综合数学
The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral…
Based on the closed operational laws in picture fuzzy numbers and strict triangular norms, we extend the Bonferroni mean (BM) operator under the picture fuzzy environment to propose the picture fuzzy interactional Bonferroni mean (PFIBM),…
In the current note, we study Lorentzian para-Kenmotsu (in brief, $LP$-Kenmotsu) manifolds admitting Ricci-Yamabe solitons (RYS) and gradient Ricci-Yamabe soliton (gradient RYS). At last by constructing a 5-dimensional non-trivial example…
This paper extends the Pythagorean Theorem to positive and negative real exponents to take the form a^n + b^n = c^n and makes use of the definition gamma = b/a >= 1. For the case of n in the set of positive real numbers, n greater than or…
Admissible orders on fuzzy numbers are total orders which refine a basic and well-known partial order on fuzzy numbers. In this work, we define an admissible order on triangular fuzzy numbers (i.e. TFN's) and study some fundamental…
The equidistribution of the double sign patterns of the Liouville function $\lambda$ is proved unconditionally. As application, it is shown that the computable real number $$\sum_{n \geq 1} \frac{1+\lambda(n)}{2^{n}}$$ is a simply normal…
If the chromatic number of Euclidean plane is larger than four, but it is known that the chromatic number of planar graphs is equal to four, then how does one explain it? In my opinion, they are contradictory to each other. This idea leads…
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of…
In this article, we give Maurer-Cartan characterizations of equivariant Lie superalgebra structures. We introduce equivariant cohomology and equivariant formal deformation theory of Lie superalgebras. As an application of equivariant…
In this paper we will prove that the vorticity belongs to L1(0; T ; L2(R3)) for the Cauchy problem of 3D incompressible Navier-Stokes equation, then the existence of a global smooth solution is obtained. Our approach is to construct a set…
This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…
Applying Littlewood's lemma in connection to Riemann's Hypothesis and exploiting the symmetry of Riemann's $xi$ function we show that almost all nontrivial Riemann's Zeta zeros are on the critical line.
Some mathematical properties of the Erd\"os number and its formal equivalents are shown. An informetric equivalent is presented: the Rousseau number. This contribution honors Ronald Rousseau for his 73th birthday.
A solution of linear systems of equations Ax=b and Ax=0 is a vital part of many computational packages. This paper presents a novel formulation based on the projective extension of the Euclidean space using the outer product (extended…
I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for an…
This work presents closed formulas for determinant, permanent, inverse, and Drazin inverse of circulant matrices with two non-zero coefficients.
In this paper we present an elementary proof for a special case of Fermat's last theorem for specific category of a, b and c. In fact, we assume that $n$ is prime and $4\rvert (n+1),$ then for $a,b$ and $c$ that $ n\nmid abc$ the equation…
In this survey we discuss derivatives of the Wright functions (of the first and the second kind) with respect to parameters. Differentiation of these functions leads to infinite power series with coefficient being quotients of the digamma…
The theory of fuzzy sets has a wide range of applications, one of which is that of fuzzy groups . The fuzzy sets were introduced by Zadeh. Even though, the story of fuzzy logic started much earlier, it was specially designed mathematically…
The Hirsch function of a given continuous function is a new function depending on a parameter. It exists provided some assumptions are satisfied. If this parameter takes the value one, we obtain the well-known h-index. We prove some…