中立型向量双曲偏微分方程的H-振动性

本文研究了一类中立型向量双曲偏微分方程边值问题的振动性.利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维泛函微分不等式正解的不存在性问题,获得了该类边值问题在Dirichlet边界条件下所有解H-振动的若干新的充分条件,其中H是Rm中的单位向量.     

具x/ζ型卷积核的奇异积分方程的求解

讨论了具x/ζ型卷积核的奇异积分方程的求解问题.通过Fourier积分变换,将所讨论的积分方程转化成在一定可解条件下与其同解意义下等价的Riemann边值问题.利用Riemann边值问题理论,分别讨论了在正则和非正则两种情况下的Riemann边值问题,进而得到相对应的x/ζ变量比型卷积核的积分方程一般解及可解条件.     

脉冲向量中立型抛物方程解的H-振动性

研究一类脉冲向量中立型抛物偏微分方程边值问题解的振动性,利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲中立型微分不等式正解的不存在性问题,并借助于一阶脉冲中立型微分不等式,给出了该类边值问题所有解H-振动的若干充分性判据,这里H是R~M中的单位向量.     

非正则型Hilbert边值问题

本文考虑了解析函数非正则型的Hilbert边值问题．利用对称扩张法将问题化为等价的正则型Riemann边值问题，获得了问题的通解及可解性条件，同时给出了问题可解的一个必要条件．     

二阶Sturm-Liouville型边值问题正解的三解定理

利用Leggett-Williams不动点定理得到了一类二阶Sturm-Liouville型边值问题正解的存在性.得到了所研究问题至少存在三个正解的充分条件.     

解抛物型方程的高精度显式差分格式

在渗流、扩散、热传导等邻域中经常会遇到求解抛物型方程的问题.在一维情形,其模型为如下初边值问题:     

抛物型边值反问题中的伪概周期解

首先推广伪概周期函数的定义, 然后对一种抛物型边值问题的反问题, 证明了伪概周期解的存在性, 唯一性和稳定性.     

双曲-双曲奇异摄动问题的指数型拟合差分格式

本文讨论带有关于x的一阶导数项的双曲奇异摄动初边值问题,在较弱的相容性条件下构造了问题的渐近解并证明了解的一致有效性.然后我们对原问题构造一个指数型拟合差分格式并建立了离散能量不等式.最后我们证明差分问题的解一致收敛于原问题的精确解.     

Hilfer-Katugampola序列分数阶微分方程边值问题Lyapunov型不等式

研究了Hilfer-Katugampola序列分数阶微分方程多点边值问题Lyapunov型不等式.首先,利用Hilfer-Katugampola分数阶微积分的定义和性质将HilferKatugampola序列分数阶微分方程边值问题等价转化为带有Green函数的积分方程问题.其次,定义相应的Banach空间并结合先验估计方法得到了Lyapunov型不等式.最后,通过给出一系列推论说明该文研究结果推广和丰富了已有文献相关工作.     

一类二阶Sturm-Liouville型边值问题多个正解的存在性

本文研究了具p-Laplace算子的二阶Sturm-Liouville型边值问题,利用锥上的不动点定理得到了所研究问题多个正解的存在性.     

Using tropical optimization to solve minimax location problems with a rectilinear metric on the line

Methods of tropical (idempotent) mathematics are applied to the solution of minimax location problems under constraints on the feasible location region. A tropical optimization problem is first considered, formulated in terms of a general semifield with idempotent addition. To solve the optimization problem, a parameter is introduced to represent the minimum value of the objective function, and then the problem is reduced to a parametrized system of inequalities. The parameter is evaluated using existence conditions for solutions of the system, whereas the solutions of the system for the obtained value of the parameter are taken as the solutions of the initial optimization problem. Then, a minimax location problem is formulated to locate a single facility on a line segment in the plane with a rectilinear metric. When no constraints are imposed, this problem, which is also known as the Rawls problem or the messenger boy problem, has known geometric and algebraic solutions. For the location problems, where the location region is restricted to a line segment, a new solution is obtained, based on the representation of the problems in the form of the tropical optimization problem considered above. Explicit solutions of the problems for various positions of the line are given both in terms of tropical mathematics and in the standard form.     

