Modification of trigonometric collocation method for impulsive periodic BVP

AbstractThe paper gives an easy-to-use technique for setting up the system of determining equations of impulsive periodic BVPs. © 1999 Elsevier Science Ltd. All rights reserved

Measure Functional Differential Equations in the Space of Functions of Bounded Variation

We establish general conditions for the unique solvability of nonlinear measure functional differential equations in terms of properties of suitable linear majorants

Evaluation of the efficiency of vending business and the perspectives of its development in the territory of Tomsk

This article assesses the effectiveness of conducting a vending business in the territory of Tomsk and develops a business plan for creating a network of vending machines for hot drinks. During the study, the authors conducted a sociological survey, the purpose of which was to identify the gastronomic preferences of potential buyers and to determine the presence or absence of demand in the market of vending trade. Also, the advantages and disadvantages of this market niche, possible problems and prospects for its development are considered

A Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalised Valuations

Any attempt to construct a realist interpretation of quantum theory founders on the Kochen-Specker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalised valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalised valuation. A key ingredient throughout is the idea that, in a situation where no normal truth-value can be given to a proposition asserting that the value of a physical quantity A lies in a set D of real numbers , it is nevertheless possible to ascribe a partial truth-value which is determined by the set of all coarse-grained propositions that assert that some function f(A) lies in f(D), and that are true in a normal sense. The set of all such coarse-grainings forms a sieve on the category of self-adjoint operators, and is hence fundamentally related to the theory of presheav

On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations

For a system of linear functional differential equations, we consider a three-point problem with nonseparated boundary conditions determined by singular matrices. We show that, to investigate such a problem, it is often useful to reduce it to a parametric family of two-point boundary value problems for a suitably perturbed differential system. The auxiliary parametrised two-point problems are then studied by a method based upon a special kind of successive approximations constructed explicitly, whereas the values of the parameters that correspond to solutions of the original problem are found from certain numerical determining equations. We prove the uniform convergence of the approximations and establish some properties of the limit and determining functions

On the numerical-analytic investigation of parametrized problems with nonlinear boundary conditions

We consider a parametrized boundary-value problem containing an unknown parameter both in the nonlinear ordinary differential equations and in the nonlinear boundary conditions. By using a suitable change of variables, we reduce the original problem to a family of those with linear boundary conditions plus some nonlinear algebraic determining equations. We construct a numerical-analytic scheme suitable for studying the solutions of the transformed boundary-value problem.Розглядається параметризована гранична задача, що мiстить невiдомий параметр у нелiнiйних звичайних диференцiальних рiвняннях i в нелiнiйних граничних умовах. Використовуючи вiдповiдну замiну змiнних, початкову задачу зведено до сiм’ї задач з лiнiйними граничними умовами та деяких нелiнiйних алгебраїчних визначальних рiвнянь. Побудовано чисельно-аналiтичну схему, яку можна використовувати для вивчення розв’язкiв перетвореної граничної задачi

Measure Functional Differential Equations in the Space of Functions of Bounded Variation

We establish general conditions for the unique solvability of nonlinear measure functional differential equations in terms of properties of suitable linear majorants