Related papers: Certain Observations on Ideals Associated With Wei…

Mimetic gravity is analysed in the framework of some extensions of General Relativity, where a function of the Gauss-Bonnet invariant in four dimensions is considered. By assuming the so-called mimetic condition, the conformal degree of…

This paper concerns algorithms that give correct answers with (asymptotic) density $1$. A dense description of a function $g : \omega \to \omega$ is a partial function $f$ on $\omega$ such that $\left\{n : f(n) = g(n)\right\}$ has density…

In continuation of [3] we discuss metrics of the form $$ G^P_f(h,k)=\int_M \sum_{i=0}^p\Phi_i(\Vol(f)) \g((P_i)_fh,k) \vol(f^*\g) $$ on the space of immersions $\Imm(M,N)$ and on shape space $B_i(M,N)=\Imm(M,N)/\on{Diff}(M)$. Here $(N,\g)$…

The paper, that continuous some previous work of Sch\"onherr & Schuricht, treats density measures on ${\mathbb R}^n$ that concentrate in any neighborhood of a Lebesgue null set. Such measures are typical for purely finitely additive…

We characterize the model spaces $K_\Theta$ in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to the singular inner factor of…

We investigate infinite dimensional modules for an affine group scheme $\mathbb G$ of finite type over a field of positive characteristic $p$. For any subspace $X \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we…

Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some regularity conditions. Unlike the univariate case, the converse also requires regularity…

We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central…

We discuss the regularity of extremal functions in certain weighted Bergman and Fock type spaces. Given an appropriate analytic function $k$, the corresponding extremal function is the function with unit norm maximizing $\text{Re}…

We study quasifinite highest weight modules over the supersymmetric extension of the $W_{1+\infty}$ algebra on the basis of the analysis by Kac and Radul. We find that the quasifiniteness of the modules is again characterized by…

Let $\mathfrak{g}=\mathfrak{g}_{\bar0}+\mathfrak{g}_{\bar1}$ be a basic classical Lie superalgebra over $\mathbb{C}$, and $e=e_{\theta}\in\mathfrak{g}_{\bar0}$ with $-\theta$ being a minimal root of $\mathfrak{g}$. Set $U(\mathfrak{g},e)$…

Modular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT partition functions that are modular invariant and have…

In this paper we have studied on $\mathcal{I}$-density function using the notion of $\mathcal{I}$-density, introduced by Banerjee and Debnath \cite{banerjee 4} where $\mathcal{I}$ is an ideal of subsets of the set of natural numbers. We…

Two-dimensional $\sigma$-models corresponding to coset CFTs of the type $ (\hat{\mathfrak{g}}_k\oplus \hat{\mathfrak{h}}_\ell )/ \hat{\mathfrak{h}}_{k+\ell}$ admit a zoom-in limit involving sending one of the levels, say $\ell$, to…

The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…

In this paper we construct a class of new irreducible modules over untwisted affine Kac-Moody algebras $\widetilde{\mathfrak{g}}$, generalizing and including both highest weight modules and Whittaker modules. These modules allow us to…

We study invariant measures for random countable (finite or infinite) conformal iterated function systems (IFS) with arbitrary overlaps. We do not assume any type of separation condition. We prove, under a mild assumption of finite entropy,…

For each prime $\ell$, let $|\cdot|_\ell$ be an extension to $\bar \Q$ of the usual $\ell$-adic absolute value on $\Q$. Suppose $g(z) = \sum_{n=0}^\infty c(n)q^n \in M_{k+\half}(N)$ is an eigenform whose Fourier coefficients are algebraic…

Mixing (or prior) density estimation is an important problem in machine learning and statistics, especially in empirical Bayes $g$-modeling where accurately estimating the prior is necessary for making good posterior inferences. In this…

Let $H(D)$ denote the space of holomorphic functions on the unit disk $D$. We characterize those radial weights $w$ on $D$, for which there exist functions $f, g \in H(D)$ such that the sum $|f| + |g|$ is equivalent to $w$. Also, we obtain…