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1.
Transfinite electrical networks have unique finite-powered voltage-current regimes given in terms of branch voltages and branch currents, but they do not in general possess unique node voltages. However, if their structures are sufficiently restricted, those node voltages will exist and will satisfy a maximum principle much like that which holds for ordinary infinite electrical networks. The structure that is imposed in order to establish these results generalized the idea of local-finiteness. Other properties that do not hold in general for transfinite networks but do hold under the imposed structure are Kirchhoff's current laws for nodes of any ranks and the permissibility of connecting pure voltage sources to such nodes. This work lays the foundation for a theory of transfinite random walks, which will be the subject of a subsequent work.This work was supported by the National Science Foundation under the grants DMS-9200738 and MIP-9200748.  相似文献   

2.
In this paper, we study the spreading of epidemics on scale-free networks with infectivity which is nonlinear in the connectivity of nodes. We will show that the nonlinear infectivity is more appropriate than constant or linear ones, and give the epidemic threshold of the SIS model on a scale-free network with nonlinear infectivity. In addition, we compare the effects of nonlinear infectivity on the epidemic threshold with two other cases on infinite and finite scale-free networks, and find some new results, such as: with unit recovery rate and nonlinear irrational infectivity, the epidemic threshold is always positive; and the epidemic threshold can increase with network size on finite networks, contrary to the findings in all previous work.  相似文献   

3.
The Adomian’s decomposition method and the homotopy perturbation method are two powerful methods which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. By theoretical analysis of the two methods, we show, in the present paper, that the two methods are equivalent in solving nonlinear equations.  相似文献   

4.
We consider the minimization problem for the functional where is an infinitely long cylinder. The density is polyconvex and assumed to be 0 on a set of wells and positive elsewhere. We show that the gradients of solutions with finite energy have to approach one component for and one component for , if the number of components is finite (among other conditions). Moreover, for certain pairs of distinct components we construct nontrivial minimizers within the class of solutions approaching the given components. We follow ideas developed in the variational study of heteroclinic connections for Lagrangian systems and we put special emphasis on multiplicity of such interface solutions. We discuss an application in the theory of nonlinear elasticity, where such solutions are called semi-necks. When a two-dimensional infinite hyperelastic strip is stretched along its infinite direction it may occur that for a given tensile load many homogeneous deformations are possible. In such a case we show by infimizing the energy functional the existence of configurations that tend asymptotically to two different homogeneous deformations. Received: 1 March 2000 / Accepted: 4 December 2000 / Published online: 4 May 2001  相似文献   

5.
Given a nonlinear infinite resistive network, an operating point can be determined by approximating the network by finite networks obtained by shorting together various infinite sets of nodes, and then taking a limit of the nodal potential functions of the finite networks. Initially, by taking a completion of the node set of the infinite network under a metric given by the resistances, limit points are obtained that represent generalized ends, which we call ``terminals,' of the infinite network. These terminals can be shorted together to obtain a generalized kind of node, a special case of a 1-node. An operating point will involve Kirchhoff's current law holding at 1-nodes, and so the flow of current into these terminals is studied. We give existence and bounds for an operating point that also has a nodal potential function, which is continuous at the 1-nodes. The existence is derived from the said approximations.

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6.
Summary In this paper we establish the existence of extremal solutions for a class of nonlinear evolution inclusions defined on an evolution triple of Hilbert spaces. Then we show that these extremal solutions are in fact dense in the solutions of the original system. Subsequently we use this density result to derive nonlinear and infinite dimensional versions of the bang-bang principle for control systems. An example of a nonlinear parabolic distributed parameter system is also worked out in detail.  相似文献   

7.
In this paper, we consider the nonlinear control systems of fractional order and its optimal controls in Banach spaces. Using the fractional calculus, Hölder’s inequality, p-mean continuity, weakly singular inequality and Leray-Schauder’s fixed point theorem with compact mapping, the sufficient condition is given for the existence and uniqueness of mild solutions for a broad class of fractional nonlinear infinite dimensional control systems. Utilizing the approximately lower semicontinuity of integral functionals and weakly compactness, we extend the existence result of optimal controls for nonlinear control systems to nonlinear fractional control systems under generally mild conditions. An example is given to illustrate the effectiveness of the results obtained.  相似文献   

8.
We study sequences of 3-dimensional solutions to the Ricci flow with almost nonnegative sectional curvatures and diameters tending to infinity. Such sequences may arise from the limits of dilations about singularities of Type IIb. In particular, we study the case when the sequence collapses, which may occur when dilating about infinite time singularities. In this case we classify the possible Gromov-Hausdorff limits and construct 2-dimensional virtual limits. The virtual limits are constructed using Fukaya theory of the limits of local covers. We then show that the virtual limit arising from appropriate dilations of a Type IIb singularity is always Hamilton's cigar soliton solution. Partially supported by NSF grant DMS-0203926.  相似文献   

9.
《偏微分方程通讯》2013,38(7-8):1265-1301
Abstract

We present sharp decay rates as time tends to infinity for solutions to linear Kleinc-Gordon and wave equations in domains with infinite boundaries like infinite waveguides, as well as the global well-posedness and the asymptotics for small data for the solutions to the associated nonlinear initial-boundary value problems.  相似文献   

