相关论文: Francois Viete and his contribution to mathematics
In this article, Joseph-Louis Lagrange analyzed those numbers which may be represented by the quadratic form $Bt^2 + Ctu + Du^2$. After proving a few theorems on the divisors of such numbers (and their possible forms), Lagrange developed a…
I discuss Ren{\'e} Thom's approach to philosophy based on his mathematical background. At the same time, I will highlight his connection with Aristotle, his criticism of the modern view of science as a predictive process, his ideas on…
An important breakthrough in understanding the geometry of Schubert varieties was the introduction of the notion of Frobenius split varieties and the result that the flag varieties G/P are Frobenius split. The aim of this article is to give…
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…
These notes are an expanded version of two series of lectures given at the winter school in mathematical physics at les Houches and at the Vietnamese Institute for Mathematical Sciences. They are an introduction to factorization algebras,…
This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of binary logical functions in the original form introduced by George Boole. A justification on historical grounds is…
In his pioneering work from 1969, Jerry Levine introduced a complete set of invariants of algebraic concordance of knots. The evaluation of these invariants requires a factorization of the Alexander polynomial of the knot, and is therefore…
The paper introduces in a new although maybe unusual form the examples of types provided by J. von Neumann and F.J. Murray in their outstanding papers on algebraic factorization (1936-1943)pursuing three main aims: speculating about the…
A recently developed computational methodology for executing numerical calculations with infinities and infinitesimals is described in this paper. The developed approach has a pronounced applied character and is based on the principle `The…
We discuss the notion of a Batalin-Vilkovisky (BV) algebra and give several classical examples from differential geometry and Lie theory. We introduce the notion of a quantum operator algebra (QOA) as a generalization of a classical…
This paper includes notes to accompany a reading of Thue's 1914 paper "Probleme uber Veranderungen von Zeichenreihen nach gegebenen Reglen", along with a translation of that paper. Thue's 1914 paper is mainly famous for proving an early…
In this survey article we discuss the question: to what extent is an algebraic variety determined by its ring of differential operators? In the case of affine curves, this question leads to a variety of mathematical notions such as the Weyl…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
This is a survey article featuring some of Wolmer Vasconcelos' contributions to commutative algebra, and explaining how Vasconcelos' work and insights have contributed to the development of commutative algebra and its interaction with other…
The method used by senior geodetic engineer Jean-Georges Affholder to determine what can be termed as the 'centre of gravity' of physical Europe in 1989 and 2004 relies on mathematical formulae which, in their only published version, happen…
We show that every affine or projective algebraic variety defined over the field of real or complex numbers is homeomorphic to a variety defined over the field of algebraic numbers. We construct such a homeomorphism by choosing a small…
Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with multiplicative structures, i.e., in…
An $n$-dimensional Lie algebra $\mathfrak{g}$ over a field $\mathbb{F}$ of characteristic two is said to be of Vergne type if there is a basis $e_1,\dots,e_n$ such that $[e_1,e_i]=e_{i+1}$ for all $2\leq i \leq n-1$ and $[e_i,e_j] =…
Fewnomial theory began with explicit bounds -- solely in terms of the number of variables and monomial terms -- on the number of real roots of systems of polynomial equations. Here we take the next logical step of investigating the…
This short article, dedicated to our beloved guru Philippe FLAJOLET (1948-2011), is a case-study in computer-generated combinatorial research, where the computer, all by itself, is using the transfer-matrix method to derive (rigorously!)…