Quasi-classical asymptotics of solutions to the matrix factorization problem with quadratically oscillating off-diagonal elements

The paper investigates the asymptotic behavior of solutions to the 2 × 2 matrix factorization (Riemann-Hilbert) problem with rapidly oscillating off-diagonal elements and quadratic phase function. A new approach to study such problems based on the ideas of the stationary phase method and M. G. Krein’s theory is proposed. The problem is model for investigating the asymptotic behavior of solutions to factorization problems with several turning points. Power-order complete asymptotic expansions for solutions to the problem under consideration are found. These asymptotics are used to construct asymptotics for solutions to the Cauchy problem for the nonlinear Schrödinger equation at large times.     

Maximally Disjoint Solutions of the Set Covering Problem

This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP-complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, extensive computational tests are given demonstrating the nature of these algorithms. These tests are carried out both on randomly generated problems and on problems found in the literature.     

On Solvability of Some Initial-Boundary Problems for Mathematical Models of the Motion of Nonlinearly Viscous and Viscoelastic Fluids

In the paper, the settings of initial-boundary and initial value problems arising in a number of models of movement of nonlinearly viscous or viscoelastic incompressible fluid are considered, and existence theorems for these problems are presented. In particular, the settings of initial-boundary value problems appearing in the regularized model of the movement of viscoelastic fluid with Jeffris constitutive relation are described. The theorems for the existence of weak and strong solutions for these problems in bounded domains are given. The initial value problem for a nonlinearly viscous fluid on the whole space is considered. The estimates on the right-hand side and initial conditions under which there exist local and global solutions of this problem are presented. The modification of Litvinov's model for laminar and turbulent flows with a memory is described. The existence theorem for weak solutions of initial-boundary value problem appearing in this model is given.     

Solution of bilevel optimization problems using the KKT approach

ABSTRACT

Using the Karush–Kuhn–Tucker conditions for the convex lower level problem, the bilevel optimization problem is transformed into a single-level optimization problem (a mathematical program with complementarity constraints). A regularization approach for the latter problem is formulated which can be used to solve the bilevel optimization problem. This is verified if global or local optimal solutions of the auxiliary problems are computed. Stationary solutions of the auxiliary problems converge to C-stationary solutions of the mathematical program with complementarity constraints.     

Scalarization in vector optimization

In this paper some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem. This will be done for weakly minimal and minimal solutions, respectively. Finally the results will be applied to a certain class of approximation problems.     

Optimal control problems for the reaction–diffusion–convection equation with variable coefficients

The solvability of optimal control problems is proved on both weak and strong solutions of a boundary value problem for the nonlinear reaction–diffusion–convection equation with variable coefficients. In the second case, the requirements for smoothness of the multiplicative control are reduced. The study of extremal problems is based on the proof of the solvability of the corresponding boundary value problems and on the qualitative analysis of their solutions properties. The large data existence results for weak solutions, the maximum principle as well as the local existence and uniqueness of a strong solution are established. Moreover, an optimal feedback control problem is considered. Using methods of the theory of topological degree for set-valued perturbations (with aspheric image sets) of generalized monotone operators, we obtain sufficient conditions for the solvability of this problem in the class of weak solutions.     

Uniqueness for second order nonlinear boundary value problems with applications to almost periodic solutions

Summary The problem of uniqueness of bounded solutions for various nonlinear boundary value problems is considered. Results for problems with an unbounded interval are obtained. The results obtained for the uniqueness of bounded solutions on the interval (−∞, ∞) are applied to the problem of proving the existence of almost periodic solutions. Entrata in Redazione il 4 aprile 1968.     

A modified quasi-boundary value method for ill-posed problems

In this paper, we study a final value problem for first order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.     

Algorithm for minimizing weighted earliness penalty in single-machine problem

In this paper, the problem of minimizing the weighted earliness penalty in a single-machine scheduling problem is addressed. For this problem, every job is assumed to be available at time zero and must be completed before or on its deadline. No tardy job is allowed. Each job has its own earliness penalty and deadline. The paper identifies several local optimality conditions for sequencing of adjacent jobs. A heuristic algorithm is developed based on these local optimality conditions. Sample problems are solved and the solutions obtained from the heuristic are compared to solutions obtained from the heuristics developed by Chand and Schneeberger. Also, comparisons are performed between the solutions obtained from the heuristic and the optimal solutions obtained from a mathematical modeling approach for problems involving 10 and 15 jobs. The results show that the developed heuristic produces solutions close to optimal in small size problems, and it also outperforms the Chand and Schneeberger's method.