A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge

This paper considers a two-stage distribution problem of a supply chain that is associated with a fixed charge. Two kinds of cost are involved in this problem: a continuous cost that linearly increases with the amount transported between a source and a destination, and secondly, a fixed charge, that incurs whenever there exists a transportation of a non-zero quantity between a source and a destination. The objective criterion is the minimisation of the total cost of distribution. A genetic algorithm (GA) that belongs to evolutionary search heuristics is proposed and illustrated. The proposed methodology is evaluated for its solution quality by comparing it with the approximate and lower bound solutions. Thus, the comparison reveals that the GA generates better solution than the approximation method and is capable of providing solution either equal or closer to the lower bound solution of the problem.     

非均匀介质GL型热弹性问题解的存在唯一性

We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo-Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.     

A hybrid algorithm for nonlinear minimax problems

In this paper, a hybrid algorithm for solving finite minimax problem is presented. In the algorithm, we combine the trust-region methods with the line-search methods and curve-search methods. By means of this hybrid technique, the algorithm, according to the specific situation at each iteration, can adaptively performs the trust-region step, line-search step or curve-search step, so as to avoid possibly solving the trust-region subproblems many times, and make better use of the advantages of different methods. Moreover, we use second-order correction step to circumvent the difficulties of the Maratos effect occurred in the nonsmooth optimization. Under mild conditions, we prove that the new algorithm is of global convergence and locally superlinear convergence. The preliminary experiments show that the new algorithm performs efficiently.     

Approximate solution of the Fredholm integral equation of the first kind in a reproducing kernel Hilbert space

An approach for solving Fredholm integral equations of the first kind is proposed for in a reproducing kernel Hilbert space (RKHS). The interest in this problem is strongly motivated by applications to actual prospecting. In many applications one is puzzled by an ill-posed problem in space C[a,b] or L²[a,b], namely, measurements of the experimental data can result in unbounded errors of solutions of the equation. In this work, the representation of solutions for Fredholm integral equations of the first kind is obtained if there are solutions and the stability of solutions is discussed in RKHS. At the same time, a conclusion is obtained that approximate solutions are also stable with respect to _∞ or _L² in RKHS. A numerical experiment shows that the method given in the work is valid.     

NON-STANDARD COMMUTATORS FOR ROUGH OSCILLATORY SINGULAR INTEGRALS

In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 〈 p 〈 ∞, the L^p-boundedness of such operators are obtained provided that their kernels belong to the spaces L^q（s^n-1） for some q 〉 1.     

The boundary value problem and the Jensen inequality for an entropy functional of a Markov diffusion process

The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, expressed through an additive functional of the diffusion process, with a Lagrangian, determined by the parameters of a controlled stochastic equation. These results include a minimum condition for the entropy functional and the functional's Jensen inequality, which both are useful for the solution of important mathematical and applied problems.     

On the index of the boundary value problem for a homogeneous Hamiltonian system of differential equations

The index of the homogeneous self-adjoint boundary value problem for the Hamiltonian systems of ordinary differential equations is introduced. It is assumed that the system has a nontrivial solution. The relationship between the index of an eigenvalue of the nonlinear eigenvalue problem and the index of the corresponding homogeneous problem is established. Properties of the index of the problem and those of the eigenvalue are examined.     

弱Hardy空间上的参数型Marcinkiewicz积分

证明了参数型Marcinkiewicz积分μΩ^p是（H^p,∞ , L^p,∞）（0〈p≤1）型的算子，这里Ω是满足Lipα条件的R^＊上的零次齐次函数．对于p=1，减弱了Ω的条件μΩ^p得到μΩ^p是（H^1,∞ , L^1,∞）型的．作为上述结果的推论，得到了μΩ^p是弱（1，1）型的算子．     

Computing finest mincut partitions of a graph and application to routing problems

Let G=(V,E,w) be an n-vertex graph with edge weights w>0. We propose an algorithm computing all partitions of V into mincuts of G such that the mincuts in the partitions cannot be partitioned further into mincuts. There are O(n) such finest mincut partitions. A mincut is a non-empty proper subset of V such that the total weight of edges with exactly one end in the subset is minimal. The proposed algorithm exploits the cactus representation of mincuts and has the same time complexity as cactus construction. An application to the exact solution of the general routing problem is described.     

Pauli problem and related mathematical problems

We formulate several mathematical modifications of the Pauli problem of recovering the particle state from the results of measuring its coordinates and momenta, including the most abstract statement of the problem for two projection-valued measures. We describe how the Pauli problem reduces to the problem of finding the eigenvectors of certain operators. The performed analysis introduces the problems of modifications of Pauli pairs, and the considered topics and formulated problems require further study. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 3–7, October, 2008.