Calculadora Científica - Symbolab
High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,...
A de Broglie-Bohm Like Model for Klein-Gordon Equation
A de Broglie-Bohm like model of Klein-Gordon equation, that leads to the correct Schrodinger equation in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum potential, the main assumpti...
On some instances of Fox's Integral Equation
We consider some applications of the non-homogeneous second order integral equation of Fox. Some new solutions to Fox's integral equation are discussed in relation to number theory....
Quadratic equation - Wikipedia
In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as a x 2 + b x + c = 0 , {\displaystyle
Classification of bounded travelling wave solutions for the Dullin-Gottwald-Holm equation
In this paper we classify all bounded travelling wave solutions for the integrable Dullin-Gottwald-Holm equation. It is shown that it decomposes in two known cases: the Camassa-Holm and the Korteweg-de Vries equation. For the former, the classificati...
Complexity Blowup for Solutions of the Laplace and the Diffusion Equation
In this paper, we investigate the computational complexity of solutions to the Laplace and the diffusion equation. We show that for a certain class of initial-boundary value problems of the Laplace and the diffusion equation, the solution operator is...
Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler eq…
For the 2D and 3D Euler equations, their existing exact solutions are often in linear form with respect to variables x,y,z. In this paper, the Clarkson-Kruskal reduction method is applied to reduce the 2D incompressible Euler equations to a system of...
On the periodic "good" Boussinesq equation
We study the well-posedness of the initial-value problem for the periodic nonlinear "good" Boussinesq equation. We prove that this equation is local well-posed for initial data in Sobolev spaces \textit{$H^s(\T)$} for $s>-1/4$, the same range of th...
Cosmological Solutions with Charged Black Holes
We consider the problem of constructing cosmological solutions of the Einstein-Maxwell equations that contain multiple charged black holes. By considering the field equations as a set of constraint and evolution equations, we construct exact initial...
On the hyperbolic Pennes equation description of the heat pulse-human cornea interaction
In this paper laser heating of human cornea is investigated. The new heat transport equation in cornea -hyperbolic Pennes equation is formulated and solved. It is shown that for ultra-short laser pulses the thermal energy propagates with finite veloc...
Dynamical Equations from a First-Order Perturbative Superspace Formulation of 10D N=1 Stri…
Utilizing a first-order perturbative superspace approach, we derive the bosonic equations of motion for the 10D, N = 1 supergravity fields. We give the Lagrangian corresponding to these equations derived from superspace geometry. Moreover, the equi...
Pentagon equation and matrix bialgebras
We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pentagon equation is extended to the non-unitary cas...
Analytic solutions of the Schrödinger equation with non-central generalized inverse quadra…
This study presents the solutions of Schrödinger equation for the Non-Central Generalized Inverse Quadratic Yukawa Potential within the framework of Nikiforov-Uvarov. The radial and angular part of the Schrödinger equation are obtained using the me...
Investigation of bifurcations in the behavior of the process equation
This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period doubling rout...
Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation
We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic,...
Majorana equation - Wikipedia
In physics, the Majorana equation is a relativistic wave equation. It is named after the Italian physicist Ettore Majorana, who proposed it in 1937 as
A Finite Equational Base for CCS with Left Merge and Communication Merge
Using the left merge and communication merge from ACP, we present an equational base (i.e., a ground-complete and $ω$-complete set of valid equations) for the fragment of CCS without recursion, restriction and relabelling. Our equational base is f...
Pillai's conjecture for polynomials
In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation \begin{equation*} p^n - q^m = f. \end{equation*} We prove that for any non-constant polynomial $ f $ there are only finitely many vectors $...
Existence and uniqueness of solutions in the Lipschitz space of a functional equation and…
In this paper, we examine the solvability of a functional equation in a Lipschitz space. As an application, we use our result to determine the existence and uniqueness of solutions to an equation describing a specific type of choice behavior model fo...
Is Gravity Actually the Curvature of Spacetime?
The Einstein equations, apart from being the classical field equations of General Relativity, are also the classical field equations of two other theories of gravity. As the experimental tests of General Relativity are done using the Einstein equatio...