序数方程法在微机辅助设计旋转叠加条纹投影片中的应用

由序数方程法推导出产生旋转叠加条纹的定片条纹方程．并设计程序绘制定片条纹和动片条纹。

Process optimization with consideration of uncertainties——An overview

Optimization under uncertainty is a challenging topic of practical importance in the Process Systems Engineering.Since the solution of an optimization problem generally exhibits high sensitivity to the parameter variations, the deterministic model which neglects the parametric uncertainties is not suitable for practical applications. This paper provides an overview of the key contributions and recent advances in the field of process optimization under uncertainty over the past ten years and discusses their advantages and limitations thoroughly. The discussion is focused on three specific research areas, namely robust optimization, stochastic programming and chance constrained programming, based on which a systematic analysis of their applications, developments and future directions are presented. It shows that the more recent trend has been to integrate different optimization methods to leverage their respective superiority and compensate for their drawbacks. Moreover, data-driven optimization, which combines mathematical programming methods and machine learning algorithms, has become an emerging and competitive tool to handle optimization problems in the presence of uncertainty based on massive historical data.

Weyl-Ordered Operator Product Formula Derived by Technique of Integration Within Weyl-Ordered Product of Operators

Based on the explicit Weyl-ordered form of Wigner operator and the technique of integration within Weylordered product of operators we derive the Weyl-ordered operator product formula. The formula is then generalized to the entangled form with the help of entangled state representations.

A New Trial Equation Method and Its Applications

As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves(ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean.We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea(19°35'N,112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors,and an acoustic Doppler current profiler(ADCP).We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories.Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width.Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries(KdV) theory than the first-order KdV model.These results indicate that the northwestern South China Sea(SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

Periodic Folded Wave Patterns for(2+1)-Dimensional Higher-Order Broer-Kaup Equation

A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.

Features and correct application of coal vitrinite reflectance index

The law of mathematical statistics, which the coal vitrinite reflectance index obeys, the existing vitrinite representing deviations, and the advantages of judging coalification and the shortage of judging coal type were analyzed. The advantages and disadvantages of various determination methods and the expression index and different methods of identifying vitrinite on the determination results were compared. The vitality of coal vitrinite reflectance depends on its full play the unique function of reflectance histogram and the systematic errors between different determination methods do not affect the application based on reflectance histogram are considered.

Effects of liquefaction-induced large lateral ground deformation on pile foundations

The pile-soil system interaction computational model in liquefaction-induced lateral spreading ground was established by the finite difference numerical method.Considering an elastic-plastic subgrade reaction method,numerical methods involving finite difference approach of pile in liquefaction-induced lateral spreading ground were derived and implemented into a finite difference program.Based on the monotonic loading tests on saturated sand after liquefaction,the liquefaction lateral deformation of the site where group piles are located was predicted.The effects of lateral ground deformation after liquefaction on a group of pile foundations were studied using the fmite difference program mentioned above,and the failure mechanism of group piles in liquefaction-induced lateral spreading ground was obtained.The applicability of the program was preliminarily verified.The results show that the bending moments at the interfaces between liquefied and non-liquefied soil layers are larger than those at the pile＇s top when the pile＇s top is embedded.The value of the additional static bending moment is larger than the peak dynamic bending moment during the earthquake,so in the pile foundation design,more than the superstructure＇s dynamics should be considered and the effect of lateral ground deformation on pile foundations cannot be neglected.

Several boundary identification methods of gravity data and application in Vientiane of Laos area

The authors studied the potential field boundary identification of the new technology in order to find out the possible fractures or contact zones using the following methods such as tilt derivative,horizontal derivative of tilt derivative,normalized standard deviation and normalized differential method. Combined with Euler deconvolution and small subdomain filtering,the actual data processing results show that these methods are all able to identify wider range extending fractures and obtain abundant geological information. The horizontal derivative of tilt derivative and normalized differential method have a better resolution for the small cutting fractures and lacunae in the studied area. They provide a reliable basis for study of the cutting relationship between fractures.

