综合数学
We consider the concepts of colored terms and multi-hypersubstitutions. Studying the multi-hypersubstitutions we find out necessary and sufficient conditions a variety to be pre-complete. Finally we give an automata realization of…
We propose a simple but interesting graph theoretic problem and posited a heuristic solution procedure, which we have christened as Vectored Route-length Minimization Search (VeRMinS). Basically, it constitutes of a re-casting of the…
This is an easy-reading which describes few geometric invariants which can be obtained from the group SL(2,R) within the Erlangen program of F.Klein.
In order to estimate the average speed of mosquitoes, a simple experiment was designed by Richard (Lu-Hsing Tsai), Tom (Po-Yu Tsai) and Robert (Hung-Ming Tsai). The result of the experiment was posted in the science exhibitions Taichung…
In this article we construct a family of expressions $\varepsilon(n)$. For each element E(n) from $\varepsilon(n)$, the convergence of the series $\sum_{n \ge n_E}{E(n)}$ can be determined in accordance to the theorems of this article. Some…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
The groupoid attached to the action of PSL(2,Z) on the irrational reals by linear fractional transformations is free.
Three formal first-order finite dialectical schemes are investigated. It is shown that schemes 1 and 2 have significantly different finite models. Further, an infinite natural number model for schemes 1, 2, 3 is constructed, and it is shown…
A characterization of congruences in free semigroups is presented.
This study proposes improved chain-ratio type estimator for estimating population mean using some known values of population parameter(s) of the second auxiliary character. The proposed estimators have been compared with two-phase ratio…
This paper concerns exact differential equations. First, I define two types of functions which I have named Basic Function of Type One and Basic Function of Type Two. I then derive the property and theorems of these functions. Finally, by…
In this paper we propose an algorithm that correctly discards a set of numbers (from a previously defined sieve) with an interval of integers. Leopoldo's Theorem states that the remaining integer numbers will generate and count the complete…
Part 1 : For more than two millennia, ever since Euclid's geometry, the so called Archimedean Axiom has been accepted without sufficiently explicit awareness of that fact. The effect has been a severe restriction of our views of space-time,…
Numbers (positive integers) are the most fundamental creatures of the human mind and the foundation to the scientific understanding of nature. Some mathematicians have suspected a link between prime numbers and secrets of creation.…
Since the theory developed by Georg Cantor, mathematicians have taken a sharp interest in the sizes of infinite sets. We know that the set of integers is infinitely countable and that its cardinality is Aleph0. Cantor proved in 1891 with…
In this article we present a simple proof of Borevich-Shafarevich's method to compute the sum of the first n natural numbers of the same power. We also prove several properties of Bernoulli's numbers.
Dirichlet computed in some particular cases the number of equivalence classes of representations of a nonzero integer by a representative system for the integral binary quadratic forms of a given discriminant. We complete this computation.
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…
In recent years, enlargement of the European Union has led to increased interest in the allocation of voting weights to member states with hugely differing population numbers. While the eventually agreed voting scheme lacks any strict…
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…