相关论文: Quotient probabilistic normed spaces and completen…
We analyse limits and colimits in the category $Part$ of partial groups, algebraic structures introduced by A. Chermak. We will prove that $Part$ is both complete and cocomplete and, in addition, that the full subcategory of finite partial…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
In this paper, we present the Cantor Intersection Theorem and a formulation of Baire Theorem in complete PM spaces. In addition, the Heine-Borel property for PM spaces is considered in detail.
Quantifying quantum coherence is a key task in the resource theory of coherence. Here we establish a good coherence monotone in terms of a state conversion process, which automatically endows the coherence monotone with an operational…
We extend the notion of exact completion on a weakly lex category to elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which freely adds effective quotients and extensional equality. We note that…
We analyze on the formalism of probability measures -functional integrals on function spaces , the problem of infinities on Euclidean field theories
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a (potentially) high-dimensional space. Based on our…
This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…
In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary…
We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings' almost purity theorem, and for which there is a natural tilting operation which exchanges characteristic 0 and…
We present systematic proofs of statements about probability representations of qudit density states in terms of standard probability distributions of dichotomic random variables. New relations and new entropic-information inequalities are…
In this paper, we continue to explore the consistence and usability of Probability Bracket Notation (PBN) proposed in our previous articles. After a brief review of PBN with dimensional analysis, we investigate probability spaces in terms…
We introduce Peano words, which are words corresponding to finite approximations of the Peano space filling curve. We then find the number of occurrences of certain patterns in these words.
We prove a numerical characterization of $\mathbb{P}^n$ for varieties with at worst isolated local complete intersection quotient singularities. In dimension three, we prove such a numerical characterization of $\mathbb{P}^3$ for normal…