Rapid Convergence of a New Wave Iterative Algorithm Used to Model a Patch Structure

The wave iterative method is a numerical method used in the electromagnetic modeling of high frequency electronic circuits. The object of the authors＇ study is to improve the convergence speed of this method by adding a new algorithm based on filtering techniques. This method requires a maximum number of iterations, noted Nmax, to achieve the convergence to the optimal value. This number wilt be reduced in order to reduce the computing time. The remaining iterations until Nmax will be calculated by the new algorithm which ensures a rapid convergence to the optimal result.

Meteorological Data Generation for the Numerical Simulation of Stratified Flow in the Joumine Reservoir, Tunisia

Dynamic numerical simulation of water conditions is useful for reservoir management. In remote semi-arid areas, however, meteorological and hydrological time-series data needed for computation are not frequently measured and must be obtained using other information. This paper presents a case study of data generation for the computation of thermal conditions in the Joumine Reservoir, Tunisia. Data from the Wind Finder web site and daily sunshine duration at the nearest weather stations were utilized to generate cloud cover and solar radiation data based on meteorological correlations obtained in Japan, which is located at the same latitude as Tunisia. A time series of inflow water temperature was estimated from air temperature using a numerical filter expressed as a linear second-order differential equation. A numerical simulation using a vertical 2-D （two-dimensional） turbulent flow model for a stratified water body with generated data successfully reproduced seasonal thermal conditions in the reservoir, which were monitored using a thermistor chain.

Unit Commitment with Production Cost Uncertainty： A Recourse Programming Method

Many studies have considered the solution of Unit Commitment problems for the management of energy networks. In this field, earlier work addressed the problem in determinist cases and in cases dealing with demand uncertainties. In this paper, the authors develop a method to deal with uncertainties related to the cost function. Indeed, such uncertainties often occur in energy networks （waste incinerator with a priori unknown waste amounts, cogeneration plant with uncertainty of the sold electricity price...）. The corresponding optimization problems are large scale stochastic non-linear mixed integer problems. The developed solution method is a recourse based programming one. The main idea is to consider that amounts of energy to produce can be slightly adapted in real time, whereas the on/off statuses of units have to be decided very early in the management procedure. Results show that the proposed approach remains compatible with existing Unit Commitment programming methods and presents an obvious interest with reasonable computing loads.

Calculation of the Energy Distribution of Electrons Emitted from Tungsten

The numerical calculation of the energy distribution of electrons emitted by the tungsten, for a triangular barrier and given reflection images, has been carried out. It is shown that the numerical solution of Schrodinger equation is the most effective method of calculation of the transparency of potential barrier among those used in work. I-V characteristics, which were calculated by the application of this method under different conditions, match the experimental data the best. The application of the numerical solution of Schrodinger equation for the calculation of transparency of the potential barrier enables the in-depth analysis of the tunnels phenomena and allows forecasting the effects which can not be received by application of Wentzel-Kramers-Brillouin approximation.

Mechanical analysis of fixed geosynthetic technique of GRPS embankment

To overcome the deficiencies of conventional geosynthetic-reinforced and pile-supported (GRPS) embankment, a new improvement technique, fixed geosynthetic technique of GRPS embankment (FGT embankment), was developed and introduced. Based on the discussion about the load transfer mechanism of FGT embankment, a simplified check method of the requirement of geosynthetic tensile strength and a mechanical model of the FGT embankment were proposed. Two conditions, the pile cap and pile beam conditions are considered in the mechanical model. The finite difference method is used to solve the mechanical model owing to the complexity of the differential equations and the soil strata. Then, the numerical procedure is programmed. Finally, a field test is conducted to verify the mechanical model and the calculated results are in good agreement with field measured data.

