Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

General conditions for the unique solvability of a non-linear nonlocal boundary-value problem for systems of non-linear functional differential equations are obtained.     

Variational formulation for a non-local elliptic problem in the theory of varistors

The electric potential in a three-dimensional non-linear conductor of electricity in series with a one-dimensional resistor and a direct current generator is studied with a nonlocal elliptic problem. We give a variational formulation and a theorem of existence and uniqueness.     

Variational approach for a p-Laplacian boundary value problem on time scales

In this paper, we study a second-order p-Laplacian dynamic equation on a periodic time scale subject to certain boundary value conditions. The variational structure of the above-mentioned boundary value problem is presented. Some new results on the existence of at least one or three distinct periodic solutions are established by means of the saddle point theorem, the least action principle as well as the three critical point theorem.     

Remarks on a non-local boundary value problem

We remark that results on existence of symmetric positive solutions obtained in some recent papers can, in fact, be deduced as special cases of some known results. We also correct the values of the principal eigenvalue previously given in some examples.     

A path probability approach to the solute transport problem

An alternative solute transport algorithm, termed the path probability approach, is presented. The method may be more effective than typical finite methods in some numerical solution problems. The method differs from predominant numerical techniques in that the conventional conservation differential is replaced by a series of equations defining solute migration in terms of a finite number of representative particle position histories and corresponding probabilities. The governing physical assumptions applied in model development are conditionally consistent with those of conventional Lagrangian and Eulerian conceptualizations, but mathematical expression and development of the problem differ from traditional approaches. The method represents dispersion orthogonal to the primary axis of advective transport explicitly, according to arbitrary user-defined probability functions; longitudinal dispersion effects result from the existence of velocity shear effects along the primary axis of movement. It is possible to incorporate Fickian dispersive processes, and thereby reproduce results obtainable with traditional stream tube models; but non-Fickian alternatives can also be explored. Simulation results of the path probability model are compared to analogous results from a representative finite difference model for a hypothetical test flow channel. The comparison demonstrated the ability of the new model to effectively generate simulation results with a computational effeciency considerably higher than conventional techniques under the conditions tested.     

On a variational approach to some non-local boundary value problems

We treat by variational methods some nonlinear elliptic b.v.p. that involve a non-local term. Our main tools are the Mountain Pass Theorem of Ambrosetti and Rabinowitz and minimization procedures.     

Variational approach to Arnold diffusion

Arnold diffusion was conjectured by Arnol'd(1964) as a typical phenomena of topological instability in classical mechanics. In this paper, we give a panorama of the researches on Arnold diffusion using the variational approaches.     

A problem of the sequential approach to a group of moving points by a third-order non-linear control system

The problem of the fastest sequential circumvention of a group of moving points by a third-order non-linear controlled object is investigated. The necessary conditions for optimality of the control and the convergence times are used in the form of Pontryagin's Maximum Principle and the conditions for smoothing the Hamiltonian. The problem is not assumed to be divisible into several successively solvable “two-point problems”.     

Variational approach to grid generation

Some mathematical aspects of the variational approach to grid generation are discussed. Existence and regularity results for 2D are presented.     

A coefficient identification problem for a mathematical model related to ductal carcinoma in situ

We consider a coefficient identification problem for a mathematical model with free boundary related to ductal carcinoma in situ (DCIS). This inverse problem aims to determine the nutrient consumption rate from additional measurement data at a boundary point. We first obtain a global‐in‐time uniqueness of our inverse problem. Then based on the optimization method, we present a regularization algorithm to recover the nutrient consumption rate. Finally, our numerical experiment shows the effectiveness of the proposed numerical method.     

A linear algebra approach to Koethe's problem and related questions

We discuss several problems on the structure of nil rings from the linear algebra point of view. Among others, a number of questions and results are presented concerning algebras of infinite matrices over nil algebras, and nil algebras of infinite matrices over fields, which are related to the famous Koethe's problem. Some questions on radicals of tensor products of algebras related to Koethe's problem are also discussed.     

An evolutionary and constructive approach to a crew scheduling problem in underground passenger transport

Operations management of subway systems is associated with combinatorial optimization problems (i.e. crew and train scheduling and rostering) which belong to the np-hard class of problems. Therefore, they are generally solved heuristically in real situations. This paper considers the problem of duty generation, i.e. identifying an optimal trips set that the conductors should complete in one workday. With regard to operational and labor conditions, the problem is to use the lowest possible number of conductors and minimize total idle time between trips. The problem is modeled and solved using a constructive hybrid approach, which has the advantage of visualizing a solution construction similar to the manual approach typically used. Our approach takes advantage of the benefits offered by evolutionary methods, which store a candidate solutions population in each stage, thus controlling the combinatorial explosion of possible solutions. The results thus obtained for problems similar to those that are solved manually in the Santiago Metro System were compared with two alternative approaches, based on tabu search and a greedy method. The hybrid method produced solutions with the minimum number of duties in six of the ten problems solved. However, the tabu search method provided better results in terms of idle time than either the hybrid method or the greedy method.     

Variational approach to impulsive evolution equations

This article uses variational method for studying existence and uniqueness of solutions for impulsive evolution equations. The main techniques include Hilbert triple, Sobolev embedding theorem, Galerkin approximation and weak convergence for passing to the limit.