The Legendre spectral Galerkin method of self-adjoint second order elliptic equations usually results in a linear system with dense and ill-conditioned coefficient matrix. In this paper, the is solved by preconditioned conjugate gradient (PCG) where preconditioner M constructed approximating variable coefficients (T+1)-term series each direction to desired accuracy. A feature proposed PCG that ...

Entangled states are undoubtedly an integral part of various quantum information processing tasks. On the other hand, absolutely separable which cannot be made entangled under any global unitary operations useless from resource theoretic perspective, and hence identifying non-absolutely can important issue for designing technologies. Here we report that nonlinear witness operators provide signi...

Abstract Conventional multidimensional statistical models of roll call votes assume that legislators’ preferences are additively separable over dimensions. In this article, we introduce an item response model allows for non-separability latent Conceptually, matters if outcomes dimensions related rather than independent in decisions. Monte Carlo simulations highlight capture via correlated ideal...

In this paper, we establish the existence and uniqueness of a strong solution to fractional mean field games system with non-separable Hamiltonians, where exponent σ∈(12,1). Our result is new for which generalizes work D.M. Ambrose integral case. The important step choose appropriate order function spaces use Banach fixed-point theorem under stronger assumptions Hamiltonians.