A fundamental result in linear algebra states that if a homogenous equation system has only the trivial solution, then there are at most as many variables equations. We prove following generalisation of this phenomenon. If possibly infinite with finitely each exists an injection from to equations maps variable which it appears.

We discuss linear algebra of infinite-dimensional vector spaces in terms algebraic (Hamel) bases. As an application we prove the surjectivity a large class partial differential operators with smooth ($\mathcal C^\infty$-coefficients) coefficients, called article \emph{regular}, acting on dual $\mathcal D^*(\Omega)$ space test-functions D(\Omega)$. The guarantees solvability corresponding equati...

In the present paper, we have studied MHD free convective two dimensional unsteady viscous incompressible flows through a porous effect bounded by an infinite vertical porous plate with constant suction. The permeability of the porous medium fluctuates in time about a constant mean, and the viscosity of fluid is assumed to vary as a linear function of temperature. The flow is permitted under th...

a two dimensional generalized thermoelastic problem of a thick circular plate of finite thickness and infinite extent subjected to continuous axisymmetric heat supply and an internal heat generation is studied within the context of generalized thermoelasticity. unified system of equations for classical coupled thermoelasticity, lord-shulman and green-lindsay theory is considered. an exact solut...

Abstract. We consider a linear-quadratic-Gaussian (LQG) optimal control problem where the generalized state space is the product of an Euclidian space and an infinite dimensional function space. This model originates from a mean field LQG game with a major player and a large number of minor players, and has importance in designing decentralized strategies in the game. We show that the underlyin...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...

‎in this paper‎, ‎an efficient algorithm for solving a system of linear‎ ‎equations based on the homotopy analysis method is presented‎. ‎the‎ ‎proposed method is compared with the classical jacobi iterative‎ ‎method‎, ‎and the convergence analysis is discussed‎. ‎finally‎, ‎two‎ ‎numerical examples are presented to show the effectiveness of the‎ ‎proposed method.‎