Resumo em Inglês:

An initial value problem is solved for the motion of an incompressible viscous conducting fluid with embedded small inert spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid-body rotation with constant angular velocity about an axis normal to the plate. The unsteady flow is generated in the fluid-particle system due to velocity tooth pulses subjected on the plate in presence of a transverse magnetic field. It is assumed that no external electric field is imposed on the system and the magnetic Prandtl number is very small. The operational method is used to derive exact solutions for the fluid and the particle velocities and the shear stress at the wall. Some limiting cases of these solutions including the steady-state results are discussed. The general solutions for the fluid velocity and the wall shear stress are examined numerically and the simultaneous effects of rotation, the magnetic field and the particles on them are determined. Finally, the present result for the fluid velocity has been compared numerically with that generated by an impulsively moved plate in a particular case when time is large.

Resumo em Inglês:

In this paper, the generalized anti-reflexive solution for matrix equations (BX = C, XD = E), which arise in left and right inverse eigenpairs problem, is considered. With the special properties of generalized anti-reflexive matrices, the necessary and sufficient conditions for the solvability and a general expression of the solution are obtained. Furthermore, the related optimal approximation problem to a given matrix over the solution set is solved. In addition, the algorithm and the example to obtain the unique optimal approximation solution are given.

Resumo em Inglês:

We present and analyze a new iterative scheme for large-scale solution of the well-known Sylvester equation. The proposed scheme is based on fixed point iteration approach and can make good use of the recently developed methods for solving block linear systems. It is shown mathematically that the iterative process converges under some assumptions on the coefficient matrices. Results on our numerical experiments with large-scale matrices are quite encouraging. In particular, the method compares favorably with the other block methods and a recently proposed method for Sylvester equation based on low-rank approximation of the right hand side matrix C.

Resumo em Inglês:

In this article we solve a nonlinear cutting stock problem which represents a cutting stock problem that considers the minimization of, both, the number of objects used and setup. We use a linearization of the nonlinear objective function to make possible the generation of good columns with the Gilmore and Gomory procedure. Each time a new column is added to the problem, we solve the original nonlinear problem by an Augmented Lagrangian method. This process is repeated until no more profitable columns is generated by Gilmore and Gomory technique. Finally, we apply a simple heuristic to obtain an integral solution for the original nonlinear integer problem.

Resumo em Inglês:

In 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in the continuous wavelet transform (CWT) of a function analyzed with different B-spline wavelets.

Resumo em Inglês:

The nonlinear conjugate gradient method is a very useful technique for solving large scale minimization problems and has wide applications in many fields. In this paper, we present a new algorithm of nonlinear conjugate gradient method with strong convergence for unconstrained minimization problems. The new algorithm can generate an adequate trust region radius automatically at each iteration and has global convergence and linear convergence rate under some mild conditions. Numerical results show that the new algorithm is efficient in practical computation and superior to other similar methods in many situations.