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We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.

We give explicit expressions for MacMahon's generalized sums-of-divisors $q$-series $A_r$ and $C_r$ by relating them to (odd) multiple Eisenstein series. Recently, these sums-of-divisors have been studied in the context of quasimodular…

Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…

The notion of subtyping has gained an important role both in theoretical and applicative domains: in lambda and concurrent calculi as well as in programming languages. The soundness and the completeness, together referred to as the…

Let $A,B\in B(H)$. In the present paper, we establish simple and interesting facts on when we have $|A||B|=|B||A|$, $|AB|=|A||B|$, $|A\pm B|\leq |A|+|B|$, $||A|-|B||\leq |A\pm B|$ and $\||A|-|B|\|\leq \|A\pm B\|$, where $|\cdot|$ denotes…

We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers $h_{n}^{\left( r\right) }$ with reciprocal binomial coefficients. These evaluations enable us to extend closed form formula of Euler sums of…

The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.

This paper presents a family of rapidly convergent summation formulas for various finite sums of the form $\sum_{k=0}^{\lfloor x\rfloor}f(k)$, where $x$ is a positive real number.

We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.

In this work we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) truncated homogeneous singular integral operators associated with $L^q$ functions on the sphere and (b) lacunary multiplier…

We improve an existing result on exponential quadrilinear sums in the case of sums over multiplicative subgroups of a finite field and use it to give a new bound on exponential sums with quadrinomials.

We construct infinite classes of almost bent and almost perfect nonlinear polynomials, which are affinely inequivalent to any sum of a power function and an affine function.

We study the effect of finite difference operators of finite order on the distribution of zeros of polynomials and entire functions.

A new kind of diagrams is presented, showing the causal structure of bimetric interactions.

Fourier series with absolutely summable coefficients provide a classical example of a commutative Banach algebra, and these notes are concerned with this and related matters.

In this note some properties of the sum of element orders of a finite abelian group are studied.

We investigate the summability of the coefficients of $m$-homogeneous polynomials and $m$-linear mappings defined on $\ell_{p}$-spaces. In our research we obtain results on the summability of the coefficients of $m$-linear mappings defined…

We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and,…

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…