Related papers: Around rational functions invertible in radicals
In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give applications to the characterization of the splitting primes…
In this paper, we first present a classification theorem of infinite-dimensional simple Novikov algebras over an algebraically closed field with characteristic 0. Then we classify all the irreducible modules of a certain…
In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…
We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical…
The properties of the Wilson rational functions ${}_{10}\phi_9$ with three different normalizations are described. For one normalization, it satisfies an $R_{II}$ recurrence relation, whereas for the two other ones, they satisfy a…
Modular categories are important algebraic structures in a variety of subjects in mathematics and physics. We provide an explicit, motivated and elementary definition of a modular category over a field of characteristic 0 as an equivalence…
Godel's theory T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0, the successor function S, and the operator R_tau for primitive recursion on objects of type tau. It is known that…
Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…
This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the…
Let $F$ be a number field with ring of integers $O_F$ and let $G$ be a finite group. We describe an approach to the study of the set of realisable classes in the locally free class group $Cl(O_FG)$ of $O_FG$ that involves applying the work…
Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we extend a well-known result about the Picard group of a semisimple group to reductive…
Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to…
Function clones are sets of functions on a fixed domain that are closed under composition and contain the projections. They carry a natural algebraic structure, provided by the laws of composition which hold in them, as well as a natural…
Let $\Sigma$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of $\Sigma$ over the field of rational functions can be algebraically generated by a finite…
We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results…
Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.
To any real rational function with generic ramification points we assign a combinatorial object, called a garden, which consists of a weighted labeled directed planar chord diagram and of a set of weighted rooted trees each corresponding to…
In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…