Related papers: Finitely Star Regular Domains
After briefly reviewing the results about polytropic stars in Palatini f(R)-theories, we first show how these results rely on the assumption of a regular function f(R). In particular, singular models allow to extend the parameter interval…
A set is star-shaped if there is a point in the set that can see every other point in the set in the sense that the line-segment connecting the points lies within the set. We show that testing whether a non-empty compact smooth region is…
We show that there exists a complete local Noetherian normal domain of prime characteristic whose perfection is a non-coherent GCD domain, answering a question of Patankar in the negative concerning characterizations of $F$-coherent rings.…
We extend the concept of a finite dimensional {\it holomorphic homogeneous regular} (HHR) domain and some of its properties to the infinite dimensional setting. In particular, we show that infinite dimensional HHR domains are domains of…
FC is a first-order logic that reasons over all factors of a finite word using concatenation, and can define non-regular languages like that of all squares (ww). In this paper, we establish that there are regular languages that are not…
Recall that a ring R is called strongly pi-regular if, for every a in R, there is a positive integer n, depending on a, such that a^n belongs to the intersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study of the notion…
After the introduction in 1994, by Okabe and Matsuda, of the notion of semistar operation, many authors have investigated different aspects of this general and powerful concept. A natural development of the recent work in this area leads to…
An integral domain $D$ is called a \emph{prime-divisor-finite domain} (PDF-domain) if every nonzero element has only finitely many nonassociate prime divisors. A domain $D$ is said to be a \emph{tightly prime-divisor-finite domain}…
We consider the lattice-ordered groups Inv$(R)$ and Div$(R)$ of invertible and divisorial fractional ideals of a completely integrally closed Pr\"ufer domain. We prove that Div$(R)$ is the completion of the group Inv$(R)$, and we show there…
Let $\mathbb{K}$ be an uncountable field of characteristic zero and let $f$ be a function from $\mathbb{K}^n$ to $\mathbb{K}$. We show that if the restriction of $f$ to every affine plane $L\subset\mathbb{K}^n$ is regular, then $f$ is a…
Let $I\subseteq{\mathbb{R_+}}$ be a non empty and non singleton interval where ${\mathbb{R_+}}$ denotes the set of all non negative numbers. A function $\Phi: I\to {\mathbb{R_+}}$ is said to be subadditive if for any $x,y$ and $x+y\in I$,…
Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are…
An integral domain $R$ is \emph{perinormal} if every local going-down overring is a localization of $R$ and \emph{globally perinormal} if every going-down overring is a localization of $R$. In this paper, I introduce notions of graded…
We study rational functions admitting a continuous extension to the real affine space. First of all, we focus on the regularity of such functions exhibiting some nice properties of their partial derivatives. Afterwards, since these…
In the present investigation, we introduce a new subclass of starlike functions defined by $\mathcal{S}^{*}_{\tau}:=\{f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\arctan z=:\tau(z)\}$, where $\tau(z)$ maps the unit disk $\mathbb {D}:= \{z\in…
Several f(R) modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that…
We investigate a compact star in the general $F(R)$ gravity. Developing a novel formulation in the spherically symmetric and static space-time with the matter, we confirm that an arbitrary relation between the mass $M$ and the radius $R_s$…
A word-to-word function is rational if it can be realized by a non-deterministic one-way transducer. Over finite words, it is a classical result that any rational function is regular, i.e. it can be computed by a deterministic two-way…
Let R be a commutative ring and I an ideal of R. A sub-ideal J of I is a reduction of I if JI^n = I^n+1 for some positive integer n. The ring R has the (finite) basic ideal property if (finitely generated) ideals of R do not have proper…
Let $T$ be a complete local (Noetherian) ring of characteristic zero. We find necessary and sufficient conditions for $T$ to be the completion of a quasi-excellent local domain. In the case that $T$ contains the rationals, we provide…