Related papers: On generalized Latt\`es maps
In this paper, we introduce and study the iterates of the following family of functions $\varphi_k$ defined on natural numbers which exhibits nice properties. $$\varphi_k(x)=\left\lbrace \begin{array}{ll} x+k, & \mbox{ if $x$ is prime;}\\…
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
We first establish several general properties of modality of algebraic group actions. In particular, we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous…
In this work we present some arithmetic properties of families of abelian $p$--extensions of global function fields, among which are their generators and their type of ramification and decomposition.
A new interpretation of zeta functions is given for F1-schemes which do not satisfy Soul\'e's condition. Functional equations for reductive groups are computed and a new definition of zeta functions attached to more general counting…
In this paper, we introduce a subclass of p-valent non-bazilavec functions of order. Some subordination relations and the inequality properties of p-valent functions are discussed. The results presented here generalize and improve some…
Let $C$ be a subset of $\mathbb{R}^n$ (not necessarily convex), $f:C\to\mathbb{R}$ be a function, and $G:C\to\mathbb{R}^n$ be a uniformly continuous function, with modulus of continuity $\omega$. We provide a necessary and sufficient…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…
We investigate similarity classes of arithmetic lattices in the plane. We introduce a natural height function on the set of such similarity classes, and give asymptotic estimates on the number of all arithmetic similarity classes,…
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the…
For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. In particular, the zero loci of those…
Suppose that $h$ and $g$ belong to the algebra $\B$ generated by the rational functions and an entire function $f$ of finite order on ${\Bbb C}^n$ and that $h/g$ has algebraic polar variety. We show that either $h/g\in\B$ or $f=q_1e^p+q_2$,…
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…
The functional calculus for normal elements in $C^*$-algebras is an important tool of analysis. We consider polynomials $p(a,a^*)$ for elements $a$ with small self-commutator norm $\|[a,a^*]\| \le \delta$ and show that many properties of…
In this paper a natural generalization of the familiar H -function of Fox namely the I -function is proposed. Convergence conditions, various series representations, elementary properties and special cases for the I -function have also been…