Related papers: Generalizations of amicable numbers
In a general algebraic setting, we state some properties of commutators of reflexive admissible relations.
In this paper, first, we define and investigate $k$-layered numbers, which are a generalization of Zumkeller numbers. After that, we generalize the concept of Zumkeller labeling and Zumkeller cordial labeling to $k$-layered labeling and…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
We prove some new results related to Tanaka's formula.
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
The Jacobian algebras are introduced and their various properties are studied.
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We present a new alternating convolution formula for the super Catalan numbers which arises as a generalization of two known binomial identities. We prove a generalization of this formula by using auxiliary sums, recurrence relations, and…
We study properties related to nice enumerability of countably categorical structures and properties related to extreme amenability of automorphism groups of these structures. The text substantially differs from the previous version. In…
In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.
In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
In this paper, we study sequences of positive numbers preserving summability. In particular, the open set property for such a family of sequences is shown. Several classes of sequences preserving summability, including polynomials, sums of…
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.
By classifying $S$-maximal amenable subgroups of algebraic groups over a global field of characteristic zero, we obtain a complete classification of maximal amenable subgroups up to commensurability in the respective arithmetic groups.…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
In the present paper our main objective is to extend the notion of $D$-sets in countable amenable groups and to discuss its connection with weak mixing for amenable group actions. Further we prove that *-notions are equivalent in the…