综合数学

Starting with an infinite set of non linear Equations for the Li-Keiper coefficients, we first specify a lower bound emerging from the infinite set and give a characterization of it. Then, we propose a possible new upper and lower bound for…

We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the…

For a group $G$, we denote by $\stackrel{\leftrightarrow}{G}$ the coarse space on $G$ endowed with the coarse structure with the base $\{\{ (x,y)\in G\times G: y\in x^F \} : F \in [G]^{<\omega} \}$, $x^F = \{z^{-1} xz : z\in F \}$. Our goal…

In this paper, we will be delving deeper into the connection between the rough theory and the ring theory precisely in the principle and maximal ideal. The rough set theory has shown by Pawlak as good formal tool for modeling and processing…

Riemann's hypothesis, formulated in 1859, concerns the location of the zeros of Riemann's Zeta function. The history of the Riemann hypothesis is well known. In 1859, the German mathematician B. Riemann presented a paper to the Berlin…

In this work I look at the distribution of primes by calculation of an infinite number of intersections. For this I use the set of all numbers which are not elements of a certain times table in each case. I am able to show that it exists a…

The aim of this paper is to discus the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of…

A class of log-trigonometric integrals are evaluated in terms of elliptic functions. From this, by using the elliptic integral singular values, one can obtain closed form evaluations of integrals such as \[…

An algebraic approximation, of order $K$, of a polyhedron correlation function (CF) can be obtained from $\gamma\pp(r)$, its chord-length distribution (CLD), considering first, within the subinterval $[D_{i-1},\, D_i]$ of the full range of…

In a series of lectures given in 2003 soon after receiving the Fields Medal for his results in the Algebraic Geometry Vladimir Voevodsky (1966-2017) identifies two strategic goals for mathematics, which he plans to pursue in his further…

In this paper, we introduce the upper and lower approximations on the invers set-valued mapping and the approximations an established on a powerful set valued homomorphism from a ring R1 to power sets of a ring R2. Moreover, the properties…

The so-called holographic principle, originally addressed to the high energy physics, suggests more generally that the information inseparatly bounded with a physical carrier (measured by its entropy) scales as the event horizon surface---a…

The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…

Let G be a Frobenius group with the Frobenius kernel N. Applying character theory, G. Frobenius proved that N was a normal subgroup of G in the year 1901. This is a celebrated application of the character theory of finite groups. In this…

This paper proves that there does not exist a polynomial-time algorithm to the the subset sum problem. As this problem is in NP, the result implies that the class P of problems admitting polynomial-time algorithms does not equal the class…

We present a new proof of a primality criterion first proved by Emmanuel Vantieghem.

We define two categories, the category $\mathfrak{F}\mathfrak{G}$ of fuzzy subgroups, and the category $\mathfrak{F}\mathfrak{C}$ of $F$-inverse covers of inverse monoids, and prove that $\mathfrak{F}\mathfrak{G}$ fully embeds into…

In this paper, we define a graph-theoretic analog for the Riemann tensor and analyze properties of the cyclic symmetry. We have developed a fuzzy graph-theoretic analog of the Riemann tensor and have analyzed its properties. We have also…

We describe the explicit form of a left greatest common divisor and a least common multiple of solutions of a solvable linear matrix equation over a commutative elementary divisor domain. We prove that these left greatest common divisor and…

We study the algebraic structure of the eigenvalues of a Hamiltonian that corresponds to a many-body fermionic system. As the Hamiltonian is quadratic in fermion creation and/or annihilation operators, the system is exactly integrable and…