Related papers: Old and New on Strongly Subadditive/Superadditive …
A new class of convex functions called functions, Young functions, strong Young functions and Orlicz functions are introduced by relaxing the definitions of functions, Young functions, strong Young functions and Orlicz functions. Then, new…
In this work, we establish new analytical results which are required for the derivation of subtle properties of the members of two classes of the generalized Feller--Spitzer distributions introduced in our forthcoming paper.
Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the notion of fine ultrafunctions which improves the older…
The difference between the terms additivity and extensivity, as well as their respective negations, is critically analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
The Additive Transform of an arithmetic function represents a novel approach to examining the interplay between multiplicative arithmetic function and additive functions. This transform concept introduces a method to systematically generate…
In this paper, we introduce two general subclasses of analytic functions by means of the principle of subordination and investigate the coefficient bounds for functions in theese classes. The well-known results are obtained as a corollary…
We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These…
We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…
In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
We define two natural classes of functions, called 2-open and 2-closed, that are closest to open and closed functions. We show that they have the following property: there are $X_i \subset X$ $ (i=1,2,...$) such that $f|X_i$ are open or…
Some notes and observations on analytic functions defined on an annulus
We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.
We study polynomial functors in the incompressible category $\text{Ver}_4^+$, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how…
We introduce notions of lax semiadditive and lax additive $(\infty,2)$-categories, categorifying the classical notions of semiadditive and additive 1-categories. To establish a well-behaved axiomatic framework, we develop a calculus of lax…
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
In this paper, strongly $(\alpha,T)$-convex functions, i.e., functions $f:D\to \R$ satisfying the functional inequality $$ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)-t\alpha\big((1-t)(x-y)\big)-(1-t)\alpha\big(t(y-x)\big)$$ for $x,y\in D$ and $t\in…
This is a survey of results, both classical and recent, on behaviour of plurisubharmonic functions near their $-\infty$-points, together with the related topics for positive closed currents.