Related papers: On One Function Defined on the Cartesian Product a…
Multiplicative arithmetic functions satisfying the parallelogram functional equation on prime numbers are investigated. It is derived that the unique solution is a quadratic function by the Goldbach's conjecture.
We use the theory of defaults and their meaning of [GS16] to develop (the outline of a) new theory of argumentation.
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
We define a function by refining Stern's diatomic sequence. We name it the {\it assembly function}. It is strictly increasing continuous. The first and the second main theorems are on an action to the function. The third theorem is on…
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
A doubly infinite set of series expansion for $1/\pi$ are reported. They follow trivially from a formal expansion for the quotient of the values taken by the gamma function for two (complex) arguments differing by an integer plus one half,…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
Norms help regulate a society. Norms may be explicit (represented in structured form) or implicit. We address the emergence of explicit norms by developing agents who provide and reason about explanations for norm violations in deciding…
We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish…
Literature considers under the name \emph{unimaginable numbers} any positive integer going beyond any physical application, with this being more of a vague description of what we are talking about rather than an actual mathematical…
New unconditional estimates of the divisor and totient functions are contributed to the literature. These results are consistent with the Riemann hypothesis and seem to solve the Nicolas inequality for all sufficiently large integers.
The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
The modified q-Bessel functions and the q-Bessel-Macdonald functions of the first and second kind are introduced. Their definition is based on representations as power series. Recurrence relations, the q-Wronskians, asymptotic…
We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely generated residually finite group. The same holds for Cartesian producs of other simple groups…
Recently, degenerate Cauchy numbers and polynomials are introduced in [10]. In this paper, we study the degenerate Cauchy numbers and polynomials which are different from the previous degenerate Cauchy numbers and polynomials. In addition,…
We introduce a new set of prime numbers functions including an exact Generating Function and a Discriminating Function of Prime Numbers neither based on prime number tables nor on algorithms. Instead these functions are defined in terms of…
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism…
A brief historical introduction for the enigmatic number Zero is given. The discussions are for popular consumption.