we study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesx_{i}. we introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by x boxtimesy. we investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

In a previous article (J. Algebra 367 (2012), 142-165) we established axiomatic parametrised Cohen-Macaulay approximation which in particular was applied to pairs consisting of finite type flat family rings and modules. this sequel study the induced maps deformation functors deduce properties like smoothness injectivity under general, mainly cohomological conditions on module.

Random Phase Approximation (RPA) is the theory most commonly used to describe excitations of many-body systems. In this article, secular equations are obtained by using three different approaches: equation motion method, Green function perturbation and time-dependent Hartree–Fock theory. Each approach emphasizes specific aspects overlooked other methods. Extensions RPA treat continuum part exci...