Search results for "COMPUTATION"
showing 10 items of 7362 documents
About Quotient Orders and Ordering Sequences
2017
Summary In preparation for the formalization in Mizar [4] of lotteries as given in [14], this article closes some gaps in the Mizar Mathematical Library (MML) regarding relational structures. The quotient order is introduced by the equivalence relation identifying two elements x, y of a preorder as equivalent if x ⩽ y and y ⩽ x. This concept is known (see e.g. chapter 5 of [19]) and was first introduced into the MML in [13] and that work is incorporated here. Furthermore given a set A, partition D of A and a finite-support function f : A → ℝ, a function Σ f : D → ℝ, Σ f (X)= ∑ x∈X f(x) can be defined as some kind of natural “restriction” from f to D. The first main result of this article ca…
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...
FORMAL CONCEPTION OF ROUGH SETS
1996
In the paper we present a formal description of rough sets within the framework of the generalized set theory, which is interpreted in the set approximation theory. The rough sets are interpreted as approximations, which are defined by means of the Pawlak's rough sets.
Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators
2013
We introduce a new approach towards proving convexity preserving properties for interpolatory subdivision schemes. Our approach is based on the relation between subdivision schemes and prediction operators within Harten's framework for multiresolution, and hinges on certain convexity properties of the reconstruction operator associated to prediction. Our results allow us to recover certain known results [10,8,1,7]. In addition, we are able to determine the necessary conditions for convexity preservation of the family of subdivision schemes based on the Hermite interpolation considered in [4].
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 P-compatible hybrid identities and hyperidentities
1994
P-compatible identities are built up from terms with a special structure. We investigate a variety defined by a set ofP-compatible hybrid identities and answer the question whether a variety defined by a set ofP-compatible hyperidentities can be solid.
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.