General Mathematics
On the 3x+1 problem, given a positive integer $N$, let $D\left( N \right) $, $O\left( N \right) $, $E\left( N \right) $ be the total iteration steps, the odd iteration steps and the even iteration steps when $N$ iterates to 1(except 1)…
This submission has been withdrawn by arXiv administration.
Hasanalizade [1] studied Deaconescu's conjecture for positive composite integer $n$. A positive composite integer $n\geq4$ is said to be a Deaconescu number if $S_2(n)\mid \phi(n)-1$. In this paper, we improve Hasanalizade's result by…
We propose a rigorous reformulation of the incompressible Navier Stokes equations, starting from the energy equation and the ideal gas law. This reformulation allows the definition of a functional over the pressure field, which is used to…
This paper investigates the generalized Hukuhara differentiability of fuzzy number-valued functions on arbitrary time scales using delta calculus. By carefully examining and improving existing results, we develop a unified and complete…
This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…
We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…
We establish the existence of common fixed points for $C_q$-commuting self-mappings satisfying a generalized Gregus-type inequality with quadratic terms in $q$-starshaped subsets of normed linear spaces. Our framework extends classical…
This study extends the mathematical framework of Hridaya Kolam patterns by applying modular arithmetic to even-ordered dot arrangements with arm counts co-prime to the number of dots. We analyze the resulting cyclic sequences that…
This article introduces a weak pseudo-inverse of a monotone function, which is applied to characterize the associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=t^{[-1]}(F(t(x),t(y)))$ where…
This paper establishes new common fixed point theorems for weakly compatible mappings in metric spaces, relaxing traditional requirements such as continuity, compatibility, and reciprocal continuity. We present a unified framework for three…
In this paper, we focus on clarifying the concept of solving equations of degree greater than six using continuous functions or hypergeometric functions and providing another proof of the non-existence of algebraic solutions for equations…
In this article, we employ a fractional version of the radius of curvature in Euler's equation for column buckling, enabling us to derive a fractional differential equation in the Caputo sense. We solve this equation and demonstrate that…
In this article, we introduce a new class of coupled fractional Lane-Emden boundary value problems. We employ a novel approach, the fractional Haar wavelet collocation method with the Newton-Raphson method. We analyze the conditions in two…
In this note we first review the concept of D-function, closely connected with Cauchy-Schwarz inequality, and then introduce the notion of P-covariance on a Hilbert space, where $P$ is an orthogonal projection. We show that when P is…
Prime numbers are fascinating by the way they appear in the set of natural numbers. Despite several results enlighting us about their repartition, the set of prime numbers is often informally qualified as misterious. In the present paper,…
There was a lot of controversy about corollary 3.12, which was described in the paper Inter-universal Teichmuller Theory III. In this article, another proof of Corollary 3.12 will be derived, where the basis of the proof will be the…
This paper first introduces the concept of p-adic number and field. Then it develops the p-adic integration and applied it to solve p-adic Schrodinger equations.
For polynomials of degree two which have no zeros, the method of accompanying variables is developed and zeros of associated vector polynomials are determined. Our flexible method uses a wide variety of possible vector-valued vector…
We present a unified framework for constructing integer solutions to $A^{n} + B^{n} = C^{n} + D^{n}$ for $n=2,3$. For $n=2$, we derive explicit formulas for any solutions via differences of squares. For $n=3$, we introduce general formulas…