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Abstract

The paper is devoted to the finding of the coefficient of one nonlinear wave equation in the mixed problem. The considered problem is reduced to the optimal control problem with proper functional. Differentiability of functional is proved and the necessary optimality conditions are derived in the form of the variational inequality. Existence of the optimal control is proved.

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Zumrud R. Safarova
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Abstract

For Peter F. Strawson, transcendental arguments were an important part of his philosophical method, referred to as a connective analysis. Both Strawson and his critical commentators have devoted a lot of effort to determining the nature, scope and purpose of those arguments. In this text, I intend, first of all, to reconstruct and characterize the basic elements of transcendental argumentation, specifying its general form, features and purpose. Secondly, I reconstruct some of the most representative examples of this argumentation. Thirdly, I refer to the basic objections against transcendental arguments formulated in the literature. Finally, I point to a few peculiarities in those arguments, commonly omitted by commentators and interpreters. The overall message of the paper is moderately positive: transcendental arguments are a legitimate way of reasoning in philosophy, and in particular, they constitute a comprehensible and well-founded part of Strawson’s connective analysis.

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Mariusz Grygianiec
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Abstract

The paper concerns a strength optimization of continuous beams with variable cross-section. The continuous beams are subjected to a dead weight and a useful load, the six (seven) combinations of loads were analyzed. Optimal design problems in structural mechanics can by mathematically formulated as optimal control tasks. To solve the above formulated optimization problems, the minimum principle was applied. The paper is an introductory and survey paper of the treatment of realistically modelled optimal control problems from application in the structural mechanics. Especially those problems are considered, which include different types of constraints. The optimization problem is reduced to the solution of multipoint boundary value problems (MPBVP) composed of differential equations. Dimension of MPBVP is usually a large number, what produces numerical difficulties. Optimal control theory does not give much information about the control structure. The correctness of the assumed control structure can be checked after obtaining the solution of the boundary problem.

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Authors and Affiliations

Leszek Mikulski
ORCID: ORCID

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