In this report, several numerical aspects and difficulties for solving a linear system derived from the time-harmonic wave equations are overviewed. The presentation begins with the derivation of the governing equation for waves propagating in general inhomogeneous media. Due to the need of numerical solutions, various discretizations based on finite difference are discussed. Some numerical met...

A constraint logic programming system for the domain of complex functions is described. The intended users of the language are scientist and engineers who often reason/compute with constraints over complex functions, such as functional equalities, diierential equations, etc. Constraints are solved by iterating several solving methods such as Laplace transformation, non-linear equation solving, ...

If the complex Schur decomposition is used to solve a real linear system, then the computed solution generally has a complex component because of roundoff error. We show that the real part of the computed solution that is obtained in this way solves a nearby real linear system. Thus, it is “numerically safe” to obtain real solutions to real linear systems via the complex Schur decomposition. Th...

A constraint logic programming system for the domain of complex functions is described. The intended users of the language are scientist and engineers who often reason/compute with constraints over complex functions, such as functional equalities, diierential equations, etc. Constraints are solved by iterating several solving methods such as Laplace transformation, non-linear equation solving, ...

The paper addresses the problem of solving equations over languages, that model the problem of synthesizing an unknown component, both in hardware and software systems. We investigate what algebraic properties must be satisfied by a composition operator so that the related language equation yields a general solution of the same form, and show sufficient conditions to derive such a largest solut...

this paper studied the mathematical method of flow with regard to two-phase boundary layer that created over the iced surface. based on experimental results, skin drag over the iced surface compared with this force that compute with slip condition. based on this results, for iced surface blasius equation solving at non-slip condition, can replace with solving the blasius equation with slip cond...

Blind source separation technique separates mixed signals blindly without any information on the mixing system. In this paper, we have used two evolutionary algorithms, namely, genetic algorithm and particle swarm optimization for blind source separation. In these techniques a novel fitness function that is based on the mutual information and high order statistics is proposed. In order to evalu...

Let A be a selfadjoint linear operator in a Hilbert space H. The DSM (dynamical systems method) for solving equation Av = f consists of solving the Cauchy problem u̇ = Φ(t, u), u(0) = u0, where Φ is a suitable operator, and proving that i) ∃u(t) ∀t > 0, ii) ∃u(∞), and iii) A(u(∞)) = f . It is proved that if equation Av = f is solvable and u solves the problem u̇ = i(A + ia)u − if, u(0) = u0, wher...

|This paper studies the behavior of a large body of neurons in the continuum limit. A mathematical characterization of such systems is obtained by approximating the inverse input-output nonlinearity of a cell (or an assembly of cells) by three adjustable linearized sections. The associative spatio-temporal patterns for storage in the neural system are obtained by using approaches analogous to s...

We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noises acting on quantum channels. If t...