相关论文: Analytical Guide and updates for "Cardinal Arithme…
This paper was written in 2015, and published in the Journal of Humanistic Mathematics. This paper announces the first issue (2015) of Enchiridion: Mathematics User's Guides, a project to produce peer-reviewed User's Guides as companions to…
We correct the statements and proofs of the (auxiliary) Propositions 4.1 and 4.2 of our paper `Evaluation of motivic functions, non-nullity, and integrability in fibers' in Advances in Mathematics, Vol. 409, Part A, Paper No. 108635, 29…
We present recent results on optimal algorithms for numerical integration and several open problems. The paper has six parts: 1. Introduction 2. Lower Bounds 3. Universality 4. General Domains 5. iid Information 6. Concluding Remarks
Some of the conclusions of an improved JWKB method by Eleuch H., Rostovtsev Y. V. and Scully M. O., EPL, 89 (2010) 50004 are clarified. The degree of approximation to exact solutions is quantitatively assessed. The improved JWKB method is…
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
Using an efficient algorithmic implementation of Caratheodory's theorem, we propose three enhanced versions of the Projection and Rescaling algorithm's basic procedures each of which improves upon the order of complexity of its analogue in…
Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations,computer algebra systems are employed. In our research, we have been using Cadabra as the main computer algebra system for several…
Real analytic generalized functions are investigated as well as the analytic singular support and analytic wave front of a generalized function in $\mathcal{G}(\Omega)$ are introduced and described.
This document provides the foundations behind the functionality provided by the $\rho$G library (https://github.com/santiontanon/RHOG), focusing on the basic operations the library provides: subsumption, refinement of directed labeled…
In this paper we provide an exhaustive survey of the current state of the mathematics of filtration enlargement and an interpretation of the key results of the literature from the viewpoint of mathematical finance. The emphasis is on…
The purpose of this article is threefold. First, it provides the reader with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a determinant should appear in her/his research.…
Some notes and observations on analytic functions defined on an annulus
We provide supplementary appendices to the paper Misere quotients for impartial games. These include detailed solutions to many of the octal games discussed in the paper, and descriptions of the algorithms used to compute most of our…
Three programs in Mathematica are presented, which produce expressions for the lowest order and the higher order corrections of the Phase Integral Approximation. First program is pertinent to one ordinary differential equation of the…
This is a shortened version of "The Limits of Mathematics--Course Outline & Software" (IBM Research Report RC 19324, December 1993) in which all Mathematica code has either been deleted or, if absolutely necessary, replaced by C code. The…
A gap in the proof of Theorem 3.5 in the paper ``A new iteration process for approximation of common fixed points for finite families of total asymtotically nonexpansive mappings". Int. J. Math. Math. Sci. vol. 2009,…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.