Related papers: More about additive representation functions for i…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

In this short note we give counterexamples to several results related to extension theorems published recently.

Two sets $A,B$ of nonnegative integers are called \emph{additive complements}, if all sufficiently large integers can be expressed as the sum of two elements from $A$ and $B$. We further call $A,B$ \emph{perfect additive complements} if…

We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.

A survey paper on some recent results on additive problems with prime powers.

Let $k\ge 2$ be an integer and let $A$ be a set of nonnegative integers. For a $k$-tuple of positive integers $\underline{\lambda} = (\lambda_{1}, \dots{} ,\lambda_{k})$ with $1 \le \lambda_{1} < \lambda_{2} < \dots{} < \lambda_{k}$, we…

The 2-adic valuation of an integer n which is the exponent of the highest power of 2 that divides n. In this paper, we give representations of certain restricted partition functions in terms of 2-adic valuation.

We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…

Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…

At a conference in Debrecen in October 2010 Nathanson announced some results concerning the arithmetic diameters of certain sets. He proposed some related results on the representation of integers by sums or differences of powers of 2 and…

Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.

We consider approximately greater than relations on fuzzy sets and discuss their properties.

I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a…

We investigate the average number of representations of a positive integer as the sum of $k + 1$ perfect $k$-th powers of primes. We extend recent results of Languasco and the last Author, which dealt with the case $k = 2$ [6] and $k = 3$…

Additive composition (Foltz et al, 1998; Landauer and Dumais, 1997; Mitchell and Lapata, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this…

A conjecture regarding the structure of expander graphs is discussed.

This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results…

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

Let A be a set of integers and let h \geq 2. For every integer n, let r_{A, h}(n) denote the number of representations of n in the form n=a_1+...+a_h, where a_1,...,a_h belong to the set A, and a_1\leq ... \leq a_h. The function r_{A,h}…

The boundedness of the kissing numbers of convex bodies has been known to Hadwiger for long. We present an application of it to the sum-product estimate…