Search results for "equation"

On the symbol homomorphism of a certain Frechet algebra of singular integral operators

1985

We prove the surjectivity of the symbol map of the Frechet algebra obtained by completing an algebra of convolution and multiplication operators in the topology generated by all L2-Sobolev norms. The proof is based on an ℝn of Egorov's theorem valid for non-homogeneous principal symbols, discussed in [5], [6]. We use the hyperbolic equation ∂u/∂t=i|D|ηu, 0<η<1, which has its characteristic flow constant at infinity, so that no differentiability of the symbol is required there.

Radó-Kneser-Choquet Theorem for simply connected domains (p-harmonic setting)

2018

A remarkable result known as Rad´o-Kneser-Choquet theorem asserts that the harmonic extension of a homeomorphism of the boundary of a Jordan domain ⌦ ⇢ R2 onto the boundary of a convex domain Q ⇢ R2 takes ⌦ di↵eomorphically onto Q . Numerous extensions of this result for linear and nonlinear elliptic PDEs are known, but only when ⌦ is a Jordan domain or, if not, under additional assumptions on the boundary map. On the other hand, the newly developed theory of Sobolev mappings between Euclidean domains and Riemannian manifolds demands to extend this theorem to the setting on simply connected domains. This is the primary goal of our article. The class of the p -harmonic equations is wide enou…

On a linear diophantine problem of Frobenius

1993

Abstract In this paper, linear diophantine problem of Frobenius is discussed. A theorem concerning the largest integer g m (a1,a2) and the smallest integer G m (a1,a2) with m different representations with a1,a2 as basis is proved.

Fixed points for multivalued mappings in b-metric spaces

2015

In 2012, Samet et al. introduced the notion ofα-ψ-contractive mapping and gave sufficient conditions for the existence of fixed points for this class of mappings. The purpose of our paper is to study the existence of fixed points for multivalued mappings, under anα-ψ-contractive condition of Ćirić type, in the setting of completeb-metric spaces. An application to integral equation is given.

Guaranteed error bounds for a class of Picard-Lindelöf iteration methods

2013

We present a new version of the Picard-Lindelof method for ordinary dif- ¨ ferential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations. peerReviewed

Analytic solution for a class of discrete-time Riccati equations arising in Nash games

1990

Lipschitz conditions,b-arcwise connectedness and conformal mappings

1982

Quadratic rational solvable groups

2012

Abstract A finite group G is quadratic rational if all its irreducible characters are either rational or quadratic. If G is a quadratic rational solvable group, we show that the prime divisors of | G | lie in { 2 , 3 , 5 , 7 , 13 } , and no prime can be removed from this list. More generally, if G is solvable and the field Q ( χ ) generated by the values of χ over Q satisfies | Q ( χ ) : Q | ⩽ k , for all χ ∈ Irr ( G ) , then the set of prime divisors of | G | is bounded in terms of k . Also, we prove that the degree of the field generated by the values of all characters of a semi-rational solvable group (see Chillag and Dolfi, 2010 [1] ) or a quadratic rational solvable group over Q is bou…

A common fixed point theorem for two weakly compatible pairs in G-metric spaces using the property E.A

2013

In view of the fact that the fixed point theory provides an efficient tool in many fields of pure and applied sciences, we use the notion of the property E.A to prove a common fixed point theorem for weakly compatible mappings. The presented results are applied to obtain the solution of an integral equation and the bounded solution of a functional equation arising in dynamic programming.

Varieties and Covarieties of Languages (Extended Abstract)

2013

AbstractBecause of the isomorphism (X×A)→X≅X→(A→X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebra-coalgebra duality goes back to Arbib and Manes, who formulated it as a duality between reachability and observability, and is ultimately based on Kalmanʼs duality in systems theory between controllability and observability. Recently, it was used to give a new proof of Brzozowskiʼs minimization algorithm for deterministic automata. Here we will use the algebra-coalgebra duality of automata as a common perspective for the study of both varieties and covarieties, which are …