A reduced-order extrapolation algorithm based on CNLSMFE formulation and POD technique for two-dimensional Sobolev equations

A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.

An efficient analytical decomposition and numerical procedure for boundary layer flow on a continuous stretching surface

An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.

(111)取向的Bi_2Ti_2O_7薄膜的介电性质

The Bi 2Ti 2O 7 thin films have been prepared on silicon by metalorganic deco mposition (MOD) technique using bismuth nitrate and titanium butoxide as source materials.The growth procedure of the Bi 2Ti 2O 7 thin films was discussed.Th e surface morphology of the Bi 2Ti 2O 7 film was studied by the Electri c Force Microscope (EFM).The crystallization of the films was studied by X r ay diffraction (XRD).The Bi 2Ti 2O 7 thin film prepared on (100) silicon subs trate was proved with strong (111) orientation.The dielectric properties and the current voltage (I V) characteristics were measured.The dielectric constant o f the Bi 2Ti 2O 7 thin films vs.temperature and frequency in the interval 100 8 00℃ were studied.The dielectric constang is 118 and dielectric loss is 0.07 res pectively at 100KHz at room temperature.The resistivity of the Bi 2Ti 2O 7 th in film is higher than 1×10 12 (Ω·cm) under the applied voltage from -5V to 5V.For films 0.4μm thick annealed at 580℃ for 40 minutes,their leakage cu r r ent density is 4.06×10 -7 A/cm 2 at an applied voltage of 15V.This shows the films have very good insulating property. We observed the obviously ferroelectric phase transition and its Curie temperatu re in the Bi 2Ti 2O 7 ceramic.Capacitance vs.temperature was measured with 27 800℃ at 1kHz,10kHz,100kHz and 1MHz,respectively.

Power Generation Expansion Planning Using an Interior Point with Cutting Plane （IP/CP） Method

The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point with cutting plane （IP/CP） method is proposed to solve the mixed-integer optimization problem of the electrical power generation expansion planning. The IP/CP method could improve the overall efficiency of the solution and reduce the computational time. Proposed method is combined with the Bender＇s decomposition technique in order to decompose the generation expansion problem into a master investment problem and a slave operational problem. The numerical example is presented to compare with the effectiveness of the proposed algorithm.

Queue Size Distribution of Geo/G/1 Queue Under the Min(N,D)-Policy

This paper considers a discrete-time Geo/G/1 queue under the Min（N, D）-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first （Min（N, D）-policy）. By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of tile transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n＋. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution, l^trthermore, the important relations between the steady state queue length distributions at different time epochs n , n and n＋ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.