Related papers: CGAlgebra: a Mathematica package for conformal geo…
An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the…
$\Gamma$-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in terms of Lie algebras and their…
The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic limit of the symmetries of a relativistic Conformal Field Theory in any dimensions. It is known to be infinite-dimensional in all spacetime dimensions. In…
Firstly we discuss briefly three different algebras named as nonrelativistic (NR) conformal: Schroedinger, Galilean conformal and infinite algebra of local NR conformal isometries. Further we shall consider in some detail Galilean conformal…
Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic…
Trimming techniques are efficient ways to generate complex geometries in Computer-Aided Design(CAD). In this paper, an improved isogeometric analysis(IGA) method for trimmed geometries is proposed. We will show that the proposed method…
In this article, we introduce and investigate a class of C$^{\ast}$-algebras generated by reduced graph products of C$^{\ast}$-algebras, augmented with families of projections naturally associated with words in right-angled Coxeter groups.…
The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R.…
Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a…
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.
We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…
This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of…
The usual Galilean contraction procedure for generating new conformal symmetry algebras takes as input a number of symmetry algebras which are equivalent up to central charge. We demonstrate that the equivalence condition can be relaxed by…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…