Related papers: Bordered magic squares: elements for a comprehensi…
The physical models of a successful unified theory about the Universe must operate in different phase of matter evolution and different fields of physics. The attempts to build such wide range theory as a bunch of theories developed for…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
Knot mosaics were introduced by Kauffman and Lomonaco in the context of quantum knots, but have since been studied for their own right. A classical knot mosaic is formed on a square grid. In this work, we identify opposite edges of the…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
Based on a previous generalization by the author of Latin squares to Latin boards, this paper generalizes partial Latin squares and related objects like partial Latin squares, completable partial Latin squares and Latin square puzzles. The…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…
There is a significant lack of unified approaches to building generally intelligent machines. The majority of current artificial intelligence research operates within a very narrow field of focus, frequently without considering the…
We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is…
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
The Chernoff bound is one of the most widely used tools in theoretical computer science. It's rare to find a randomized algorithm that doesn't employ a Chernoff bound in its analysis. The standard proofs of Chernoff bounds are beautiful but…
We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.
This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is E795 in the Enestrom index. This paper studies how to construct magic squares with certain numbers of cells, in particular 9, 16, 25 and 36. It considers some…
The presence of a period-doubling cascade in dynamical systems that depend on a parameter is one of the basic routes to chaos. It is rarely mentioned that there are virtually always infinitely many cascades whenever there is one. We report…
The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a given cubic pyramid into a conforming set of congruent…
After a short review of the Method of Recursive Counting we introduce a general algebraic description of recursive lattice building. This provides a rigorous framework for discussion of method's limitations.
A procedure that generates parallelograms from any quadrilateral is presented. If the original quadrilateral is itself a parallelogram, then the procedure gives squares. Hence, when applied two times, this procedure generates squares from…
In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post processing algorithms for connectivity editing and mesh…