We study conjugate duality with arbitrary coupling functions. Our only tool is a certain support property, which is automatically fulfilled in the two most widely used special cases, namely the case where the underlyi...
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We study conjugate duality with arbitrary coupling functions. Our only tool is a certain support property, which is automatically fulfilled in the two most widely used special cases, namely the case where the underlying space is a topological vector space and the coupling functions are the continuous linear ones, and the case where the underlying space is a metric space and the coupling functions are the continuous ones. We obtain thereby a simultaneous axiomatic extension of these two classical models. Also included is a condition for global optimality, which requires only the mentioned support property.
The aim of this paper is to introduce the dual notion of interval conjugate implications, the interval coimplications, as interval representations of corresponding conjugate fuzzy coimplications. Using the canonical r...
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The aim of this paper is to introduce the dual notion of interval conjugate implications, the interval coimplications, as interval representations of corresponding conjugate fuzzy coimplications. Using the canonical representation, this paper considers both the correctness and the optimality criteria, in order to provide interpretation for fuzzy coimplications as the non-truth degree of conditional rule in expert systems and study the action of interval automorphisms on such interval fuzzy connectives. It is proved that interval automorphisms acting on N-dual interval coimplications preserve the main properties of interval implications discussed in the literature including the duality principle. Lastly, the action of interval automorphisms on interval classes of border, model and S-coimplications are considered, summarized in commutative diagrams. (C) 2013 Elsevier Inc. All rights reserved.
This paper proposes a Variational Boundary Integral Equation for time harmonic elasticity, using conjugate functions. A bilinear hermitian form for the variational formulation, as well as an a posteriori error indicat...
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This paper proposes a Variational Boundary Integral Equation for time harmonic elasticity, using conjugate functions. A bilinear hermitian form for the variational formulation, as well as an a posteriori error indicator are proposed. The method does not involve hypersingular integrals in the finite part sense and preserves the symmetrical structures of equations.
This paper deals with multicriteria fractional problems. Since this problems in general are not convex, the basic problem will be transformed into a convex optimization problem by using an extension of the conception ...
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This paper deals with multicriteria fractional problems. Since this problems in general are not convex, the basic problem will be transformed into a convex optimization problem by using an extension of the conception of Dinkelbach to vector optimization. It will be formulated a dual problem to the transformed optimization problem, where conjugate functions are used. There will be proved strong and converse duality theorems with conclusions to basic fractional problem.
We find all pairs of real analytic functions f and g in R(n) such that vertical bar del f vertical bar = vertical bar del g vertical bar and (del f)(del g) = 0.
We find all pairs of real analytic functions f and g in R(n) such that vertical bar del f vertical bar = vertical bar del g vertical bar and (del f)(del g) = 0.
It is well known that certain properties of continuous functions on the circle T related to the Fourier expansion can be improved by a change of variable, i.e., by a homeomorphism of the circle onto itself. One of the...
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It is well known that certain properties of continuous functions on the circle T related to the Fourier expansion can be improved by a change of variable, i.e., by a homeomorphism of the circle onto itself. One of the results in this area is the Jurkat-Waterman theorem on conjugate functions, which improves the classical Bohr-Pal theorem. In the present work we propose a short and technically very simple proof of the Jurkat-Waterman theorem. Our approach yields a stronger result.
We consider Fourier series of summable functions from spaces "wider" than L-1. We describe classes phi(L) which contain conjugate functions, where their conjugate Fourier series converge. The obtained result...
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We consider Fourier series of summable functions from spaces "wider" than L-1. We describe classes phi(L) which contain conjugate functions, where their conjugate Fourier series converge. The obtained results are more general than A. N. Kolmogorov theorems on the convergence of Fourier series in metrics weaker than that of L-1.
As is well known, there is a close relationship between rational and piecewise-polynomial approximations of functions. This relationship is manifested in the most vivid way in the case of approximations in Lebesgue sp...
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As is well known, there is a close relationship between rational and piecewise-polynomial approximations of functions. This relationship is manifested in the most vivid way in the case of approximations in Lebesgue spaces L-p for 0 < p < infinity, 1/p is not an element of N. In the present paper, in particular, it is shown that the rate of uniform rational approximation of functions is described rather well using the rate of uniform piecewise-polynomial approximations of the function itself and its conjugate function. The converse is also true.
In this paper we use the tools of the convex analysis in order to give a suitable characterization for the epigraph of the conjugate of the pointwise maximum of two proper, convex and lower semicontinuous functions in...
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In this paper we use the tools of the convex analysis in order to give a suitable characterization for the epigraph of the conjugate of the pointwise maximum of two proper, convex and lower semicontinuous functions in a normed space. By using this characterization we obtain, as a natural consequence, the formula for the biconjugate of the pointwise maximum of two functions, provided the so-called Attouch-Brezis regularity condition holds.
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