Related papers: On some extension theorems for multifunctions
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
In this note, we give short inductive proofs of two known results on $k$-extendible graphs based on a property proved in [Qinglin Yu, A note on $n$-extendable graphs. Journal of Graph Theory, 16:349-353, 1992].
This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.
We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
Withdrawn by author - Superseded by arXiv:0910.5106 [math.FA].
The use of nonstandard methods to characterize properties of weak, strong and mixed extensions of congruences to ultrafilters has been the main topic of several recent papers. We show that similar methods can be used to characterize the…
In this paper we will establish a structure theorem concerning the extension of analytic objects associated to germs of dimension one foliations on surfaces, through one-dimensional barriers. As an application, an extension theorem for…
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given…
In this paper, we give a simple counter example to the famous Hodge conjecture.
In this paper we are concerned with the space of tempered ultrahyperfunctions corresponding to a proper open convex cone. A holomorphic extension theorem (the version of the celebrated edge of the wedge theorem) will be given for this…
This note provides a counterexample to a theorem announced in the last part of the paper ''Analysis of direct searches for discontinuous functions'', Mathematical Programming Vol. 133, pp.~299--325, 2012. The counterexample involves an…
In this note, we state various generalisations of the Nakano vanishing theorem under weak positivity assumptions, and compare them with the known results.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
In this note we elaborate on a recent counter-example to the Nelson-Seiberg theorem and to its generalizations. We provide sufficient conditions for the existence of such counter-examples, finding new ones. We claim that these…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.