Related papers: Sexagesimal Calculations in Ancient Sumer
Supersymmetry has been studied for over three decades by physicists, its superset even longer by mathematicians, and superspace has proven to be very useful both conceptually and in facilitating computations. However, the (1) necessary…
A series of peculiar, visual alignments between the pyramids of the pharaohs of the 4, 5 and 6 Egyptian dynasties exists. These alignments governed from the very beginning the planning of the funerary monuments of successive kings and, in…
Recently, Araci-Acikgoz-Sen derived some interesting identities on weighted q-Euler polynomials and higher-order q-Euler polynomials from the applications of umbral calculus (See [1]). In this paper, we develop the new method of q-umbral…
In this paper, new schemes for a squarer, multiplier and divider of complex numbers are proposed. Traditional structural solutions for each of these operations require the presence some number of general-purpose binary multipliers. The…
In this paper, we study some properties of Euler polynomials arising from umbral calculus. Finally, we give some interesting identities of Euler polynomials using our results. Recently, Dere and Simsek have studied umbral calculus related…
During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles…
We consider the following "partition and sum" operation on a natural number: Treating the number as a long string of digits insert several plus signs in between some of the digits and carry out the indicated sum. This results in a smaller…
We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
Participation of mathematicians in the implementation of economic projects in Poland, in which mathematics-based methods played an important role, happened sporadically in the past. Usually methods known from publications and verified were…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
Recently it has been discovered that on a stone tablet over 3800 years old, the Plimpton-322 table, are carved the geometric relations that exist between the sides of 15 right triangles chosen in a very special way. Due to its property as a…
The main purpose of this paper is to establish some new properties of Horadam numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between Horadam and…
Field experiments are often difficult and expensive to make. To bypass these issues, industrial companies have developed computational codes. These codes intend to be representative of the physical system, but come with a certain amount of…
All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…
This article covers how a computer algebra system (CAS) wxMaxima can be explored for teaching and learning Single-Variable and Multivariable Calculus for Korean digital natives. We present several examples where \emph{wxMaxima} can handle…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the…
By means of the notion of umbrae indexed by multisets, a general method to express estimators and their products in terms of power sums is derived. A connection between the notion of multiset and integer partition leads immediately to a way…
The horologia are ancient ephemerides, tables of durations of the days and nights during all months of the year. The algorithms used to compute the horologia are here presented and the results are compared with the tables computed by…