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The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
A higher order difference equation may be generally defined in an arbitrary nonempty set S as: \[ f_{n}(x_{n},x_{n-1},...,x_{n-k})=g_{n}(x_{n},x_{n-1},...,x_{n-k}) \] where $f_{n},g_{n} :S^{k+1}\rightarrow S$ are given functions for…
A quadratic form f is said to have semigroup property if its values at points of the integer lattice form a semigroup under multiplication. A problem of V. Arnold is to describe all binary integer quadratic forms with semigroup property. If…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
In this note, we study a factorization result for graded decomposition maps associated with the specializations of graded algebras. We obtain results previously known only in the ungraded setting.
This paper contains an account of arbitrary cubic function fields of characteristic three. We define a standard form for an arbitrary cubic curve and consider its function field. By considering an integral basis for the maximal order of…
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularities of plane algebraic curves, and on the other, show how…
In this note, we show that the algebraicity of the Fourier coefficients of half-integral weight modular forms can be determined by checking the algebraicity of the first few of them. We also give a necessary and sufficient condition for a…
This article explains the relationship between analytic and algebraic order in case of abstract pseudo-differential operators for a regular spectral triple.
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
We continue our studies on semilattice ordered algebras. This time we accept constants in the type of algebras. We investigate identities satisfied by such algebras and describe the free objects in varieties of semilattice ordered algebras…
There exists a particular subset of algebraic power series over a finite field which, for different reasons, can be compared to the subset of quadratic real numbers. The continued fraction expansion for these elements, called…
Some partial orderings which compare probability distributions with the expo- nential distribution, are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which de-…
In this paper we completely classify semifields of order $2^8=256$ containing a nucleus of order $2^4=16$. We introduce new invariants for semifields, and apply new computational techniques for calculating old invariants. Together these…
It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to…
The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…
In this paper we give an algorithm for the computation of all the Arf numerical semigroups with a given genus. Moreover, we generalize the concept of genus of a numerical semigroup to good semigroups of $\mathbb{N}^r$ and we give a…
We observe algebraic derivations on an affine domain B defined over an algebraically closed field of characteristic 0, which are called locally finite derivations in commutative and non-commutative contexts in other references. We observe…
Let $f\_1,\ldots, f\_s$ be formal power series (respectively polynomials) in thevariable $x$. We study the semigroup of orders of the formal series inthe algebra $K[[ f1,\ldots, f\_s]] \subseteq K[[ x ]]$ (respectively the semigroup of…
This paper introduces a novel approach to the axiomatic theory of quadratic forms. We work internally in a category of certain partially ordered sets, subject to additional conditions which amount to a strong form of local presentability.…