Related papers: Filtrations
This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…
In this paper we review some old and new results about the enlargement of filtrations problem, as well as their applications to credit risk and insider trading problems. The enlargement of filtrations problem consists in the study of…
Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.
The major steps in the development of our knowledge about neutrinos are reviewed. The basics of neutrino oscillation formalism is presented. Neutrino oscillations in the framework of three-neutrino mixing are considered. The evidence for…
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density…
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
A tame filtration of an algebra is defined by the growth of its terms, which has to be majorated by an exponential function. A particular case is the degree filtration used in the definition of the growth of finitely generated algebras. The…
This is a book on derived foliations, that are a generalisation of classical foliations in the context of derived geometry. The text starts with the basic definitions and constructions, then explore foliated cohomology (with crystal…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
We give an elementary introduction to the theory of supermembranes.
A concise guide to very basic bicategory theory, from the definition of a bicategory to the coherence theorem.
The aim of this paper is twofold. One is to give a definition of the Euler characteristic of infinite acyclic categories with filtrations and the other is to prove the invariance of the Euler characteristic under the subdivision of finite…
In this exploratory article, we draw attention to the common formal ground among various estimators such as the belief functions of evidence theory and their relatives, approximation quality of rough set theory, and contextual probability.…
This paper traces the history of compactness from the original motivating questions, through the development of the definition, to a generalization of sequential compactness in terms of nets and filters.
The article is devoted to linear quasigroups and some of their generalizations. In the first part main definitions and notions of the theory of quasigroups are given. In the second part some elementary properties of linear quasigroups and…
This chapter amalgamates some foundational developments and calculations in factorization homology.
We construct a fundamental theory of the derived category of non-finite bi-filtered complexes.