Fedir M. Sokhats’kyi recently posed four problems concerning parastrophic equivalence between generalized quasigroup functional equations. Sava Krstić in his PhD thesis established a connection between generalized quadratic quasigroup functional equations and connected cubic graphs. We use this connection to solve two of Sokhats’kyi’s problems, giving also complete characterization of parastrop...

The possibility of calibrating a camera based on the identification of matching points in several views of a scene taken by the same camera has been shown by Maybank and Faugeras ([13, 4]). Using techniques of Projective Geometry they showed that each pair of views of the scene can be used to provide two quadratic equations in the five unknown parameters of the camera. A method of solving these...

Abstract: The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Vilenkin-Fourier series is of weak type (1,1). Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1), provided that the supremum in the maximal operator is tak...

Kung-Traub conjecture states that an iterative method without memory for finding the simple zero of a scalar equation could achieve convergence order 2d−1, and d is the total number of function evaluations. In an article “Babajee, D.K.R. On the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations, Algorithms 2016, 9, 1, doi:10.3390/a9010001”, the author has shown that Kun...

Abstract In this work, we study the existence of one and exactly solution x ? C [ 0 , 1 ] x\in C\left[0,1] , for a delay quadratic integral equation Volterra-Stieltjes type. As special cases fractional order Ch...

A generalization of the Hopf–Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimen...

Now, the formula does not provide us with a solution that is written in decimal form; to get such a solution we need to evaluate the above expression. To this end, since most computers perform additions, subtractions, multiplications, and even divisions very fast, we should focus on the need to take a squareroot. In short, the “explicit” solution for the quadratic equation actually reduces our ...