Boundary Value and Inverse Problems for Some Classes of Nonclassical Operator-Differential Equations

We consider the solvability of boundary valueproblems and some inverse problems for operator-differentialequations of odd order which can be referred to as mixed typeequations since the coefficient of the higher order time derivative can change sign.Studying the general classes of boundary value problems with nonlocal boundary conditions,we establish the existence and uniqueness theorems of regular solutions under some conditions on data.

     

Solvability of Inverse Extremal Problems for Stationary Heat and Mass Transfer Equations

We consider inverse extremal problems for the stationary system of heat and mass transfer equations describing the propagation of a substance in a viscous incompressible heat conducting fluid in a bounded domain with Lipschitz boundary. The problems consist in finding some unknown parameters of a medium or source densities from a certain information of a solution. We study solvability of the direct boundary value problem and the inverse extremal problem, justify application of the Lagrange principle, introduce and analyze the optimality systems, and establish sufficient conditions for uniqueness of solutions.     

On Some Inverse Problems for First Order Operator-Differential Equations

Siberian Mathematical Journal - We study solvability of the inverse problems of recovering an unknown function on the nonlinear right-hand side of a first order operator-differential equation in...     

Universal Objects in Some Classes of Clifford Topological Inverse Semigroups

We construct universal objects in various classes of Clifford topological inverse semigroups. In particular, we show that each compact Abelian topological inverse semigroup with Lawson maximal semilattice embeds into a power of the cone over the circle.     

On Some Classes of Nonlocal Boundary-Value Problems for Singular Parabolic Equations

Mathematical Notes - We study the solvability of nonlocal boundary-value problems for singular parabolic equations of higher order in which the coefficient of the time derivative belongs to a space...     

Extremal Problems in Some Classes of Holomorphic Functions

Let PRΛ_n be the class of holomorphic functions with positive real part and real Taylor coefficients the first m + 1 of which are common for all these functions. We find: a) The extreme points of the class PRΛ_n. b) The extrema of {f(r): f ∈ PRΛ_n}, {f′(r): f ∈ PRΛ_n} and {f′(r): f ∈ PRΛ_n}. We also solve respective problems for typical real functions.     

Inverse Problem for Equations of Complex Heat Transfer

Computational Mathematics and Mathematical Physics - The inverse problem with integral overdetermination for the equations of complex heat transfer, including the $${{P}_{1}}$$ approximation for...     

Application of the Fast Automatic Differentiation Technique for Solving Inverse Coefficient Problems

Computational Mathematics and Mathematical Physics - Results obtained by the authors in solving inverse coefficient problems are overviewed. The inverse problem under consideration is to determine...     

On the WGSC Property in Some Classes of Groups

The property of quasi-simple filtration (or qsf) for groups has been introduced in literature more than 10 years ago by S. Brick. This is equivalent, for groups, to the weak geometric simple connectivity (or wgsc). The main interest of these notions is that there is still not known whether all finitely presented groups are wgsc (qsf) or not. The present note deals with the wgsc property for solvable groups and generalized FC-groups. Moreover, a relation between the almost-convexity condition and the Tucker property, which is related to the wgsc property, has been considered for 3-manifold groups.     

An Approximate Method for Solving an Inverse Coefficient Problem for the Heat Equation

Journal of Applied and Industrial Mathematics - We construct a numerical method for recovering a variable coefficient in the Cauchy problem and also in the initial boundary value problem for the...     

Some Optimization Problems in Advertising Media Planning

This is an account of the first stage of a multi-stage research programme in the planning of advertising media schedules. The problems of securing maximum impact and maximum coverage in an intense campaign of short duration for a fixed outlay are discussed. A precise solution of the Impact problem and an approximate solution of the Coverage problem are outlined. These solutions are currently being used, but test results are not yet available. This is, therefore, an interim statement and not a completed case history.     

On the Two-dimensional Inverse Scattering Problems in Electromagnetics

In recent years, inverse scattering problems have received much attention because of their important applications. Given the incident and scattered waves, an inverse scattering problem in general is to determine the properties of the scatterer. In radar or sonar a known incident wave and observed scattered wave are used to detect the properties and the presence of aircraft or submarine objects; in MRI scanning, tomography X-rays and ultrasound, scattered waves are used to determine the presence or properties of tumors by detecting density variations, to name a few. In this article, we are concerned with the two-dimensional electromagnetic inverse scattering problem. An iterative algorithm for the transversal electric waves will be given based on a singular domain integral equation formulation. Basic features of a scattering object such as shape, location and index of refraction will be recovered from measurements of the field scattered by the object (when illuminated by electromagnetic waves with the magnetic vector polarized along the cylinder axis). Some numerical experiments are included to illustrate the efficiency of the algorithm.     

Convergence of Distributed Optimal Controls on the Internal Energy in Mixed Elliptic Problems when the Heat Transfer Coefficient Goes to Infinity

We consider a steady-state heat conduction problem P _α with mixed boundary conditions for the Poisson equation depending on a positive parameter α , which represents the heat transfer coefficient on a portion Γ ₁ of the boundary of a given bounded domain in R ⁿ . We formulate distributed optimal control problems over the internal energy g for each α . We prove that the optimal control g_ op _α and its corresponding system u_ g_ op _α α and adjoint p_ g_ op _α α states for each α are strongly convergent to g _op , u_ g _op and p _ g _op , respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control, and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation with a different boundary condition on the portion Γ ₁ . We use the fixed point and elliptic variational inequality theories.     

Convergence of Distributed Optimal Controls on the Internal Energy in Mixed Elliptic Problems when the Heat Transfer Coefficient Goes to Infinity

We consider a steady-state heat conduction problem P _α with mixed boundary conditions for the Poisson equation depending on a positive parameter α , which represents the heat transfer coefficient on a portion Γ ₁ of the boundary of a given bounded domain in R ⁿ . We formulate distributed optimal control problems over the internal energy g for each α . We prove that the optimal control g_ op _α and its corresponding system u_ g_ op _α α and adjoint p_ g_ op _α α states for each α are strongly convergent to g _op , u_ g _op and p _ g _op , respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control, and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation with a different boundary condition on the portion Γ ₁ . We use the fixed point and elliptic variational inequality theories.     

一些类型的数学规划问题的全局最优解

本文对严格单调函数给出了几个凸化和凹化的方法，利用这些方法可将一个严格单调的规划问题转化为一个等价的标准D．C．规划或凹极小问题．本文还对只有一个严格单调的约束的非单调规划问题给出了目标函数的一个凸化和凹化方法，利用这些方法可将只有一个严格单调约束的非单调规划问题转化为一个等价的凹极小问题．再利用已有的关于D．C．规划和凹极小的算法，可以求得原问题的全局最优解．