Comparison of two kinds of approximate proximal point algorithms for monotone variational inequalities

This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ＂Error bounds for proximal point subproblems and associated inexact proximal point algorithms＂ published in 2000. They are both prediction- correction methods which use the same inexactness restriction; the only difference is that they use different search directions in the correction steps. This paper also chooses an optimal step size in the two versions of the APPA to improve the profit at each iteration. Analysis also shows that the two APPAs are globally convergent under appropriate assumptions, and we can expect algorithm 2 to get more progress in every iteration than algorithm 1. Numerical experiments indicate that algorithm 2 is more efficient than algorithm 1 with the same correction step size,

L~∞-Error Estimate of a Nonconfoming Rectangular Plate Element

In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.

An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations

The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.

Exciting Forces for a Wave Energy Device Consisting of a Pair of Coaxial Cylinders in Water of Finite Depth

Two coaxial vertical cylinders-one is a riding hollow cylinder and the other a solid cylinder of greater radius at some distance above an impermeable horizontal bottom,were considered.This problem of diffraction by these two cylinders,which were considered as idealization of a buoy and a circular plate,can be considered as a wave energy device.The wave energy that is created and transferred by this device can be appropriately used in many applications in lieu of conventional energy.Method of separation of variables was used to obtain the analytical expressions for the diffracted potentials in four clearly identified regions.By applying the appropriate matching conditions along the three virtual boundaries between the regions,a system of linear equations was obtained,which was solved for the unknown coefficients.The potentials allowed us to obtain the exciting forces acting on both cylinders.Sets of exciting forces were obtained for different radii of the cylinders and for different gaps between the cylinders.It was observed that changes in radius and the gap had significant effect on the forces.It was found that mostly the exciting forces were significant only at lower frequencies.The exciting forces almost vanished at higher frequencies.The problem was also investigated for the base case of no plate arrangement,i.e.,the case having only the floating cylinder tethered to the sea-bed.Comparison of forces for both arrangements was carried out.In order to take care of the radiation of the cylinders due to surge motion,the corresponding added mass and the damping coefficients for both cylinders were also computed.All the results were depicted graphically and compared with available results.

Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.

Doubly Periodic Wave Solutions of Jaulent-Miodek Equations Using Variational Iteration Method Combined with Jacobian-function Method

One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.

Solution of Travelling Wave for Nonlinear Disturbed Long-Wave System

The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.

An Uncertain Programming Model for Land Use Structure Optimization to Promote Effectiveness of Land Use Planning

Land use structure optimization(LUSO) is an important issue for land use planning. In order for land use planning to have reasonable flexibility, uncertain optimization should be applied for LUSO. In this paper, the researcher first expounded the uncertainties of LUSO. Based on this, an interval programming model was developed, of which interval variables were to hold land use uncertainties. To solve the model, a heuristics based on Genetic Algorithm was designed according to Pareto Optimum principle with a confidence interval under given significance level to represent LUSO result. Proposed method was applied to a real case of Yangzhou, an eastern city in China. The following conclusions were reached. 1) Different forms of uncertainties ranged from certainty to indeterminacy lay in the five steps of LUSO, indicating necessary need of comprehensive approach to quantify them. 2) With regards to trade-offs of conflicted objectives and preferences to uncertainties, our proposed model displayed good ability of making planning decision process transparent, therefore providing an effective tool for flexible land use planning compiling. 3) Under uncertain conditions, land use planning effectiveness can be primarily enhanced by flexible management with reserved space to percept and hold uncertainties in advance.

A Study of Three Variants of Gerund Construction from the Contrastive Perspective of Social and Natural Academic Abstracts on Construction Grammar Theory

English gerund construction is a system composed of 3 variants, including "Gerund + Φ", "Gerund + of + NP", and "Gerund + NP". The noun and verb attributes of the 3 variants are recursive, and in theory their frequencies vary regularly in different styles. An abstract is placed before the beginning of an academic papers, which has the basic characteristics of conciseness and generalization, and has special requirements for the use of gerunds. The purpose of this study was to empirically explore the system of gerund construction in abstracts of natural science and social science papers, and to specifically explore the inherent characteristics of noun and verb properties of the 3 variants. For this purpose, two corpora were constructed, one is about abstracts of natural science papers, and the other is about abstracts of social science papers. Finally, the results of chi-square test showed that there was no significant difference in the frequencies of the 3 variants in the abstracts of natural science and social science papers, and the two corpora can be studied as a whole. In the combined corpus, there were significant differences in the frequencies of the 3 gerund variants. The frequencies of these 3 variants and their gerund properties showed a recursive change.

Method and application of wavelet shrinkage denoising based on genetic algorithm

Genetic algorithm (GA) based on wavelet transform threshold shrinkage (WTS) and translation-invariant threshold shrinkage (TIS) is introduced into the method of noise reduction, where parameters used in WTS and TIS, such as wavelet function, decomposition levels, hard or soft threshold and threshold can be selected automatically. This paper ends by comparing two noise reduction methods on the basis of their denoising performances, computation time, etc. The effectiveness of these methods in-troduced in this paper is validated by the results of analysis of the simulated and real signals.

Explicit Solutions for a New (2+1)-Dimensional Coupled mKdV Equation

An integrable （2＋1）-dimensional coupled mKdV equation is decomposed into two （1 ＋1）-dimensional soliton systems, which is produced from the compatible condition of three spectral problems. With the help of decomposition and the Darboux transformation of two （1＋1）-dimensional soliton systems, some interesting explicit solutions of these soliton equations are obtained.

