We study the band structure of semiconductor nanowires with quantum dots embedded in them. The is calculated using Rayleigh–Ritz variational method. consider two different types, one type defined by electrostatic potentials applied to nanowire, while other adding materials offsets respect parameters nanowire. are particularly interested appearance discrete energy levels gap between conduction a...

This paper may be regarded as a new numerical method for the analysis of triangular thin plates using the natural area coordinates. Previous studies on the solution of triangular plates with different boundary conditions are mostly based on the Rayleigh-Ritz principle which is performed in the Cartesian coordinates. Consequently, manipulation of the geometry and numerical calculation of the int...

We study the band structure of semiconductor nanowires with quantum dots embedded in them. The is calculated using Rayleigh–Ritz variational method. consider two different types, one type defined by electrostatic potentials applied to nanowire, while other adding materials offsets respect parameters nanowire. are particularly interested appearance discrete energy levels gap between conduction a...

The finite temperature effective potential of the Abelian Higgs Model is studied using the self-consistent composite operator method, which can be used to sum up the contributions of daisy and superdaisy diagrams. The effect of the momentum dependence of the effective masses is estimated by using a Rayleigh-Ritz variational approximation.

We consider the problem of computing PageRank. The matrix involved is large and cannot be factored, and hence techniques based on matrix-vector products must be applied. A variant of the restarted refined Arnoldi method is proposed, which does not involve Ritz value computations. Numerical examples illustrate the performance and convergence behavior of the algorithm. AMS subject classification ...

Microvibrations at frequencies between 1 and 1000 Hz generated by on-board equipment can propagate through a satellite's structure and hence signiicantly reduce the performance of sensitive payloads. This paper describes a Lagrange-Rayleigh-Ritz method for developing models suitable for the design of active control schemes. Here Loop Transfer Recovery based controller design methods are employe...

Multigrid algorithms are the method of choice for solving large Ritz-Galerkin systems for elliptic boundary value problems. Using b-spline bases provides geometric flexibility as well as many computational advantages and permits particularly efficient and elegant implementations. This is described for a fairly general discretization which covers all principal features of b-spline elements.

The generalized minimum residual method (GMRES) is well known for solving large nonsymmetric systems of linear equations. It generally uses restarting, which slows the convergence. However, some information can be retained at the time of the restart and used in the next cycle. We present algorithms that use implicit restarting in order to retain this information. Approximate eigenvectors determ...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...