Search results for "algebra"

OnK 0-functions and regular extension operators

1992

Renormalization and Knot Theory

1997

We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and report on recent results in support of this connection.

Faithful representations of left C*-modules

2010

The existence of a faithful modular representation of a left module $$ \mathfrak{X} $$ over a C*-algebra $$ \mathfrak{A}_\# $$ possessing sufficiently many traces is proved.

The role of virtual work in Levi-Civita's parallel transport

2015

The current literature on history of science reports that Levi-Civita’s parallel transport was motivated by his attempt to provide the covariant derivative of the absolute differential calculus with a geometrical interpretation (For instance, see Scholz in The intersection of history and mathematics, Birkhauser, Basel, pp 203–230, 1994, Sect. 4). Levi-Civita’s memoir on the subject was explicitly aimed at simplifying the geometrical computation of the curvature of a Riemannian manifold. In the present paper, we wish to point out the possible role implicitly played by the principle of virtual work in Levi-Civita’s conceptual reasoning to formulate parallel transport.

Construction of Fibred Categories

2019

In Section 5, we introduce methods from classical homological algebra (i.e. using mostly the language of derived categories of abelian categories and their Verdier quotients) to construct the main examples of premotivic categories of interest in this book, while, in Section 6, we study how to check that the localization axiom holds in practice. Section 7 is devoted to the process of obtaining new fibred categories from old ones, by considering homotopy theoretic modules over a ring object.

New Families of Symplectic Runge-Kutta-Nyström Integration Methods

2001

We present new 6-th and 8-th order explicit symplectic Runge-Kutta-Nystrom methods for Hamiltonian systems which are more efficient than other previously known algorithms. The methods use the processing technique and non-trivial flows associated with different elements of the Lie algebra involved in the problem. Both the processor and the kernel are compositions of explicitly computable maps.

Did Pindar’s scheme really exist?

2017

Abstract: A Greek construction in which the verb is in the 3rd sg. form, while the subject is in the 3rd pl. and, in most cases, in post–verbal position, is called Pindar’s scheme inasmuch as it occurs most frequently in the poems of this author. Various explanations have been provided for this construction and it has also been interpreted as an error. The paper is an attempt at an overall syntactic explanation of the available data.

Elliptic convolution operators on non-quasianalytic classes

2001

For those nonquasianalytic classes in which an extension of the classical Borel's theorem holds we show that every elliptic convolution operator is the composition of a translation and an invertible ultradifferential operator. This answers a question asked by Chou in: La transformation de Fourier complexe et l'equation de convolution, LNM 325, Berlin-Heidelberg-New York (1973).

Examples of Indexed PIP-Spaces

2009

This chapter is devoted to a detailed analysis of various concrete examples of pip-spaces. We will explore sequence spaces, spaces of measurable functions, and spaces of analytic functions. Some cases have already been presented in Chapters 1 and 2. We will of course not repeat these discussions, except very briefly. In addition, various functional spaces are of great interest in signal processing (amalgam spaces, modulation spaces, Besov spaces, coorbit spaces). These will be studied systematically in a separate chapter (Chapter 8).

Physical applications of algebras of unbounded operators

2007

During the past 20 years a long series of papers concerning algebras of unbounded operators appeared in the literature, papers which, though being originally motivated by physical arguments, contain almost no physics at all. On the contrary the mathematical aspects of these algebras have been analyzed in many details and this analysis produced, up to now, the monographes [32] and [2]. Some physics appeared first in [28] and [31], in the attempt to describe systems with a very large (1024) number of degrees of freedom, following some general ideas originally proposed in the famous Haag and Kastler’s paper, [27], on QM∞.