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The aim of this thesis is to give a concise introduction to homotopy type theory, to Aczel's constructive set theory and to simplicial sets and their homotopy theory in particular referring to their standard model structure, showing some of…

Logic · Mathematics 2014-11-21 Cesare Gallozzi

We introduce the so-called weak Pinsker dynamical filtrations, whose existence in any ergodic system follows from the universality of the weak Pinsker property, recently proved by Austin. These dynamical filtrations appear as a potential…

Dynamical Systems · Mathematics 2025-04-02 Séverin Benzoni

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition…

Nuclear Theory · Physics 2015-05-28 X. Viñas , P. Schuck , M. Farine

Factorization, in the sense defined for inclusive hard scattering, is discussed for diffractive hard scattering. A factorization theorem similar to its inclusive counterpart is presented for diffractive DIS. For hadron-hadron diffractive…

High Energy Physics - Phenomenology · Physics 2009-10-30 Arjun Berera

A flow is homotopy continuous if it is indefinitely divisible up to S-homotopy. The full subcategory of cofibrant homotopy continuous flows has nice features. Not only it is big enough to contain all dihomotopy types, but also a morphism…

Algebraic Topology · Mathematics 2007-05-23 Philippe Gaucher

The problem of factorization of a nonextensive probability distribution is discussed. It is shown that, in general, the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the…

Statistical Mechanics · Physics 2007-05-23 Q. A. Wang , M. Pezeril , L. Nivanen , A. Le Mehaute

Let $R$ be a commutative unital ring. A well-known factorization problem is whether any matrix in $\mathrm{SL}_n(R)$ is a product of elementary matrices with entries in $R$. To solve the problem, we use two approaches based on the notion of…

Commutative Algebra · Mathematics 2019-02-12 Evgueni Doubtsov , Frank Kutzschebauch

Given a join semilattice $S$ with a minimum $\hat{0}$, the quarks (also called atoms in order theory) are the elements that cover $\hat{0}$, and for each $x \in S \setminus \{\hat{0}\}$ a factorization (into quarks) of $x$ is a minimal set…

Combinatorics · Mathematics 2023-05-02 Khalid Ajran , Felix Gotti

This paper introduces the notion of weakly globular double categories, a particular class of strict double categories, as a way to model weak 2-categories; it explores its use in defining a double category of fractions, and shows that the…

Category Theory · Mathematics 2013-03-28 Simona Paoli , Dorette Pronk

We investigate weak approximation away from a finite set of places for a class of biquadratic fourfolds inside $\mathbb{P}^3 \times \mathbb{P}^2$, some of which appear in the recent work of Hassett--Pirutka--Tschinkel.

Algebraic Geometry · Mathematics 2025-03-07 Nick Rome

This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…

Probability · Mathematics 2014-10-06 Liang Hong

The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.

Logic · Mathematics 2024-12-03 Fatemeh Shirmohammadzadeh Maleki

We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small constant-depth circuit or formula, then…

Computational Complexity · Computer Science 2025-07-01 Somnath Bhattacharjee , Mrinal Kumar , Shanthanu S. Rai , Varun Ramanathan , Ramprasad Saptharishi , Shubhangi Saraf

The two model-theoretic concepts of weak saturation and weak amalgamation property are studied in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly…

Category Theory · Mathematics 2025-08-06 Ivan Di Liberti

This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…

Data Structures and Algorithms · Computer Science 2019-08-01 Richard Kueng , Joel A. Tropp

In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…

Numerical Analysis · Mathematics 2021-11-05 D. Barrios Rolanía , J. C. García-Ardila

To appear in J. Funct. Spaces and Appl.

Functional Analysis · Mathematics 2008-06-27 Pascal Lefevre , Daniel Li , Herve Queffelec , Luis Rodriguez-Piazzaa

These lectures describe the most important theoretical methods in b-physics. We discuss the formalism of effective weak Hamiltonians, heavy quark effective theory, the heavy quark expansion for inclusive decays of b-hadrons and, finally,…

High Energy Physics - Phenomenology · Physics 2007-05-23 Gerhard Buchalla

We introduce the strong recursive skeletonization factorization (RS-S), a new approximate matrix factorization based on recursive skeletonization for solving discretizations of linear integral equations associated with elliptic partial…

Numerical Analysis · Mathematics 2018-02-13 Victor Minden , Kenneth L. Ho , Anil Damle , Lexing Ying

Let $(M,\Gamma)$ be a Hopf--von Neumann algebra, so that $M_\ast$ is a completely contractive Banach algebra. We investigate whether the product of two elements of $M$ that are both weakly almost periodic functionals on $M_\ast$ is again…

Functional Analysis · Mathematics 2011-10-27 Volker Runde