Related papers: The Generalized Superfactorial, Hyperfactorial and…
We study a notion of generalized H\"older continuity for functions on $\mathbb{R}^d$. We show that for any bounded function $f$ of bounded support and any $r>0$, the $r$-oscillation of $f$ defined as $osc_r f (x):= \sup_{B_r(x)} f -…
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems,…
The previous paper [4] proved the existence of primitive polynomials and primitive normal polynomials of degree n with k prescribed coefficients in the finite field GF(q) for all sufficiently large q. This paper presents a loger versions of…
For $p$ prime, let $\mathcal{H}^n$ be the linear span of characteristic functions of hyperplanes in $(\mathbb{Z}/p^k\mathbb{Z})^n$. We establish new upper bounds on the dimension of $\mathcal{H}^n$ over $\mathbb{Z}/p\mathbb{Z}$, or…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…
We make several comments on the recent work in Ref.~\cite{Rogers:2024nhb} while also reaffirming and adding to the work in Ref.~\cite{Pitonyak:2023gjx}. We show that the factorization formula for $e^+e^-\to (h_1\cdots h_n)\, X$ in…
We introduce the notion of a pseudomultiplier of a Hilbert space $\mathcal H$ of functions on a set $\Omega$. Roughly, a pseudomultiplier of $\mathcal H$ is a function which multiplies a finite-codimensional subspace of $\mathcal H$ into…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
A new characterization of provably recursive functions of first-order arithmetic is described. Its main feature is using only terms consisting of 0, the successor S and variables in the quantifier rules, namely, universal elimination and…
We express some general type of infinite series such as $$ \sum^\infty_{n=1}\frac{F(H_n^{(m)}(z),H_n^{(2m)}(z),\ldots,H_n^{(\ell m)}(z))} {(n+z)^{s_1}(n+1+z)^{s_2}\cdots (n+k-1+z)^{s_k}}, $$ where $F(x_1,\ldots,x_\ell)\in\mathbb…
This paper is a continuation of the research of our previous work and considers quaternionic generalized Carath\'eodory functions and the related family of generalized positive functions. It is addressed to a wide audience which includes…
We consider new series expansions for variants of the so-termed ordinary geometric square series generating functions originally defined in the recent article titled "Square Series Generating Function Transformations" (arXiv: 1609.02803).…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local $O(d,d)$ transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to…
In the present paper we derive a unified new integral whose integrand contains products of Fox $H$-function and a general class of polynomials having general arguments. A large number of integrals involving various simpler functions follow…
The class of type-two basic feasible functionals ($\mathtt{BFF}_2$) is the analogue of $\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments.…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
In this paper we give an integral representation of an $n$-convex function $f$ in general case without additional assumptions on function $f$. We prove that any $n$-convex function can be represented as a sum of two $(n+1)$-times monotone…