Effect of Gaussian Noise Amplitude on Translation Error Estimated Using Double-Wayland Algorithm

The Wayland algorithm has been improved in order to evaluate the degree of visible determinism for dynamical systems that generate time series. The objective of this study is to show that the Double-Wayland algorithm can distinguish between time series generated by a deterministic process and those generated by a stochastic process. The authors conducted numerical analysis of the van der Pol equation and a stochastic differential equation as a deterministic process and a Ganssian stochastic process, respectively. In case of large S/N ratios, the noise term did not affect the translation error derived from time series data, but affected that from the temporal differences of time series. In case of larger noise amplitudes, the translation error from the differences was calculated to be approximately 1 using the Double-Wayland algorithm, and it did not vary in magnitude. Furthermore, the translation error derived from the differenced sequences was considered stable against noise. This novel algorithm was applied to the detection of anomalous signals in some fields of engineering, such as the analysis of railway systems and bio-signals.

The Application of the Combined Method for Selection of Optimal Excitation Parameters

The quality as well as reliability of electrical energy transmitted to consumers is one of the main parameters of successful operation of the power system. The searching of optimal coefficient＇s combination of PSS （power system stabilizer） is the main goal of this article. The possibility of application of the new combined approach for the optimal excitation＇s settings search is presented. MC （Monte Carlo） method, in order to search and select the optimal combination of excitation system, was applied. The proposed method has been researched with a mathematical model of the power system. This model has been built using Matlab/Simulink software. Paper shows advantages and disadvantages of the proposed methods.

三维显示中基于彩色叠栅条纹的视差障栅参数设计

为确定三维显示中视差障栅(PB)的最优参数,提出一种基于彩色叠栅条纹的PB参数设计方法。液晶显示器(LCD)和PB简化为相应参数的黑白光栅模型,而具有特定参数的特定辐射光栅作为周期和倾角变化的PB模型,通过序数方程和傅里叶分析方法分析特定辐射光栅和LCD单色等效黑白光栅的叠加图样,由此推断出不同PB周期的低频主导条纹频率组项,然后利用傅里叶理论的部分和提取方法(PSE)分析不同PB周期的低频主导叠栅条纹的强度轮廓,得出PB的最佳节距和相应倾斜角度。实验结果表明,所设计的PB三维显示系统没有出现降低像质的叠栅条纹,具有较好的三维显示效果。

On the Exponential Diophantine Equation x^2 + (3a^2 -1)~m = (4a^2 -1)~n

We apply a new, deep theorem of Bilu, Hanrot ＆ Voutier and some fine results on the representation of the solutions of quadratic Diophantine equations to solve completely the exponential Diophantine equation x^2＋（3a^2-1）^m = （4a^2-1）^n when 3a^2-1 is a prime or a prime power.

Vectorial optical fields： recent advances and future prospects

Driven by their potential applications, vectorial optical fields with spatially inhomogeneous states of polarization within the cross section have drawn significant attention recently. This work intends to review some of the latest development of this rapidly growing field of optics and offer a general overview of the current status of this field in a few areas. Mathematical descriptions of generalized vectorial optical fields are provided along with several special examples. A time-reversal methodology for the creation of a wide variety of exotic optical focal fields with prescribed characteristics within the focal volume is presented. Recently developed methods for the generation of vectorial optical fields that utilize fiber lasers,digital lasers, vectorial optical field generator, metasurfaces or photoalignment liquid crystals are summarized. The interactions of these vectorial optical fields with various micro-and nano-structures are presented and the prospects of their potential applications are discussed. The connection of vectorial optical fields with higher dimensionality in quantum information is summarized.

High Accuracy Split-Step Finite Difference Method for Schrdinger-KdV Equations

In this article, two split-step finite difference methods for Schrodinger-KdV equations are formulated and investigated. The main features of our methods are based on:(i) The applications of split-step technique for Schrodingerlike equation in time.(ii) The utilizations of high-order finite difference method for KdV-like equation in spatial discretization.(iii) Our methods are of spectral-like accuracy in space and can be realized by fast Fourier transform efficiently. Numerical experiments are conducted to illustrate the efficiency and accuracy of our numerical methods.