstly, we present some results, including the boundedness of solutions and the permanence of system. Secondly, we construct a Lyapunov function to give the global asymptotically stable of the positive equilibrium under some parameter conditions. Finally, we analyed the influence of the time delay on the system and showed that the occurrence of small range of periodic motion.     

POSITIVE PERIODIC SOLUTIONS OF THE FIRST- ORDER SINGULAR DISCRETE SYSTEMS

In this paper, we study two kinds of first-order singular discrete systems. By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.     

An efficient step method for a system of differential equations with delay

Using the step method, we study a system of delay differential equations and we prove the existence and uniqueness of the solution and the convergence of the successive approximation sequence using the Perov''s contraction principle and the step method. Also, we propose a new algorithm of successive approximation sequence generated by the step method and, as an example, we consider some second order delay differential equations with initial conditions.     

An inventory model for non-instantaneous deteriorating items with quadratic demand rate and shortages under trade credit policy

noindent In this paper, we propose an appropriate inventory model for non-instantaneous deteriorating items over quadratic demand rate with permissible delay in payments and time dependent deterioration rate. In this model, the completely backlogged shortages are allowed. In several existing results, the authors discussed that the deterioration rate is constant in each cycle. However, the deterioration rate of items are not constant in real world applications. Motivated by this fact, we consider that the items are deteriorated with respect to time. To minimize the total relevant inventory cost, we prove some useful theorems to illustrate the optimal solutions by finding an optimal cycle time with the necessary and enough conditions for the existence and uniqueness of the optimal solutions. Finally, we discuss the numerical instance and sensitivity of the proposed model.     

Stability Analysis of an Enterprise Competitive Model with Time Delay

A three-dimensional enterprise competitive model with time delay is considered. Where the delay is regarded as bifurcation parameters. By analyzing the corresponding characteristic equation of positive equilibrium,the local stability of positive equilibrium is regarded. By using the normal form method and center manifold theorem, we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are shown to illustrate the obtained results.     

Global analysis for a delayed SIV model with direct and environmental transmissions

In this paper, we propose a new SIV epidemic model with time delay, which also involves both direct and environmental transmissions. For such model, we first introduce the basic reproduction number $\mathscr{R}$ by using the next generation matrix. And then global stability of the equilibria is discussed by means of Lyapunov functionals and LaSalle''s invariance principle for delay differential equations, which shows that the infection-free equilibrium of the system is globally asymptotically stable if $\mathscr{R}<1$ and the epidemic equilibrium of the system is globally asymptotically stable for $\m