Related papers: Quadratic Equations in Elamite Mathematics

H. J. S. Smith proved Fermat's two-square theorem using the notion of palindromic continuants. In this paper we extend Smith's approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of…

It appears that, along with many of my friends and colleagues, I had been brainwashed by the great and tragic lives of Abel and Galois to believe that no general formulas are possible for roots of equations higher than quartic. This seemed…

Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…

We give a uniform estimate for solutions of prescribed scalar curvature type equation in dimension 4.

This paper gives parametric solutions to quartic equations of the type,(4-3-3),(4-4-4),(4-5-5) and (4-6-6), According to Lander, Parkin, and Selfridge (2) conjecture, there are non-trivial solutions of the quartic…

Solving Quadratic equation is one of the intrinsic interests as it is the simplest nonlinear equations. A novel approach for solving Quadratic Equation based on Genetic Algorithms (GAs) is presented. Genetic Algorithms (GAs) are a technique…

Sylvester-type matrix equations have applications in areas including control theory, neural networks, and image processing. In this paper, we establish the necessary and sufficient conditions for the system of Sylvester-type quaternion…

We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.

The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.

We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.

We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.

This manuscript reviews theoretical results and applications related to quadratic forms in Gaussian random variables. It summarizes definitions, canonical representations, exact and approximate distributional results, numerical inversion…

In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed…

We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the…

A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion…

We construct examples of nodal quartic double solids that admit uniformly rational, and so elliptic in Gromov' sense, small algebraic resolutions.

Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…

This paper is concerned with the problem of finding $n$ distinct squares such that, on excluding any one of them, the sum of the remaining $n-1$ squares is a square. While parametric solutions are known when $n=3$ and $n=4$, when $n > 4$,…

In this article we consider the question of the existence of positive symmetric solutions to the problems of the following type $\Delta u=a\left( \left\vert x\right\vert \right) h\left( u\right) +b\left( \left\vert x\right\vert \right)…

Using the circle method, we obtain asymptotic formulae for the number of integer solutions to certain quadratic polynomials that are uniform in the coefficients of the polynomial.