Related papers: On Some Fractional order Binomial sequence spaces …
We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences $(x_k)$ such that $x_k x_{2k}=0$ for all…
We introduce a shifted version of the binomial theorem, and use it to study some remarkable trigonometric integrals and their explicit rewriting in terms of binomial multiple sums. Motivated by the expressions of area generating functions…
It is widely believed that the continued fraction expansion of every irrational algebraic number $\alpha$ either is eventually periodic (and we know that this is the case if and only if $\alpha$ is a quadratic irrational), or it contains…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…
Rationals are known to form interesting and computationally rich structures, such as Farey sequences and infinite trees. Little attention is being paid to more general, systematic exposition of the basic properties of fractions as a set.…
We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…
In this paper, by using the theory of circulant matrices we study some matrices over finite fields which involve the quadratic character and trinomial coefficients.
A minimal separating set is found for the algebra of matrix invariants of several 2x2 matrices over an infinite field of arbitrary characteristic
We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…
We investigate compositional iteration of fractional order for transseries. For any large positive transseries $T$ of exponentiality 0, there is a family $T^{[s]}$ indexed by real numbers $s$ corresponding to teration of order $s$. It is…
We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant,…
A tensor space is a vector space equipped with a finite collection of multilinear forms. The length of a tensor space is its length as a representation of its symmetry group. Infinite dimension tensor spaces of finite length are special,…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure…
We develop summation by parts (SBP) approach for generating high-order finite-difference schemes on the interval and propose new sets of schemes up to the 12th order. The coefficients of the schemes are governed by values of grid spacing…
We construct explicitly in any finite field of the form Fq[x]/(x^m-a) elements with multiplicative order at least 2^{(2m)^(1/2)}
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…
We present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the…
In this study, we define new paranormed sequence spaces by combining a double sequential band matrix and a diagonal matrix. Furthermore, we compute the $\alpha-,\beta-$ and $\gamma-$ duals and obtain bases for these sequence spaces. Besides…