Related papers: How to Construct a Large Table of Babylonian Mathe…
In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
Integration by parts (IBP) has acquired a bad reputation. While it allows us to compute a wide variety of integrals when other methods fall short, its implementation is often seen as plodding and confusing. Readers familiar with tabular IBP…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
In the paper, I considered construction of algebra of fractions of algebra with conjugation. I also considered algebra of polynomials and algebra of rational mappings over algebra with conjugation.
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
We propose a systematic method to produce potentially good recursive towers over finite fields. The graph point of view, so as some magma and sage computations are used in this process. We also establish some theoretical functional…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a…
Given positive coprime integers $a$ and $b$ and a natural number $h$, we obtain reciprocity relations which can be used to quickly evaluate summations like $\sum_{i=1}^{h} \{\frac{ib}{a}\}^2$ and $\sum_{i=1}^{h} \lfloor \frac{ib}{a}…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
In this article, a model is proposed using Bayesian techniques to account for the high correlation between many observed set of contingency tables. In many real life data this high correlation is encountered. Simulation studies are also…
After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such…
A method for successive synthesis of the Weyl matrix on the square lattice is proposed. It allows one to compute the Weyl matrix of a large graph by adding new edges and solving elementary systems of linear algebraic equations at each step.…
We give a survey of the following six closely related topics: (i) a general method for constructing a soliton hierarchy from a splitting of a loop algebra into positive and negative subalgebras, together with a sequence of commuting…
We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.
One of the greatest achievements of Greek mathematics is the proof that the square root of 2 is irrational. It has not been thought that the Babylonians appreciated the concept of irrationality and certainly that they did not prove that the…