Mathematics

2021, Mathematics, Ukraine / 20.07.2021

Seymour’s Second Neighborhood Conjecture states that every simple digraph without loops or two-cycles contains a vertex whose second neighborhood is at least as large as its first. In this project we show that from existence of a counterexample to Second Neighborhood Conjecture it follows that there exist strongly-connected counterexamples with both low and high density (dense and sparse graph). We...

2021, Mathematics, Turkey / 20.07.2021

This project is analyzed in three parts. In the first part, Covid-19 and winter diseases that show similar symptoms are distinguished by using fuzzy soft set matrices. In the second part, while calculating the Covid-19 follow-up treatment priority, a risk score algorithm is created with the help of six criteria: age, hypertension, cardiovascular disease, cancer, chronic kidney failure and diabetes....

2021, Mathematics, Switzerland / 20.07.2021

Most nations and their healthcare systems have been overwhelmed by the COVID-19 pandemic. Mass testing is central to rapid tracing and breaking the chain of community transmission. However, corona testing can be prohibitively expensive, especially for poorer nations. We develop and present testing protocols based on the group testing technique, in which several samples are pooled and evaluated as a...

2021, Mathematics, Poland / 19.07.2021

A seemingly simple question – "where lies the center of the triangle?" – turns out to lack an easy answer. Many different constructions emerged during centuries of mathematical discussion. Each of these points is somehow special, and none is a better fit for "the triangle center" than the others. There is even an "Encyclopedia of Triangle Centers" containing more than...

2021, Czechia, Mathematics / 19.07.2021

In the text we provide a gentle introduction to algebraic number theory and show its applications in solving certain difficult diophantine equations. We begin with a quick summary of the theory of quadratic residues, before diving into a select few areas of algebraic number theory. Our article is accompanied by a worked problem and a list of other problems solved...

2020, Mathematics, Poland / 19.07.2021

Pell’s equation is a well-known Diophantine equation, which has been studied since ancient times -first by the Greek (the famous cattle problem of Archimedes) and Indian mathematicians (Bhaskara, Brahmagupta), and then in Europe (Brouncker, Euler, Fermat, Lagrange). Pell’s equation is related to many important problems in mathematics, and has applications mainly in algebraic number theory and theory of continued fractions....

2020, Belarus, Mathematics / 14.07.2021

In 1962, Oystein Ore asked in which graphs there is exactly one geodesic between any two vertices. He called such graphs geodetic. In this paper, we systematically study the properties of geodetic, as well as antipodal graphs, in each vertex of which has exactly one antipode (the vertex farthest from it). We find necessary and sufficient conditions and obtain results...