The numerical approximation of integrals containing strongly singular integrals, in particular Cauchy principal value integrals, is a major issue connected, e.g., to the boundary integral approach for many types of partial differential equations. Whereas the one-dimensional ∗Institut für Angewandte Mathematik, Technische Universität Braunschweig, Pockelsstraße 14, D-38106 Braunschweig, Germany....

We consider a class of vectorial integrals with linear growth, where, as a key feature, some degenerate/singular behavior is allowed. For generalized minimizers of these integrals in BV, we establish interior gradient regularity and — as a consequence — uniqueness up to constants. In particular, these results apply, for 1 < p < 2, to the singular model integrals ∫ Ω (1 + |∇w(x)|) 1 p dx . MSC (...

Fuzzy integrals, in general, and Sugeno integrals, in particular, are well known aggregation operators. They can be used in a great variety of decision making applications. Nevertheless, their use is not easy as their interpretation is not straightforward. In this paper we study the interpretation of fuzzy integrals, focusing on Sugeno ones, and we show their application to fuzzy inference syst...

Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the “principle of conditioning”, to study their stable convergence towards mixtures of infinitely divisible distributions. Our results apply, in particular, to multiple integrals with respect to independently scattered and square ...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

Abstract. We derive some Hodge integral identities by taking various limits of the Mariño-Vafa formula using the cut-and-join equation. These identities include the formula of general λg-integrals, the formula of λg−1-integrals on Mg,1, the formula of cubic λ integrals on Mg, and the ELSV formula relating Hurwitz numbers and Hodge integrals. In particular, our proof of the MV formula by the cut...

In this article, under certain parametric conditions, we study the first integrals of the Duffing-van der Pol-type oscillator equations which include the van der Pol and the Duffing oscillator systems, as particular cases. After making a series of variable transformations and applying the PrellerSinger method, we find the first integrals of the simplified equations without complicated calculati...

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i &amp; ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i &amp; ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

There are two basic types of improper integrals. Integrals with an infinite limit are defined as the limit of a series of proper integrals as one of the limits approaches infinity. Improper integrals with finite limits are needed when the integrand does not have a finite limiting value as the variable of integration approaches a particular “critical” value. In this case, the improper integral i...