Search results for " COMPUTATION"

Bornological structures on many-valued sets

2017

The History of Algebra in Mathematics Education

2006

In this chapter, we analyse key issues in algebra history from which some lessons can be extracted for the future of the teaching and learning of algebra. A comparative analysis of two types of pre-Vietan languages (before 16th century), and of the corresponding methods to solve problems, leads to conjecture the presence of didactic obstacles of an epistemological origin in the transition from arithmetic to algebraic thinking. This illustrates the value of historic and critical analysis for basic research design in mathematics education. Analysing the interrelationship between different evolution stages of the sign system of symbolic algebra and vernacular language supports the inference th…

Geometric interpretation of the optimality conditions in multifacility location and applications

1991

Geometrical optimality conditions are developed for the minisum multifacility location problem involving any norm. These conditions are then used to derive sufficient conditions for coincidence of facilities at optimality; an example is given to show that these coincidence conditions seem difficult to generalize.

Indefinite integrals of special functions from integrating factors

2019

Some general integrals are presented which were obtained from two integrating factors f(x) and fˆ(x) for the first two and last two terms, respectively, of the second-order linear ordinary differen...

Numerical evaluation of multiple polylogarithms

2004

Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for arbitrary complex arguments and without any restriction on the weight. We have implemented these algorithms with arbitrary precision arithmetic in C++ within the GiNaC framework.

On Meet-Complements in Cohn Geometries

1993

Within the frame of projective lattice geometry, the present paper investigates classes of meet-complements in Cohn geometries and especially in Ore and Bezout geometries. The algebraic background of these geometries is given by torsion free modules over domains — in particular Ore and Bezout domains. 1

A note on multiple summing operators and applications

2018

We prove a new result on multiple summing operators and, among other results and applications, we provide a new extension of Littlewood’s 4 / 3 inequality to m-linear forms.

Polish G-spaces and continuous logic

2017

Abstract We extend the generalised model theory of H. Becker from [2] to the case of Polish G -spaces when G is an arbitrary Polish group. Our approach is inspired by logic actions of Polish groups which arise in continuous logic.

Unification in superintuitionistic predicate logics and its applications

2018

AbstractWe introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) structural completeness, etc. For this aim we apply modified specific notions, introduced in proposition…

A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches

2015

We present a symbolic manipulation algorithm for the efficient automated implementation of rigorously spin-free coupled cluster (CC) theories based on a unitary group parametrization. Due to the lack of antisymmetry of the unitary group generators under index permutations, all quantities involved in the equations are expressed in terms of non-antisymmetric tensors. Given two tensors, all possible contractions are first generated by applying Wick's theorem. Each term is then put down in the form of a non-antisymmetric Goldstone diagram by assigning its contraction topology. The subsequent simplification of the equations by summing up equivalent terms and their factorization by identifying co…