综合数学
Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…
Even though four theorems are actually proved in this paper, two are the main ones,Teorems 1 and 3. In Theorem 1 we show that if a and be are odd squarefree positive integers satisfying certain quadratic residue conditions; then there…
Using the concept of fuzzy field, we have considered the fuzzy field of real and complex numbers and thereafter we have established a few standard results of real and complex numbers with respect to a membership function.
The purpose of these notes is to present a fairly complete proof of the classification Theorem for compact surfaces. Other presentations are often quite informal (see the references in Chapter V) and we have tried to be more rigorous. Our…
Some basic mathematical tools such as convex sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging and robotics. This report may be viewed…
Gencev has recently reported a closed form summation for an infinite series involving the harmonic numbers and the central binomial numbers. This note indicates a possible approach to the proof involving the dilogarithm function.
Isotopes of C-loops with unique non-identity squares are shown to be both C-loops and A-loops. The relationship between C-loops and Steiner loops is further studied. Central loops with the weak and cross inverse properties are also…
Each triangle has three exterior or external circles tangential to the three straight lines containing the three sides of the triangle.Among the preliminaries in this paper, is deriving formulas for the radii of the three exterior circles…
Infinite sequences are considered in the framework of classical logic from a new point of view.
Given a triangle ABC, a new triangle A'B'C' can be formed as follows: Draw the perpendicular to the line AB at the pointA; then the perpendicular to the line BC at B, and lastly the perpendicular to the line CA at C.the two triangles ABC…
This paper has been withdrawn by the author due to an error.
New Mersenne conjectures. The problems of simplicity, common prime divisors and free from squares of numbers $L(n) = 2^{2n}\pm2^n\pm1$ are investigated. Wonderful formulas $gcd $ for numbers $L (n) $ and numbers repunit are proved.
Taking a new approach towards analyzing the Collatz Problem, or, 3x+1 conjecture. Introducing some new functions, the Collatz-2 and Collatz-3 sequences, as well as deducing results related to Collatz-2 and Collatz-3 sequences.
In the beginning of this paper, we present the general solution to the trigonometric equation asinx+bcosx=c. After that, we focus on the case when a^2+b^2=c^2. In this case, the general solution is expressed in terms of the acute angle…
This paper is an overview of results that show the Brouwer fixed-point theorem (BFPT) to be essentially non-constructive and non-computable. The main results, the counter-examples of Orevkov and Baigger, imply that there is no procedure for…
This short note deals with some applications of the Beta function
The first part of this paper defines recursive interactions by means of logistic functions and derives a general result on the way interacting systems evolve in attractors. It also defines the notion of coevolution trajectory and presents a…
We give examples and counterexamples concerning varieties in which every tolerance is representable as $R \circ R^-$, for some reflexive and admissible relation $R$.
In this paper we consider some analytical relations between gamma function $\Gamma(z)$ and related functions such as the Kurepa's function $K(z)$ and alternating Kurepa's function $A(z)$. It is well-known in the physics that the Casimir…
The aim of this paper is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of…