Related papers: Certain Observations on Ideals Associated With Wei…
Publication bias, the fact that studies identified for inclusion in a meta analysis do not represent all studies on the topic of interest, is commonly recognized as a threat to the validity of the results of a meta analysis. One way to…
Given $T\subset\mathbb{R}$ and a metric space $M$, we introduce a nondecreasing sequence of pseudometrics $\{\nu_n\}$ on $M^T$ (the set of all functions from $T$ into $M$), called the \emph{joint modulus of variation}. We prove that if two…
For functions $f: \mathcal{P}\rightarrow \mathbb{C}$ on partitions, Bloch and Okounkov defined a power series $\langle f\rangle_q$ that is the "weighted average" of $f$. As Fourier series in $q=e^{2\pi i z}$, such $q$-brackets generate the…
We investigate infinite dimensional modules for a linear algebraic group $\mathbb G$ over a field of positive characteristic $p$. For any subcoalgebra $C \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we consider…
Ab initio modeling of molecular electronics is nowadays routinely performed by combining the Density Functional Theory (DFT) and Nonequilibrium Green function (NEGF) techniques. This method has its roots in the current formula given by Meir…
Gowers introduced, for d\geq 1, the notion of dimension-d uniformity U^d(f) of a function f: G -> \C, where G is a finite abelian group and \C are the complex numbers. Roughly speaking, if U^d(f) is small, then f has certain…
Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs…
When we elastically impose a homogeneous, affine deformation on amorphous solids, they also undergo an inhomogeneous, non-affine deformation, which can have a crucial impact on the overall elastic response. To correctly understand the…
Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example. to calculate the density distribution of the molecules in the…
A semi-relativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach…
The paper present new definitions for weighted DT moduli. Similarly, we a general outcome in an equivalence of moduli of smoothness are obtained. It is known that, any $r \in \mathbb{N}_{\circ}$ , $0<p \leq \infty$, $1 \leq \eta \leq r$ and…
In a recent article (2022) we proved with L. Zaj\'i\v{c}ek that if $ G\subset\R^n $ is an unbounded open convex set that does not contain a translation of a convex cone with non-empty interior, then there exist $ f:G\to\R $ and a concave…
A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure,…
We obtain a complete characterization of the entire functions $g$ such that the integral operator $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ is bounded or compact, on a large class of Fock spaces $\mathcal{F}^\phi_p$, induced by…
We study the density of the weights of Generalized Reed--Muller codes. Let $RM_p(r,m)$ denote the code of multivariate polynomials over $\F_p$ in $m$ variables of total degree at most $r$. We consider the case of fixed degree $r$, when we…
Chebotarev's density theorem asserts that the prime ideals are equidistributed among the conjugacy classes of the Galois group of any normal extension of number fields. An effective version of this theorem was first established by Lagarias…
In this paper we study the growth of ideals in $\mathbb{Z}[t]/(f)$ for a monic cubic polynomial $f$. We also compute the ideal zeta function of $\mathbb{Z}[t]/(t^n)$ for any $n \in \mathbb{N}$.
Gross-Oliveira-Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excited-state densities. The ensemble energy (i.e. the…
In this paper we study the Morse property for functions related to limit functions of mean field equations on a smooth, compact surface $\Sigma$ with boundary $\partial\Sigma$. Given a Riemannian metric $g$ on $\Sigma$ we consider functions…
Rosenfeld's fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of Mobius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set…