Related papers: On the Construction of Even Order Magic Squares
We show the 3 by 3 magic square of squares problem equivalent to solving quartic polynomials with certain factorization constraints over an abelian extension of the rationals. We analyze a particular case in which said extension is assumed…
Squaring the circle is impossible, but it can be squared approximately. Ramanujan gave a construction correct to eight decimal places. In his book Mathographics, Dixon gave constructions correct to three decimal places. In this article, we…
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,…
Processors may find some elementary operations to be faster than the others. Although an operation may be conceptually as simple as some other operation, the processing speeds of the two can vary. A clever programmer will always try to…
Linearizing two partial orders to maximize the number of adjacencies and minimize the number of breakpoints is APX-hard. This holds even if one of the two partial orders is already a linear order and the other is an interval order, or if…
We present a simple procedure for explicitly constructing a companion basis for a quiver mutation equivalent to a simply-laced Dynkin quiver.
We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell's equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…
In this exploratory article, we present a constructive method for scattering points on the surface of $d$ dimensional spheres which we believe is new and of interest. Indeed, the problem of uniformly distributing points on spheres is an…
A fake octagon is a genus two translation surface with only one singular point and the same periods as the octagon. Existence of infinitely many fakes was first established by McMullen in 2007, and more generally follows from dynamical…
The paper presents a simple and concise proof of correctness of the magic transformation. We believe it may provide a useful example of formal reasoning about logic programs. The correctness property concerns the declarative semantics. The…
Determining if a point is in a polygon or not is used by a lot of applications in computer graphics, computer games and geoinformatics. Implementing this check is error-prone since there are many special cases to be considered. This holds…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
This paper is concerned with the description of exceptional simple Lie algebras as octonionic analogues of the classical matrix Lie algebras. We review the Tits-Freudenthal construction of the magic square, which includes the exceptional…
A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.
The aim of this paper is to give a simple construction of the free skew-brace over a set $X$.
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
For prime powers q we use "strongly orthogonal" linear Sudoku solutions of order q^2 to construct ordered orthogonal arrays of type OOA (4,s,2,q), and for each q we present a range of values of s for which these constructions are valid.