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We introduce the so-called BT-category of borelian-topological spaces: it will be a natural frame for a measurable classification of usual foliations and laminations. We focus on the two-dimensional case: borelian laminations by surfaces.…

Dynamical Systems · Mathematics 2007-05-23 M. Bermúdez , G. Hector

The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that i) implies ii) in characteristic 0, using…

Algebraic Geometry · Mathematics 2023-03-14 Yves André

We introduce the mixed Bourgain-Morrey spaces and obtain their preduals. The boundedness of Hardy-Littlewood maximal operator, iterated maximal operator, fractional integral operator, singular integral operator on these spaces is proved.…

Functional Analysis · Mathematics 2025-11-12 Tengfei Bai , Pengfei Guo , Jingshi Xu

We prove that in some cases definable thin sets (including chains) of Borel partial orderings are necessarily countably cofinal. This includes the following cases: analytic thin sets, ROD thin sets in the Solovay model, and $\Sigma^1_2$…

Logic · Mathematics 2018-08-16 Vladimir Kanovei , Vassily Lyubetsky

In this paper, we focus on two classes of D-invariant polynomial subspaces. The first is a classical type, while the second is a new class. With matrix computation, we prove that every ideal projector with each D-invariant subspace…

Numerical Analysis · Mathematics 2011-02-17 Zhe Li , Shugong Zhang , Tian Dong

A class of the Benjamin-Bona-Mahony-Burgers (BBMB) equations with time-dependent coefficients is investigated with the Lie symmetry point of view. The set of admissible transformations of the class is described exhaustively. The complete…

Exactly Solvable and Integrable Systems · Physics 2017-10-02 Olena Vaneeva , Severin Pošta , Christodoulos Sophocleous

Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the…

Statistics Theory · Mathematics 2017-05-29 Christiane Görgen , Anna Bigatti , Eva Riccomagno , Jim Q. Smith

We show that bounded type implies finite type for a constructible subcategory of the module category of a finitely generated algebra over a field, which is a variant of the first Brauer-Thrall conjecture. A full subcategory is constructible…

Representation Theory · Mathematics 2025-07-31 Kevin Schlegel , Andres Fernandez Herrero

This article develops a practical technique for studying representations of $\Bbbk$-linear categories arising in the categorification of quantum groups. We work in terms of locally unital algebras which are $\mathbb{Z}$-graded with graded…

Representation Theory · Mathematics 2025-08-05 Jonathan Brundan

We give an algorithm for computing Segre classes of subschemes of arbitrary projective varieties by computing degrees of a sequence of linear projections. Based on the fact that Segre classes of projective varieties commute with…

Algebraic Geometry · Mathematics 2015-11-30 Corey Harris

This contribution presents a comprehensive analysis of Colombeau (-type) algebras in the range between the diffeomorphism invariant algebra introduced in Part I and Colombeau's original algebra. Along the way, it provides several…

Functional Analysis · Mathematics 2007-05-23 Michael Grosser

We consider an abelian variety defined over a number field. We give conditional bounds for the order of its Tate-Shafarevich group, as well as conditional bounds for the N\'eron-Tate height of generators of its Mordell-Weil group. The…

Number Theory · Mathematics 2020-01-15 Andrea Surroca Ortiz

We prove a model theoretic Baire category theorem for $\tilde\tau_{low}^f$-sets in a countable simple theory in which the extension property is first-order and show some of its applications. We also prove a trichotomy for minimal types in…

Logic · Mathematics 2013-11-19 Ziv Shami

It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…

Functional Analysis · Mathematics 2014-02-26 Valentin Ferenczi , Alain Louveau , Christian Rosendal

Let $n>1$ be an integer. The algebras of the title, which we abbreviate as algebras of type $n$, are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, which are generated by an element of degree $1$ and an element…

Rings and Algebras · Mathematics 2025-01-29 Sandro Mattarei , Simone Ugolini

In this article, we obtain new results for Fourier restriction type problems on compact Lie groups. We first provide a sharp form of $L^p$ estimates of irreducible characters in terms of their Laplace-Beltrami eigenvalue and as a…

Analysis of PDEs · Mathematics 2023-12-25 Yunfeng Zhang

We investigate the relation of countable closed subsets of the reals with respect to continuous monotone embeddability; we show that there are exactly aleph_1 many equivalence classes with respect to this embeddability relation. This is an…

Logic · Mathematics 2007-05-23 Arnold Beckmann , Martin Goldstern , Norbert Preining

Using the classical universal coefficient theorem of Rosenberg-Schochet, we prove a simple classification of all localizing subcategories of the Bootstrap category of separable complex C*-algebras. Namely, they are in bijective…

K-Theory and Homology · Mathematics 2012-02-21 Ivo Dell'Ambrogio

With the help of semi-neighborhoods of the diagonal, classes of Baire spaces are defined: $\Delta$, $\Delta_h$ and $\Delta_s$ Baire spaces. These classes of spaces are studied with the help of topological games. They are useful in studying…

General Topology · Mathematics 2024-10-29 Evgenii Reznichenko

We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…

Algebraic Geometry · Mathematics 2016-07-26 Annette Bachmayr , Michael Wibmer
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