Related papers: Renewal Theory and Geometric Infinite Divisibility
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
We examine Hilbert bimodules which possess a (generally unbounded) involution. Topics considered include a linking algebra representation, duality, locality, and the role of these bimodules in noncommutative differential geometry.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
Integrating Amdahl's and Amdahl-like laws with Divisible Load Theory promises mathematical design methodology that will make possible the efficient design of tomorrow's systems.
Certain renewal theorems are extended to the case that the rate of the renewal process goes to 0 and, more generally, to the case that the drift of the random walk goes to infinity. These extensions are motivated by and applied to the…
We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
We extend a functional limit theorem for symmetric $U$-statistics [Miller and Sen, 1972] to asymmetric $U$-statistics, and use this to show some renewal theory results for asymmetric $U$-statistics. Some applications are given.
Isoparametric hypersurfaces and their application to special geometries
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
Examples of repeatable procedures and maps are found in the open quantum dynamics of one qubit that interacts with another qubit. They show that a mathematical map that is repeatable can be made by a physical procedure that is not.
In this paper, we give a purely cohomological interpretation of the extension problem for (super) Lie algebras; that is the problem of extending a Lie algebra by another Lie algebra. We then give a similar interpretation of infinitesimal…
We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing…
In this paper, by using the residue theorem and asymptotic formulas of trigonometric and hyperbolic functions at the poles, we establish many relations involving two or more infinite series of trigonometric and hyperbolic trigonometric…
In this note the range-renewal structure of general independent and identically distributed samplings is discussed, which is a natural extension of the result in Chen et al (arXiv:1305.1829).
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set…
Several terms in an asynptotic estimate for the renewal mass function ina discrete random walk which has positive mean and regularly varying right-hand tail are given. Similar results are given for the renewal density function in the…