Dimension estimate of the global attractor for a semi-discretized chemotaxis-growth system by conservative upwind finite-element scheme

In this paper we continue systematic study of the dimension estimate of the global attractors for the chemotaxis-growth system and its finite-element approximations. Utilizing a conservative upwind finite-element scheme we managed significantly to improve dimension estimates with respect to the chemotactic parameter.     

一类奇异拟线性椭圆型方程组的可解性

研究了一类P-Laplacian方程组边值问题正径向整体解的存在性和唯一性.首先,利用隐函数定理证明了该问题的局部解的存在性与唯一性,以及解对初值的连续依赖性.最后,证明了该问题存在唯一的正径向整体解.     

Univariate Global Optimization with Multiextremal Non-Differentiable Constraints Without Penalty Functions

This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints can lead to complex feasible regions being collections of isolated points and intervals having positive lengths. The case is considered where the order the constraints are evaluated is fixed by the nature of the problem and a constraint i is defined only over the set where the constraint i−1 is satisfied. The objective function is defined only over the set where all the constraints are satisfied. In contrast to traditional approaches, the new algorithm does not use any additional parameter or variable. All the constraints are not evaluated during every iteration of the algorithm providing a significant acceleration of the search. The new algorithm either finds lower and upper bounds for the global optimum or establishes that the problem is infeasible. Convergence properties and numerical experiments showing a nice performance of the new method in comparison with the penalty approach are given. This research was supported by the following grants: FIRB RBNE01WBBB, FIRB RBAU01JYPN, and RFBR 04-01-00455-a. The author thanks Prof. D. Grimaldi for proposing the application discussed in the paper. An erratum to this article is available at .     

An ILP based hierarchical global routing approach for VLSI ASIC design

The use of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been growing at a very fast pace. The level of integration as measured by the number of logic gates in a chip has been steadily rising due to the rapid progress in processing and interconnect technology. The interconnect delay in VLSI circuits has become a critical determiner of circuit performance. As a result, circuit layout is starting to play a more important role in today’s chip designs. Global routing is one of the key sub-problems of circuit layout which involves finding an approximate path for the wires connecting the elements of the circuit without violating resource constraints. In this paper, several integer programming (ILP) based global routing models are fully investigated and explored. The resulting ILP problem is relaxed and solved as a linear programming (LP) problem followed by a rounding heuristic to obtain an integer solution. Experimental results obtained show that the proposed combined WVEM (wirelength, via, edge capacity) model can optimize several global routing objectives simultaneously and effectively. In addition, several hierarchical methods are combined with the proposed flat ILP based global router to reduce the CPU time by about 66% on average for edge capacity model (ECM).     

Asymptotic stability of the relativistic Maxwellian

Global classical solutions near the relativistic Maxwellian are constructed for the relativistic Boltzmann equation in both a periodic box and the whole space. For both cases, we are able to get the non‐negativity of the global solution under less restriction than in (Publ. Res. Inst. Math. Sci. 1993; 29 :301–347) on the scattering kernel. Copyright © 2006 John Wiley & Sons, Ltd.     

One-leg variable-coefficient formulas for ordinary differential equations and local–global step size control

In this paper we discuss a class of numerical algorithms termed one-leg methods. This concept was introduced by Dahlquist in 1975 with the purpose of studying nonlinear stability properties of multistep methods for ordinary differential equations. Later, it was found out that these methods are themselves suitable for numerical integration because of good stability. Here, we investigate one-leg formulas on nonuniform grids. We prove that there exist zero-stable one-leg variable-coefficient methods at least up to order 11 and give examples of two-step methods of orders 2 and 3. In this paper we also develop local and global error estimation techniques for one-leg methods and implement them with the local–global step size selection suggested by Kulikov and Shindin in 1999. The goal of this error control is to obtain automatically numerical solutions for any reasonable accuracy set by the user. We show that the error control is more complicated in one-leg methods, especially when applied to stiff problems. Thus, we adapt our local–global step size selection strategy to one-leg methods.     

具有功能性反应的非自治竞争系统的持续性

本文讨论了具有 类功能性反应的非自治扩散竞争系统 .在一定条件下证明了系统是持续的 ,给出了系统全局渐近稳定的充分条件 .     

一个带毒生化反应竞争模型正平衡解的全局稳定性

研究两个微生物竞争同一营养,而其中一个竞争者会产生毒素抑制另一竞争者且产物系数γi(S)(i=1,2)为一般的非减可导函数时的生化反应模型,指出两篇文献中存在的问题,分析系统平衡点的稳定性,三维系统经历Hopf分支的条件和由此产生的周期解的稳定性.证明系统中某一微生物物种处于竞争劣势而趋于灭绝时另一微生物物种和营养在二维稳定流形上极限环的存在性.并用具体的实例验证文中所得结论.     

在分子晶体中的一类广义非线性Schroedinger方程组的初边值问题

研究了在分子晶体中的一类广义非线性Schroedinger方程组的初边值问题．应用先验估计的方法，得到了整体解的存在性．     

广义Kuramoto-Sivashinsky方程强解的全局吸引子的存在性

Using a new method developed in[5],we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H3per(Ω)and H4per(Ω).