Related papers: Some new $I_\lambda$-lacunary statistical converge…
We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin…
In this work, we introduce some new generalized sequence space related to the space l(p). Furthermore we investigate some topological properties as the completeness, the isomorphism and also we give some inclusion relations between this…
We derive Onsager-Machlup functionals for countable product measures on weighted $\ell^p$ subspaces of the sequence space $\mathbb{R}^{\mathbb{N}}$. Each measure in the product is a shifted and scaled copy of a reference probability measure…
We review a new formalism based on Orlicz spaces for the description of large regular statistical systems. Our presentation includes both classical and quantum systems. The presented approach has the advantage that statistical mechanics is…
Let $\mathbb N$ be the set of positive integers, and denote by $\lambda(A)=\inf\{t>0:\sum_{a\in A} a^{-t}<\infty\}$ the convergence exponent of $A\subset\mathbb N$. For $0<q\le 1$, $0\le q\le 1$, respectively, the admissible ideals…
In this paper, we define and study a class $\mathcal{R}_{c}$ of norms on $L^{\infty}\left( \mathbb{T}\right) $, called $continuous\ rotationally\ symmetric \ norms$, which properly contains the class $\left \{ \left \Vert \cdot \right \Vert…
In recent years, it has been shown that some classical inequalities follow from a local stochastic dominance for naturally associated random polytopes. We strengthen planar isoperimetric inequalities by attaching a stochastic model to some…
We show that in Lorentzian manifolds, sectional curvature bounds of the form $\mathcal{R}\le K\,$, as defined by Andersson and Howard, are closely tied to space-time convex and $\lambda$-convex ($\lambda>0$) functions, as defined by Gibbons…
In this paper, Lusternik-Schinrelmann and geometric category of finite spaces are considered. We define new numerical invariants of these spaces derived from the geometric category and present an algorithmic approach for its effective…
In this lecture notes I concentrate on the classic and widely applicable characterization of higher order statistics by joint moments, a.k.a. higher order correlation functions, and directly related statistics. I put special emphasis on…
We develop the Stienstra-Beukers theory of supercongruences in the setting of the Catalan-Larcombe-French sequence. We also give some applications to other sequences.
The maximal Orlicz space such that the mixed logarithmic means of multiple Fourier series for the functions from this space converge in $L_{1}$-norm is found.
Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $< C_\alpha | \alpha < \lambda^+ >$ with the following remarkable guessing property:…
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…
We characterize when an Orlicz space $L^A$ is almost compactly (uniformly absolutely continuously) embedded into a Lorentz space $L^{p,q}$ in terms of a balance condition involving parameters $p,q\in[1,\infty]$, and a Young function $A$. In…
By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we…
In this paper we study the notion of $\mathcal{I}$ and $\mathcal{I^*}$-equal convergence in linear 2-normed spaces and some of their properties. We also establish the relationship between them.
We develop a calculus based on graph enumeration for $S_n$-equivariant motivic invariants of graphically stratified moduli spaces. We apply our theory to the Deligne--Mumford moduli space $\overline{\mathcal{M}}_{g, n}$ and to the space of…
We develop the stochastic two-scale convergence method in the framework of Orlicz-Sobolev spaces, in order to deal with the homogenization of coupled stochastic-periodic problems in such spaces. One fundamental in this topic is the…
Let $(\varphi_i)_{i=1}^n$ be mutually orthogonal functions on a probability space such that $\|\varphi_i\|_\infty \leq 1 $ for all $i \in [n]$. Let $\alpha > 0$. Let $\Phi(u) = u^2 \log^{\alpha}(u)$ for $u \geq u_{0}$, and $\Phi(u) =…