Related papers: Certain Observations on Ideals Associated With Wei…
We extend Wolff's theorem concerning ideals on H-infinity(D) to the matrix case, giving conditions under which an H-infinity solution G to the equation FG = H exists for all z in D, where F is an m-by-infinity matrix of functions in…
Gowers introduced the notion of uniformity norm $\|f\|_{U^k(G)}$ of a bounded function $f:G\rightarrow\mathbb{R}$ on an abelian group $G$ in order to provide a Fourier-theoretic proof of Szemeredi's Theorem, that is, that a subset of the…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
In this paper, we define new functionals generalizing scientometric indices proposed by Mesiar and G\k{a}golewski in 2016 to overcome some limitations of h-index. These functionals are integrals with respect to a monotone measure as well as…
A variety of norm inequalities related to Bergman and Dirichlet spaces induced by radial weights are considered. Some of the results obtained can be considered as generalizations of certain known special cases while most of the estimates…
We report on a numerical study of the density matrix functional introduced by Lieb, Solovej and Yngvason for the investigation of heavy atoms in high magnetic fields. This functional describes {\em exactly} the quantum mechanical ground…
The main focus of this paper is on the problem of relating an ideal $I$ in the polynomial ring $\mathbb Q[x_1, \dots, x_n]$ to a corresponding ideal in $\mathbb F_p[x_1,\dots, x_n]$ where $p$ is a prime number; in other words, the…
We study (two-sided) ideals $I$ in the enveloping algebra $\U(\frak g_\infty)$ of an infinite-dimensional Lie algebra $\frak g_\infty$ obtained as the union (equivalently, direct limit) of an arbitrary chain of embeddings of simple…
Given a smooth algebraic variety X with an action of a connected reductive linear algebraic group G, and an equivariant D-module M, we study the G-decompositions of the associated V-, Hodge, and weight filtrations. If M is the localization…
For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with…
In this expository paper aimed at a general mathematical audience, we discuss how to combine certain classic theorems of set-theoretic inner model theory and effective descriptive set theory with work on Hilbert's tenth problem and…
We continue the study on Kurzweil--Stieltjes integration on compact lines initiated in [doi:10.1007/s11117-025-01161-9]. Given a real valued function $G$ on a compact line, the presented integral is called the Kurzweil--Stieltjes integral…
The main goal of this paper is to compute two related numerical invariants of a primitive ideal in the universal enveloping algebra of a semisimple Lie algebra. The first one, very classical, is the Goldie rank of an ideal. The second one…
A universal stellar initial mass function (IMF) should not be expected from theoretical models of star formation, but little conclusive observational evidence for a variable IMF has been uncovered. In this paper, a parameterization of the…
In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar $f$, dubbed as density function, which…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable…
A wealth of observations recently challenged the notion of a universal stellar initial mass function (IMF) by showing evidences in favour of a variability of this statistical indicator as a function of galaxy properties. I present…
In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules $L$ over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras $\mathfrak{g}$. The problems…
In this paper we consider the problem of finding the {\em densest} subset subject to {\em co-matroid constraints}. We are given a {\em monotone supermodular} set function $f$ defined over a universe $U$, and the density of a subset $S$ is…