General Mathematics
This article is a short introduction to the theory of the groups of points of elliptic curves over finite fields. It is concerned with the elementary theory and practice of elliptic curves cryptography, the new generation of public key…
In this paper, we presents a characterization of compact subsets of the fuzzy number space equipped with the level convergence topology. Based on this, it is shown that compactness is equivalent to sequential compactness on the fuzzy number…
We give an elementary proof to Hasse theorem.
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.
This article is an updated version of the article that was published in the Electronic Journal of Differential Equations on 10. July 2010. Two footnotes have been added. One corrects a minor error not influencing the proof, the second is…
In this book I treat the structure of D-module which has countable basis. If we do not care for topology of D-module, then we consider Hamel basis. If norm is defined in D-module, then we consider Schauder basis. In case of Schauder basis,…
Admin note: withdrawn by arxiv admin due to use of pseudonym against arXiv policy.
In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we…
We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…
We propose a new approach at Fermat's Last Theorem (FLT) solution: for each FLT equation we associate a polynomial of the same degree. The study of the roots of the polynomial allows us to investigate the FLT validity. This technique,…
We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…
The method of application of areas as presented in Euclid's Elements, is employed to generate the three conics as the loci of points with Cartesian coordinates satisfying quadratic equations with coefficients defined by the initial settings…
Maximal planar graph refers to the planar graph with the most edges, which means no more edges can be added so that the resulting graph is still planar. The Four-Color Conjecture says that every planar graph without loops is 4-colorable.…
A regular truncated pyramid with rectangular bases;consists of two rectangular bases whose centers are orthogonally aligned with respect to the parallel planes containing their bases; and two pairs of congruent isosceles trapezoids(the four…
The presented material continues the previous article (arxiv:1007.1059) and also is devoted to the equivalent conversion between the graphs. The examining of the transformation of the vertex graphs into the edge graphs (together with the…
As of this date of this version, this monograph (part I and II) contains most of the technical results relative to the Robinson-styled nonstandard modeling of natural languages and certain associated linguistic processes such as deduction…
In this paper, the spinor formulation of Darboux frame on an oriented surface is given. Also, the relation between the spinor formulation of Frenet frame and Darboux frame are obtained.
This short note contributes a new zero-free region of the zeta function. This zero-free region has the form {s : Re(s) > a}, where a = 21/40.