Related papers: Constructing Even Order Magic Squares By Consecuti…
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…
This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using…
The aim of this paper is to present a recursive construction of simple t-designs for arbitrary t. The construction is of purely combinatorial nature and it requires finding solutions for the indices of the ingredient designs that satisfy a…
Many applications require multi-dimensional numerical integration, often in the form of a cubature formula. These cubature formulas are desired to be positive and exact for certain finite-dimensional function spaces (and weight functions).…
The main purpose of this paper is twofold. We first want to analyze in details the meaningful geometric aspect of the method introduced in the previous paper [12], concerning regularity of families of irreducible, nodal "curves" on a…
Matrix code allows one to discover algorithms and to render them in code that is both compilable and is correct by construction. In this way the difficulty of verifying existing code is avoided. The method is especially important for…
In this short note we propose a new method for construction new nice arrangement on the sphere $S^d$ using the spaces of spherical harmonic.
Explicit algorithms are developed for constructing odd order n pandiagonal latin cubes in 3 and 4 dimensions, and these are used to construct pandiagonal magic cubes and 4 dimensional hypercubes, respectively. It is established that these…
Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…
This paper introduces a novel and efficient partitioning technique for quicksort, specifically designed for real-world data with duplicate elements (50-year-old problem). The method is referred to as "equal quicksort" or "eqsort". Based on…
The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of…
We study 4-by-4 squares formed by cards from the EvenQuads deck. EvenQuads is a card game with 64 cards where cards have 3 attributes with 4 values in each attribute. A quad is four cards with all attributes the same, all different, or half…
The aim of this note is to show that any even perfect number, other than $6$, can be written as the sum of 5 cubes of natural numbers. We also conjecture that any even perfect number, other than $6$, can be written as the sum of only 3…
Given two regular graphs with consistent rotation maps, we produce a constructive method for a consistent rotation map on their Cartesian product. This method will be given as a simple set of rules of addition and table look ups. We assume…
A shuffle of two strings is formed by interleaving the characters into a new string, keeping the characters of each string in order. A string is a square if it is a shuffle of two identical strings. There is a known polynomial time dynamic…
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
This paper is about producing a new kind of the pairs which we call it MS-pairs. To produce these pairs, we use an algorithm for dividing a natural number $x$ by two for two arbitrary numbers and consider their related graphs. We present…
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…
We have found a "non-purely-constructive" method of acquiring algebraic cycles involving multiple steps. This note tries to present the main idea in the last step by concentrating on an example of 4-folds. The method demonstrates a contrast…
In this paper; we prove that all sequences can be broken up in cycles. Each cycle follows the same pattern: 1) Upward trajectory. Odd and even numbers alternate until the cycle reaches an upper bound 2) Downward trajectory. Two or more…