Quasi-Lovász Extensions on Bounded Chains

Quasi-Lovász Extensions and Their Symmetric Counterparts

We introduce the concept of quasi-Lovász extension as being a mapping f : I → IR defined over a nonempty real interval I containing the origin, and which can be factorized as f(x1, . . . , xn) = L(φ(x1), . . . , φ(xn)), where L is the Lovász extension of a pseudo-Boolean function ψ : {0, 1} → IR (i.e., the function L : IR → IR whose restriction to each simplex of the standard triangulation of [...

Propositional Proofs in Frege and Extended Frege Systems (Abstract)

We discuss recent results on the propositional proof complexity of Frege proof systems, including some recently discovered quasipolynomial size proofs for the pigeonhole principle and the Kneser-Lovász theorem. These are closely related to formalizability in bounded arithmetic.

On extension of fuzzy measures to aggregation functions

In the paper we study a method extending fuzzy measures on the set N = {1, . . . , n} to n-ary aggregation functions on the interval [0, 1]. The method is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. This approach generalizes the wellknown Lovász and Owen extensions of fuzzy measures. We focus our attention on the special class o...

Extensions of Baer and quasi-Baer modules

Polynomially bounded solutions of the Loewner‎ ‎differential equation in several complex variables

‎We determine the‎ ‎form of polynomially bounded solutions to the Loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally‎ ‎Lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[A(tau)...