General Mathematics
We establish some common fixed point results for four transformations in vector S-metric spaces by using the notion of weakly compatibility (WC) and occasionally weakly compatibility (OWC). The first theorem is proved by using the concept…
This article examines the Bouton-Lie group invariants of the Navier-Stokes equation (NSE) for incompressible fluids. Bouton's theory is applied to the general scaling transformation admitted by the NSE and is used to derive all self-similar…
In 2016 Izadi and Nabardi (b) showed (4-2-4) has infinitely many integer solutions. They used a specific congruent number elliptic curve.In 2019 Janfada and Nabardi,item C, showed that a necessary condition for n to have an integral…
In this paper we will show how to constructed an Skew-Field with trace-preserving endomorphisms of the affine plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in…
This paper introduces a description of Endomorphisms of the translation group in an affine plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and…
We suggest a closed solution for the roots of polynomial trinomial algebraic equation $$z^n+xz^{n-1}-1=0$$ with an appropriate $x$. This solution is a minor modification to the work of Mikhalkin (Mikhalkin E N, 2006. On solving general…
Smarandache (2003) introduced a new set-valued fuzzy logic called (nonstandard) neutrosophic logic by using Robinson's nonstandard analysis. However, its definition involved many errors including the illegal use of nonstandard analysis. In…
If A is infinite and well-ordered, then |2^A|<=|Part(A)|<=|A^A|.
If two random variables X and A are functionally related via f(X)=A for some strictly monotone continuously differentiable function f:R->R, the distribution of X may easily be computed from the distribution of A.
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
The paper examines the structure of the periodic continued fraction for $\sqrt{d}$ and gives formulae for the central term as well as the repeated partial quotients occurring in its period.
Relations among various musical concepts are investigated through a new concept, musical icosahedron that is the regular icosahedron each of whose vertices has one of 12 tones. First, we found that there exist four musical icosahedra that…
Let ``Faulhaber's formula'' refer to an expression for the sum of powers of integers written with terms in n(n+1)/2. Initially, the author used Faulhaber's formula to explain why odd Bernoulli numbers are equal to zero. Next, Cereceda gave…
The existence of infinitely many consecutive prime triples $p_n$, $ p_{n+1}$, and $p_{n+2}$ as $n \to \infty$, is sufficient to prove that the Catalan constant $\beta(2)=0.9159655941\ldots $ is an irrational number. This note provides the…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
The Collatz conjecture is a famous math problem that was introduced by Lothar Collatz in 1937, and nobody has yet succeeded in proving or disproving it. In this article, I will analyze this problem with a new approach and I will discuss my…
This article provides new asymptotic results for the summatory Mobius function $\sum_{p \leq x} \mu(p+a) =O \left (x(\log x)^{-c} \right )$ and the summatory Liouville function $\sum_{p \leq x} \lambda(p+a) =O \left (x(\log x)^{-c} \right…
In this treatise on the theory of the continuum of the surreal numbers of J.H. Conway, is proved ,that the three different techniques and hierarchies of the continuums of the transfinite real numbers of Glayzal A. (1937) defined through…
This paper discusses the properties the spaces of fuzzy sets in a metric space equipped with the endograph metric and the sendograph metric, respectively. We fist give some relations among the endograph metric, the sendograph metric and the…
The theory of fuzzy mathematics has been proven very effective for defining and solving optimization problems. Fuzzy quadratic programming (FQP) is a consequence of this approach. In this paper, an algorithm has been proposed to solve FQP…