10.
In this paper, we present a new receding horizon neural robust control scheme for a class of nonlinear systems based on the linear differential inclusion (LDI) representation of neural networks. First, we propose a linear matrix inequality (LMI) condition on the terminal weighting matrix for a receding horizon neural robust control scheme. This condition guarantees the nonincreasing monotonicity of the saddle point value of the finite horizon dynamic game. We then propose a receding horizon neural robust control scheme for nonlinear systems, which ensures the infinite horizon robust performance and the internal stability of closed-loop systems. Since the proposed control scheme can effectively deal with input and state constraints in an optimization problem, it does not cause the instability problem or give the poor performance associated with the existing neural robust control schemes.  相似文献   

11.
In this paper,we first introduce the concept of k-globally asymptotic stabi- lity and present a differential-difference inequality with infinite delay.By com- bining nonlinear inequality and nonlinear variation-of-parameters formula,we derive the k-globally asymptotic stability criteria for nonlinear neutral system with infinite delay.In the end of this paper,an example is given to illustrate our theory.  相似文献   

12.
In this paper we exhibit axiomatizations for the theories of existentially closed posets and existentially closed semilattices. We do this by considering an infinite axiomatization which characterizes these structures in terms of embeddings of finite substructures, an axiomatization which exists for any locally finite universal class with a finite language and with the joint embedding and amalgamation properties. We then find particular finite subsets of these axioms which suffice to axiomatize both classes. Research supported by an NSERC Postdoctoral Fellowship. Research supported by NSERC Grant No. A7256.  相似文献   

13.
We determine the critical blow-up exponent for a Keller-Segel-type chemotaxis model, where the chemotactic sensitivity equals some nonlinear function of the particle density. Assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution. Furthermore, we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails.  相似文献   

14.
双环网是计算机互连网络和通讯系统的一类重要拓扑结构,已广泛应用于计算机互连网络拓扑结构的设计中.利用L形瓦理论,结合中国剩余定理和二次同余方程的性质,给出了不同于参考文献中的任意k紧优双环网的无限族的构造方法,证明了对任意正整数k,若n(t)=3t2 At B,A=1,3,5,对于一定的B>(k 1)2,均存在正整数t,使得{G(n(t);s(t))}是k紧优双环网的无限族,而且这样的无限族有无穷多类.作为定理的应用,给出了多类新的k紧优双环网的无限族.  相似文献   

15.
Two-dimensional optical orthogonal codes (2-D OOCs) are of current practical interest in fiber-optic code-division multiple-access networks as they enable optical communication at lower chip rate to overcome the drawbacks of nonlinear effects in large spreading sequences of one-dimensional codes. A 2-D OOC is said to be optimal if its cardinality is the largest possible. In this paper, we develop some constructions for optimal 2-D OOCs using combinatorial design theory. As an application, these constructions are used to construct an infinite family of new optimal 2-D OOCs with auto-correlation 1 and cross-correlation 1.  相似文献   

16.
We exhibit linear problems for which every linear algorithm has infinite error, and show a (mildly) nonlinear algorithm with finite error. The error of this nonlinear algorithm can be arbitrarily small if appropriate information is used. We illustrate these examples by the inversion of a finite Laplace transform, a problem arising in remote sensing.  相似文献   

17.
本文给出了一种方法用于构造k-紧优双环网络无限族(k≥1),并用此方法构造出了4族3-紧优无限族,3族新的4-紧比无限族,3族5-紧优无限族及2族6-紧优无限族.  相似文献   

18.
In this paper we obtain for the first time nonlinear conditions for the existence of the exponential trichotomy of skew-product flows in infinite dimensional spaces. We treat the most general case without any additional assumptions concerning the cocycle and without assuming a priori the existence of the projection families. We show that an inedit assembly of integral conditions imply the existence of the exponential trichotomy with all of its properties and we prove that the imposed conditions are also necessary. Our results generalize the previous studies on this topic and provide as particular cases many interesting situations, among which we mention the detection of the exponential trichotomy of general non-autonomous systems.  相似文献   

19.
复杂动态网络的有限时间同步   总被引:1,自引:0,他引:1  
陈姚  吕金虎 《系统科学与数学》2009,29(10):1419-1430
复杂网络无处不在,同步是自然界中广泛存在的一类非常重要的非线性现象.过去10年,人们对复杂网络的同步开展了系统而深入的研究,包括恒等同步、广义同步、簇同步以及部分同步等.上述大部分结果中对同步速度的刻画往往是渐进的,只有当时间趋于无穷的时候,网络才能实现同步,而对于网络能够在多长时间内可以实现同步却知之甚少.作者以几类典型的非线性耦合的复杂动态网络为例,深入探讨了复杂动态网络的有限时间同步的规律.具体而言,基于上述几类典型的复杂动态网络,证明了在某些合适的条件下,网络能够在有限时间内实现精确同步.此外,用一个典型的数值仿真实例验证了上述有限时间同步的准则.有限时间同步有效地避免了网络只有在无穷时刻才能实现同步的问题,对网络同步的实际工程应用具有基本的现实意义.  相似文献   

20.
We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit no nonnegatively curved metrics. Received February 11, 2000 / Published online February 5, 2001  相似文献   

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