Search results for " Algebra"

SIMULATION OF THE HEAT TRANSPORT PROBLEMS WITH RADIATION IN PLATE

2001

In the literature [1 -5 ] simple and effective algorithms for mathematical modelling processes of distribution of heat in multilayered spaces are created. In the given work the way of improvement o f accuracy of algorithms is considered at approximation of integrals derivatives more the supreme orders are used.

The F-pure threshold of quasi-homogeneous polynomials

2018

Abstract Inspired by the work of Bhatt and Singh [3] we compute the F-pure threshold of quasi-homogeneous polynomials. We first consider the case of a curve given by a quasi-homogeneous polynomial f in three variables x , y , z of degree equal to the degree of xyz and then we proceed with the general case of a Calabi–Yau hypersurface, i.e. a hypersurface given by a quasi-homogeneous polynomial f in n + 1 variables x 0 , … , x n of degree equal to the degree of x 0 ⋯ x n .

Testing experimental designs in liquid chromatography (I): Development and validation of a method for the comprehensive inspection of experimental de…

2020

The basis of interpretive optimisation in liquid chromatography is the prediction of resolution, from appropriate solute retention models. The reliability of the process depends critically on the quality of the experimental design. This work develops, validates and applies a general methodology aimed to evaluate the quality of any training experimental design, which will be applied in Part II to design optimisation. The methodology is based on the systematic evaluation of the uncertainties associated to the prediction of retention times in comprehensive scans of both isocratic and gradient experimental conditions. It is able to evaluate comprehensively experimental designs of arbitrary comp…

The Vibrational Stretching States of the Pyramidal Molecules: Application to the Arsine and Stibine.

2002

Zariski Closed Algebras in Varieties of Universal Algebra

2014

Highly Enantioselective Friedel−Crafts Alkylations of Indoles with Simple Enones Catalyzed by Zirconium(IV)−BINOL Complexes

2007

Complexes of BINOL-based ligands with Zr(OtBu)4 catalyze the Friedel-Crafts alkylation reaction of indoles and pyrrole with nonchelating beta-substituted alpha,beta-enones at room temperature affording the expected products with good yields and ee above 95% in most of the studied examples.

Extending CSG with projections: Towards formally certified geometric modeling

2015

We extend traditional Constructive Solid Geometry (CSG) trees to support the projection operator. Existing algorithms in the literature prove various topological properties of CSG sets. Our extension readily allows these algorithms to work on a greater variety of sets, in particular parametric sets, which are extensively used in CAD/CAM systems. Constructive Solid Geometry allows for algebraic representation which makes it easy for certification tools to apply. A geometric primitive may be defined in terms of a characteristic function, which can be seen as the zero-set of a corresponding system along with inequality constraints. To handle projections, we exploit the Disjunctive Normal Form,…

Algebraic Properties to Optimize kNN Queries

2011

International audience; New applications that are being required to employ Database Management Systems (DBMSs), such as storing and retrieving complex data (images, sound, temporal series, genetic data, etc.) and analytical data processing (data mining, social networks analysis, etc.), increasingly impose the need for new ways of expressing predicates. Among the new most studied predicates are the similarity-based ones, where the two commonest are the similarity range and the k-nearest neighbor predicates. The k-nearest neighbor predicate is surely the most interesting for several applications, including Content-Based Image Retrieval (CBIR) and Data Mining (DM) tasks, yet it is also the mos…

Semantic aware RSS query algebra

2010

International audience; Existing XML query algebras are not fully appropriate to retrieve RSS news items mainly due to three reasons: 1) RSS is text rich and its content is dependent on the wording and verbification of the author, thus semantic aware operators are needed; 2) news items are dynamic and consequently time oriented retrieval is needed; 3) a news item may evolve through time, or overlap with other news items and hence identifying relationships between items is also needed. In this paper, we aim to solve these issues by providing a dedicated RSS algebra based on semantic-aware operators that consider RSS characteristics. The provided operators are application domain specific and …

OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS

2010

The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…