Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

关于特征函数T(r,f)与T(r,1/f)的关系

本文研究亚纯函数f(z)与1/f(z)的特征函数T(r,f)与T(r,1/f)之间的关系。由Jensen公式推导出了它们的关系式,从而证明了特征函数T(r,f)与T(r,1/f)之间只相差一个常数。     

时变线性系统特征根判稳的推广

本文研究了二维时变线性系统零解的稳定性，给出了一些允许系数矩阵主对角元变号，系数矩阵特征根变号的判定稳定性的充分条件。     

Fiberings with Fiber RP（κ）

Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP（ξ^κ）] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.     

一类图的特征多项式与匹配多项式

本文对一类具有对称轴的图A_n(n≥0),得到了它的特征多项式及匹配多项式的精确表达式;同时还得到A_(?)的完美匹配数。     

The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay

In this paper, we consider an autonomous predator-prey Lotka-Volterra system in which individuals in the population may belong to one of two classes: the immatures and the matures, the age to maturity is represented by a time delay. By using eigenvalue analysis, principal term analyze method, reduction to absurdity, and iterative method, we obtain some simple conditions for global asymptotic stability of the unique positive equilibrium point. Moreover, a condition that the prey population in the system get extinction and the predator population in the system get permanence will be obtained. Meanwhile the theorems extend the corresponding conclusions in which there have no two stage structures.     

线性常微分方程组解的特征数的估计

复数域上线性系统ｘ＝Ａ（ｔ）ｘ，当Ａ（ｔ）＝（ａｉｊ（ｔ））ｎ×ｎ具有（ｎ，Ｎ，ｒ） 差异性质且ｒｎ时，解的特征数ｊ有估计λｊ－ｌｉｍｔ→∞１ｔ∫ｔｔ０Ｒｅａｊ（τ）ｄτｎ－１ｒ＋１－ｎｌｉｍｔ→∞１ｔ∫ｔｔ０Ａ（τ）ｄτ，ｊ＝１，２，…，ｎ，其中Ａ（ｔ）＝ｍａｘ｛｜ａｉｊ（ｔ）｜：ｉ，ｊ＝１，２，…，ｎ，ｉ≠ｊ．｝     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.     

欧拉示性数在确定不动点方面的一些应用

本文根据空间的欧拉示性数是否为零．来确定该空间的自映射是否有不动点的几个方面的应用。