Related papers: $A_\infty$ condition for general bases revisited: …
We study the sharpness of the side condition in a recent characterization of a limiting class $B_\infty$ of B\'ekoll\'e-Bonami weights by Aleman, Pott and Reguera. This side condition bounds the oscillation of a weight on the top halves of…
In this paper, our aim is to obtain a new generalization of the well-kown Rhoades' contractive condition. To do this, we introduce the notion of an $S$-normed space. We extend the Rhoades' contractive condition to $S$-normed spaces and…
The structure and dynamics of the standard model and gravity are described by a Clifford valued connection and its curvature.
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…
We study the expression complexity of two basic problems involving the comparison of primitive positive formulas: equivalence and containment. In particular, we study the complexity of these problems relative to finite relational…
The basic representation of $\A$ is studied. The weight vectors are represented in terms of Schur functions. A suitable base of any weight space is given. Littlewood-Richardson rule appears in the linear relations among weight vectors.
Categorical studies of recursive data structures and their associated reasoning principles have mostly focused on two extremes: initial algebras and induction, and final coalgebras and coinduction. In this paper we study their in-betweens.…
Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\beta$-ensembles. The conditioning is that…
We review the status of a certain (infinite) class of four-dimensional generally covariant theories propagating two degrees of freedom that are formulated without any direct mention of the metric. General relativity itself (in its Plebanski…
A new version of tetrad gravity in globally hyperbolic, asymptotically flat at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is obtained by using a new parametrization of arbitrary cotetrads to define a set of…
A generalization to the Gibbons-Hawking-York boundary term for metric $f(R)$ gravity theories is introduced. A redefinition of the Gibbons-Hawking-York term is proposed. The proposed new definition is used to derive a consistent set of…
We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
Albiac and Wojtaszczyk introduced property (A) to characterize $1$-greedy bases. Later, Dilworth et al. generalized the concept to $C$-property (A), where the case $C = 1$ gives property (A). They (among other results) characterized greedy…
Fix an integer $ n$ and number $d$, $ 0< d\neq n-1 \leq n$, and two weights $ w$ and $ \sigma $ on $ \mathbb R ^{n}$. We two extra conditions (1) no common point masses and (2) the two weights separately are not concentrated on a set of…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
We give an intrinsic characterization of the closure under shifts $\widehat{\cal A}$ of a given strictly unital $A_\infty$-category ${\cal A}$. We study some arithmetical properties of its higher operations and special conflations in the…
We study a categorical condition on relations, which is a categorical formulation of J\'onsson's characterisation of congruence distributive varieties. Categories satisfying these conditions need not be varieties; for instance, the dual of…
We consider the concept of a generalised manifold in the O(d,d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are…