A stepsize control algorithm for SDEs with small noise based on stochastic Runge–Kutta Maruyama methods

A variable stepsize control algorithm for solution of stochastic differential equations (SDEs) with a small noise parameter ?? is presented. In order to determine the optimal stepsize for each stage of the algorithm, an estimate of the global error is introduced based on the local error of the Stochastic Runge?CKutta Maruyama (SRKM) methods. Based on the relation of the stepsize and the small noise parameter, the local mean-square stochastic convergence order can be different from stage to stage. Using this relation, a strategy for producing and controlling the stepsize in the numerical integration of SDEs is proposed. Numerical experiments on several standard SDEs with small noise are presented to illustrate the effectiveness of this approach.     

Balanced fuzzy particle swarm optimization

In the present study an extension of particle swarm optimization (PSO) algorithm which is in conformity with actual nature is introduced for solving combinatorial optimization problems. Development of this algorithm is essentially based on balanced fuzzy sets theory. The classical fuzzy sets theory cannot distinguish differences between positive and negative information of membership functions, while in the new method both kinds of information “positive and negative” about membership function are equally important. The balanced fuzzy particle swarm optimization algorithm is used for fundamental optimization problem entitled traveling salesman problem (TSP). For convergence inspecting of new algorithm, method was used for TSP problems. Convergence curves were represented fast convergence in restricted and low iterations for balanced fuzzy particle swarm optimization algorithm (BF-PSO) comparison with fuzzy particle swarm optimization algorithm (F-PSO).     

Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities

In this paper, the problem of chaos synchronization between two different uncertain chaotic systems with input nonlinearities is investigated. Both master and slave systems are perturbed by model uncertainties, external disturbances and unknown parameters. The bounds of the model uncertainties and external disturbances are assumed to be unknown in advance. First, a simple linear sliding surface is selected. Then, appropriate adaptive laws are derived to tackle the model uncertainties, external disturbances and unknown parameters. Subsequently, based on the adaptive laws and Lyapunov stability theory, a robust adaptive sliding mode control law is designed to guarantee the existence of the sliding motion. Two illustrative examples are presented to verify the usefulness and applicability of the proposed technique.     

On Felbin-type Fuzzy 2-normed Spaces and Its Fuzzy Ⅰ-topologies

In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two Ⅰ-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy Ⅰ-topologie...     

Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method

The similarity transform for the steady three-dimensional problem of a condensation film on an inclined rotating disk gives a system of nonlinear ordinary differential equations which are analytically solved by applying a newly developed method namely the homotopy analysis method (HAM). The analytic solutions of the system of nonlinear ordinary differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. The velocity and temperature profiles are shown and the influence of the Prandtl number on the heat transfer and the Nusselt number is discussed in detail. The validity of our results is verified by numerical results.     

A nonlinear theory for shells with slowly varying thickness

We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface. To cite this article: M. Lewicka et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

A hybrid scatter search for the discrete time/resource trade-off problem in project scheduling

We develop a heuristic procedure for solving the discrete time/resource trade-off problem in the field of project scheduling. In this problem, a project contains activities interrelated by finish-start-type precedence constraints with a time lag of zero, which require one or more constrained renewable resources. Each activity has a specified work content and can be performed in different modes, i.e. with different durations and resource requirements, as long as the required work content is met. The objective is to schedule each activity in one of its modes in order to minimize the project makespan. We use a scatter search algorithm to tackle this problem, using path relinking methodology as a solution combination method. Computational results on randomly generated problem sets are compared with the best available results indicating the efficiency of the proposed algorithm.     

On element-centralizers in finite groups

For any group G, let |Cent(G)| denote the number of centralizers of its elements. A group G is called n-centralizer if |Cent(G)| = n. In this paper, we find |Cent(G)| for all minimal simple groups. Using these results we prove that there exist finite simple groups G and H with the property that |Cent(G)| = |Cent(H)| but ${G\not\cong H}$ . This result gives a negative answer to a question raised by A. Ashrafi and B. Taeri. We also characterize all finite semi-simple groups G with |Cent(G)| ≤  73.     

Evolutionary Algorithms for Approximate Optimal Control of the Heat Equation with Thermal Sources

In this paper, optimal control problem (OCP) governed by the heat equation with thermal sources is considered. The aim is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. To obtain an approximate solution of this problem, a partition of the time-control space is considered and the discrete form of the problem is converted to a quasi assignment problem. Then by using an evolutionary algorithm, an approximate optimal control function is obtained as a piecewise linear function. Numerical examples are given to show the proficiency of the presented algorithm.     

Uniqueness for inverse Sturm–Liouville problems with a finite number of transmission conditions

We establish various uniqueness results for inverse spectral problems of Sturm–Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the cases of classical Robin and of eigenparameter dependent boundary conditions.