Cosine functions revisited

Integrated Cosine Functions

In order to the second order Cauchy problem (CP2): x"(t) Ax(t), z(O) z E D(A"), z"(O) y D(A") on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS WITH LINEAR MEMBERSHIP FUNCTIONS-REVISITED

Recently, Gasimov and Yenilmez proposed an approach for solving two kinds of fuzzy linear programming (FLP) problems. Through the approach, each FLP problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. Then, the crisp problem is solved by the use of the modified subgradient method. In this paper we will have another look at the earlier defuzzifi...

Forms, Functional Calculus, Cosine Functions and Perturbation

In this article we describe properties of unbounded operators related to evolutionary problems. It is a survey article which also contains several new results. For instance we give a characterization of cosine functions in terms of mild well-posedness of the Cauchy problem of order 2, and we show that the property of having a bounded H∞-calculus is stable under rank-1 perturbations whereas the ...

Stability for generators of cosine functions

Q-valued Functions Revisited

Abstract. In this note we revisit Almgren’s theory of Q-valued functions, that are functions taking values in the space AQ(R) of unorderedQ-tuples of points in R. In particular: • we give shorter versions of Almgren’s proofs of the existence of Dir-minimizing Qvalued functions, of their Hölder regularity and of the dimension estimate of their singular set; • we propose an alternative intrinsic ...