Soliton Solutions for a Negative Order AKNS Equation Hierarchy

In this paper,bilinear form of a negative order AKNS equation hierarchy is given.The soliton solutionsare obtained through Hiorta's direct method.

Darboux Transformation and Grammian Solutions for Nonisospectral Modified Kadomtsev-Petviashvili Equation with Symbolic Computation

In the present paper, under investigation is a nonisospectral modified Kadomtsev-Petviashvili equation, which is shown to have two Painleve branches through the Painleve analysis. With symbolic computation, two Lax pairs for such an equation are derived by applying the generalized singular manifold method. Furthermore, based on the two obtained Lax pairs, the binary Darboux transformation is constructed and then the N-th-iterated potential transformation formula in the form of Grammian is also presented.

Influence analysis of local heat source on internal temperature distribution of power transformer

Oil immersed power transformer is the main electrical equipment in power system.Its operation reliability has an important impact on the safe operation of power system.In the process of production,installation and operation,its insulation structure may be damaged,resulting in partial discharge and even breakdown inside the transformer.In this paper,S9-M-100/10 oil immersed distribution transformer is taken as the research object,and the distribution laws of electromagnetic field and temperature field in transformer under normal operation,inter turn short circuit and inter layer short circuit are simulated and analyzed.The simulation results show that under normal conditions,the temperatures at the oil gap between the transformer core and the high and low voltage windings and the middle position of the high-voltage winding are high.When there are inter turn and inter layer short circuit faults,the electromagnetic loss of the fault part of the transformer increases,and the temperature rises suddenly.The influence of the two faults on the internal temperature field of the transformer is different,and the influence of the inter turn short circuit fault on the temperature nearby is obvious.The analysis results can provide reference for the thermal fault interpretation and fault classification of transformer.

Comparison of two approximal proximal point algorithms for monotone variational inequalities

Proximal point algorithms （PPA） are attractive methods for solving monotone variational inequalities （MVI）. Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions ofPPA （APPA） are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm Ⅰ; in the same way, Algorithm Ⅱ is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm Ⅱ usually outperforms Algorithm Ⅰ. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm Ⅱ to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some numerical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.

A predictor-corrector interior-point algorithmfor monotone variational inequality problems

Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.

Inhibition of Differentiation by Transforming Growth Factor β1 in Rhabdomyosarcoma Cells

OBJECTIVE To study the effect of transforming growth factor β1 （TGF-β1） on differentiation of rhabdomyosarcoma （RMS） cells METHODS RD （human embryonal RMS cell line） cells, cultured in differentiation medium containing 9-cis retinoic acid （9CRA）, were treated with TGF-β1. Proliferation of the cells was examined by the MTT assay. The differentiation specific proteins （sarcomeric actin and MyHC） and myogenic transcription factors （MyoD1 and myogenin） in the RD cells were assessed by immunofluorescence staining. RESULTS Compared to control cells, treatment with lower concentrations of TGF-β1 （0.1 and 0.2 ng/ml） induced an increase in OD values after 4 d （P〈0.01）, whereas higher concentrations of TGF-β1 （2 and 5 ng/ml） led to a reduction of cell viability （P〈0.01）. After exposure to 9CRA, the viability of the cells decreased significantly （P〈0.01）, while sarcomeric actin, MyHC and myogenin were induced. These changes were antagonized by TGF-β1 （0.1 ng/ml）. No changes were observed in expression of MyoD1. CONCLUSION The RMS cells, derived from myogenic progenitors are committed to a myogenic fate, but are arrested in the differentiation course by the addition of TGF-β1 which represses some of the myogenic transcription factors.

Optimizing bus services with variable directional and temporal demand using genetic algorithm

As a major mode choice of commuters for daily travel, bus transit plays an important role in many urban and metropolitan areas. This work proposes a mathematical model to optimize bus service by minimizing total cost and considering a temporally and directionally variable demand. An integrated bus service, consisting of all-stop and stop-skipping services is proposed and optimized subject to directional frequency conservation, capacity and operable fleet size constraints. Since the research problem is a combinatorial optimization problem, a genetic algorithm is developed to search for the optimal result in a large solution space. The model was successfully implemented on a bus transit route in the City of Chengdu, China, and the optimal solution was proved to be better than the original operation in terms of total cost. The sensitivity of model parameters to some key attributes/variables is analyzed and discussed to explore further the potential of accruing additional benefits or avoiding some of the drawbacks of stop-skipping services.

Calculation of earth pressure based on disturbed state concept theory

The theoretical formulations of Coulomb and Rankine still remain as the fundamental approaches to the analysis of most gravity-type retaining wall,with the assumption that sufficient lateral yield will occur to mobilize fully limited conditions behind the wall.The effects of the magnitude of wall movements and different wall-movement modes are not taken into consideration.The disturbance of backfill is considered to be related to the wall movement under translation mode.On the basis of disturbed state concept(DSC),a general disturbance function was proposed which ranged from-1 to 1.The disturbance variables could be determined from the measured wall movements.A novel approach that related to disturbed degree and the mobilized internal frictional angle of the backfill was also derived.A calculation method benefited from Rankine's theory and the proposed approach was established to predict the magnitude and distribution of earth pressure from the cohesionless backfill under translation mode.The predicted results,including the magnitude and distribution of earth pressure,show good agreement with those of the model test and the finite element method.In addition,the disturbance parameter b was also discussed.