On the numerical solution of a certain class of non-linear cauchy problems arising from integral equation theory

Summary A numerical algorithm for solving a system of non-linear partial differential integral equations is presented. These equations result from applying the method of invariant imbedding to the solution of a certain class ofFredholm integral equations of the second kind [2]. The algorithm is compared with a more standard method of solution and some numerical results presented.     

On the analysis and solution of certain geographical optimal covering problems

The article formulates, analyses and suggests solutions to some optimal covering problems that often arise in association with geographical coordinates, albeit their mathematical form may be detached from this background. It shows that under a general formulation no favorable mathematical properties can be deduced beyond the “center of gravity”, and thus that computational algorithms are seemingly the best resort for resolving the problem. An algorithm that is based on the steepest descent approach and that exploits the “center of gravity” property is devised, and is shown as a detector of local minima points. A release from the “locality trap” is provided by a stochastic algorithm.Every part of the paper is accompanied by illustrative examples, either of an analytical nature on a segment of the real line or of a numerical nature by computer programs.     

Effective diagonalization strategies for the solution of a class ofoptimal design problems

It is shown that it is possible to obtain optimal diagonalization strategies for the discretization of semiinfinite minimax optimal design problems. Both exact and approximate methods for the computation of these optimal diagonalization strategies are proposed. The algorithms for computing approximate diagonalization strategies yield very good approximations in much less computing time than needed to compute an optimal diagonalization strategy exactly. The proposed diagonalization strategies can be implemented by using estimation schemes to obtain approximations to the various quantities which determine an optimal strategy. Experimental results, involving the solution of optimal loop-shaping problems for multivariable linear feedback systems, show that the use of these implementable strategies leads to considerable savings in computer time over alternative approaches     

Complexity of some problems in Petri nets

We consider the complexity of several standard problems for various classes of Petri nets. In particular, the reachability problem, the liveness problem and the k-boundedness problems are analyzed. Some polynomial time and polynomial space complete problems for Petri nets are given. We then show that the problem of deciding whether a Petri net is persistent is reducible to reachability, partially answering a question of Keller. Reachability and boundedness are proved to be undecidable for the Time Petri net introduced by Merlin. Also presented is the concept of controllability, i.e., the capability of a set of transitions to disable a given transition. We show that the controllability problem requires exponential space, even for 1-bounded nets.     

Non-polynomial spline for solution of boundary-value problems in plate deflection theory

In this paper a non-polynomial quintic spline function is applied to the numerical solution of a certain fourth-order, two-point boundary-value problem occurring in plate deflection theory. Direct methods of orders two, four, and six have been obtained which lead to five-diagonal linear systems. Boundary formulae of various orders have been developed to retain the bandwidth of the coefficient matrix as five. Convergence analysis of the sixth-order method is given. Numerical results are provided to demonstrate the superiority of our methods.     

Queueing Petri nets with product form solution

The product form results recently published for stochastic Petri nets are combined with the well-known product form results for queueing networks in the model formalism of queueing Petri nets yielding the class of product form queueing Petri nets. This model class includes stochastic Petri nets with product form solution and BCMP queueing networks as special cases. We introduce an arrival theorem for the model class and present an exact aggregation approach extending known approaches from queueing networks.     

一种模糊Petri网参数优化的有效算法

以蚁群算法为基础,提出了一种带交叉、变异因子的模糊Petri网参数值寻优的有效方法。仿真实验的结果表明,新算法无需依赖经验数据,有效找到模糊Petri网的理想参数,从而提高了模糊Petri网对知识的分析和推理能力。     

Product form solution for generalized stochastic Petri nets

In this paper, we show the structural characteristics that a particular class of generalized stochastic Petri nets must exhibit in order for their stationary probabilities to have a product-form. Sufficient conditions for identifying such a class are derived and proven with the development of a series of transformations that can also be used to construct, for any GSPN of the class, an equivalent SPN. These resulting SPNs represent the structures that can be analyzed with standard methods for product-form SPNs to establish whether the original GSPNs have product-form solutions and to compute their performance indices with effective approaches based on computationally efficient algorithms that avoid the generation of their underlying state spaces.     

A solution strategy for distributed uncertain economic dispatch problems via scenario theory

In this paper, an uncertain economic dispatch problem (EDP) is considered for a group of coopertive agents. First, let eachagent extract a set of samples (scenarios) from the uncertain set, and then a scenario EDP is obtained using these scenarios.Based on the scenario theory, a prior certification is provided to evaluate the probabilistic feasibility of the scenario solutionfor uncertain EDP. To facilitate the computational task, a distributed solution strategy is proposed by the alternating directionmethod of multipliers (ADMM) and a finite-time consensus strategy. Moreover, the distributed strategy can solve thescenario problem over a weight-balanced directed graph. Finally, the proposed solution strategy is applied to an EDP for apower system involving wind power plants.     

Large finite elements method for the solution of problems in the theory of elasticity

In contrast to conventional finite element (CFE) formulations, the large finite element (LFE) concept is based on subdividing the region under consideration into a small number of LFE and using in each of them an appropriate parametric displacement field such that the governing differential problem equations are satisfied a priori (Trefftz's method). Where relevant, known local solutions in the vicinity of a stress concentration or stress singularity are used as a convenient expansion basis. The boundary conditions, as well as the continuity across the interfaces, are implicitly imposed by an appropriate variational functional.

The LFE concept attempts to combine the flexibility of the conventional FE method with the accuracy and high convergence rate of the Trefftz's method. The paper summarises the principal results obtained and shows that the practical efficiency of the LFE analysis is superior to a CFE solution, for both regular and singular problems.