Related papers: Idempotent mathematics and interval analysis
In this article we give a panoramic view on semi-classical analysis.
An approach to schedule development in project management is developed within the framework of idempotent algebra. The approach offers a way to represent precedence relationships among activities in projects as linear vector equations in…
The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants that one associates with data sets. Here we introduce a…
We study special idempotents (as described by Bushnell and Kutzko) and split idempotents in the context of module and derived categories for idempotented algebras. We then characterize these concepts for path algebras of quivers.
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
We consider reusing established non-probabilistic output analyses (either forward or backwards) that yield over-approximations of a program's pre-image or image relation, e.g., interval analyses. We assume a probability measure over the…
We characterize the idempotent stable range one $2\times 2$ matrices over commutative rings and in particular, the integral matrices with this property. Several special cases and examples complete the subject.
In this paper, we shall establish a rather general asymptotic formula in short intervals for a classe of arithmetic functions and announce two applications about the distribution of divisors of square-full numbers and integers representable…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
Results on approximate deduction in the context of the calculus of evidence of Dempster-Shafer and the theory of interval probabilities are reported. Approximate conditional knowledge about the truth of conditional propositions was assumed…
This paper provides answers to several open problems about equational theories of idempotent semifields. In particular, it is proved that (i) no equational theory of a non-trivial class of idempotent semifields has a finite basis; (ii)…
We study the symmetry in short intervals of arithmetic functions with non-negative exponential sums.
In this paper we introduce a class of mathematical objects called \emph{extensors} and develop some aspects of their theory with considerable detail. We give special names to several particular but important cases of extensors. The…
The usual step-down and step-up multiple testing procedures most often lack an important intuitive, practical, and theoretical property called the interval property. In short, the interval property is simply that for an individual…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.
We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
Estimates of some integrals related to variations of smooth functions are presented.