Related papers: On analysis in algebras and modules
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
Various applications of quantum algebraic techniques in nuclear structure physics and molecular physics are briefly reviewed. Contains 81 references.
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
We provide a short introduction to the main features of the algebraic approach to quantum field theories.
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…
In this article, we will showcase some analytical concepts that can be used to tackle Functional Equations (FE) in the positive real numbers domain. Such concepts and related techniques have occasionally appeared in recent High School Math…
In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…
We study extensions of standard description logics to the framework of polyadic modal logic. We promote a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities. As a…
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
A method of local approximation of holomorphic solutions of algebraic equations is discussed
So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…
In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
In this paper, we present an algebraic approach to idempotent functional analysis, which is an abstract version of idempotent analysis. The basic concepts and results are expressed in purely algebraic terms. We consider idempotent versions…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…