ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

基于Non stationary-CNN-Transformer的海浪有效波高预测

针对海浪有效波高序列波动性、随机性较强,难以精确预测以及模型无法高效挖掘深层特征间关系的问题,提出一种基于Non stationary-CNN-Transformer模型的海浪有效波高预测方法。首先,使用平稳化模块减弱海浪时序数据的非平稳性;其次,利用一维卷积神经网络(CNN)提取相关数据间的深层特征并构建特征向量;最后,使用含有平稳性注意力的Transformer描述波高序列的时间依赖性捕捉到序列之间的全局关系,通过逆归一化处理后获得有效波高预测结果。该方法可消除海浪时序数据的非平稳性,提升数据的预测效果,并具有优异的特征提取能力且善于处理大规模时间序列数据。在实验中应用澳大利亚的浮标实测数据,通过7组对比实验分别预测0.5、3、6、12和24 h的有效波高,对所提模型进行全方位、多角度的验证。算例研究结果表明,该文所提模型在不同时间段精度有明显提升。

Microstructure and mechanical properties of stationary shoulder friction stir welding joint of 2A14-T62 aluminum alloy

2A14-T62 butt joint was successfully welded by stationary shoulder friction stir welding(SSFSW)method.The results showed that using a pin with small shoulder could broaden the process window,and under a rotation speed of 2000 r/min and welding speed of 30 mm/min,joint with smooth surface,small reduction in thickness and little inner defects was obtained.The weld nugget zone was approx-imately circular,which was a unique morphology for SSFSW.The heat-affected zone(HAZ)and thermo-mechanically affected zone(TMAZ)were both quite narrow due to the lower heat input and slight mechanical action of the stationary shoulder.The fraction of high angle grain boundaries(HAGBs)exhibited a“W”shape along horizontal direction(from advancing side to retreating side),and the minim-um value located at HAZ.The average ultimate tensile strength and elongation of the joint were 325 MPa and 4.5%,respectively,with the joint efficiency of 68.3%.The joint was ductile fractured and the fracture surface contained two types of dimples morphology in different re-gions of the joint.Microhardness distribution in the joint exhibited a“W”shape,and the difference along the thickness direction was negli-gible.The joint had strong stress corrosion cracking susceptibility,and the slow stain rate tensile strength was 139 MPa.Microcrack and Al2O3 particulates were observed at the fracture surface.

Robust edge detection based on stationary wavelet transform

By combining multiscale stationary wavelet analysis with fuzzy c-means, a robust edge detection algorithm is presented. Based on the translation invafiance built in multiscale stationary wavelet transform, components in different transformed sub-images corresponding to a pixel are employed to form a feature vector of the pixel. All the feature vectors are classified with unsupervised fuzzy c-means to segment the image, and then the edge pixels are checked out by the Canny detector. A series of images contaminated with different intensive Gaussian noises are used to test the novel algorithm. Experiments show that fairly precise edges can be checked out robustly from those images with fairly intensive noise by the proposed algorithm.

Separation Properties of a New Polysiloxane-Anchored β-Cyclodextrin Derivative as Gas Chromatography Stationary Phase

A new capillary gas chromatography stationary phase, monokis (2,6 di O benzyl 3 O propyl (3’)) hexakis(2,6 di O benzyl 3 O methyl) β CD bonded polysiloxane, was synthesized. It exhibited separation abilities to disubstituted benzene isomers and some chiral solutes. It was also found that the polarity of CD derivatives can be lowered both by chemically bonding it to polysiloxane and by diluting it in polysiloxane. The separation abilities of the polysiloxane anchored CDs (SP CD) are higher than that of the unbonded CDs (S CD) and the diluted S CD at lower column temperature. Hydrosilylation reaction is one of the best methods to lower the operating temperature of CDs.

The stationary phase analysis of the Kirchhoff-type d emigrated field

In the literature,stationary phase analysis of Kirchhoff-type demigrated fields is carried out mainly under the following two conditions：（1） The considered isochrone and the target reflector are tangential to each other;（2） The spatial duration of the wavelet of the depthmigrated image is short.For the isochrones that are not tangential to the target reflector and for the depth-migrated images that have a large spatial duration,the published stationary phase equation for the demigrated field will become invalid.For performing the stationary phase analysis of the Kirchhoff-type demigrated field under the conditions that the considered isochrone and the target reflector are not tangential to each other and that the spatial duration of the wavelet of the depth-migrated image is not short（the general conditions）,I derive the formulas for the factors appearing in the stationary phase formula in two dimensions,from which I find that for different isochrones the horizontal coordinates of the stationary point of the depth difference function are different.Also,the equation for the Kirchhoff-type demigrated field consists of two parts.One is the true-amplitude demigrated signal and the other is the amplitude distortion factor.From these facts the following two conclusions can be drawn：（1） A demigrated signal is composed of many depth-migrated images and one depth-migrated image trace provides only one sample to the demigrated signal;and（2） The amplitude distortion effect is an effect inherent in the Kirchhoff-type demigration and cannot be eliminated during demigration.If this effect should be eliminated,one should do an amplitude correction after demigration.

TVAR Time-frequency Analysis for Non-stationary Vibration Signals of Spacecraft

Predicting the time-varying auto-spectral density of a spacecraft in high-altitude orbits requires an accurate model for the non-stationary random vibration signals with densely spaced modal frequency. The traditional time-varying algorithm limits prediction accuracy, thus affecting a number of operational decisions. To solve this problem, a time-varying auto regressive （TVAR） model based on the process neural network （PNN） and the empirical mode decomposition （EMD） is proposed. The time-varying system is tracked on-line by establishing a time-varying parameter model, and then the relevant parameter spectrum is obtained. Firstly, the EMD method is utilized to decompose the signal into several intrinsic mode functions （IMFs）. Then for each IMF, the PNN is established and the time-varying auto-spectral density is obtained. Finally, the time-frequency distribution of the signals can be reconstructed by linear superposition. The simulation and the analytical results from an example demonstrate that this approach possesses simplicity, effectiveness, and feasibility, as well as higher frequency resolution.

Stationary Subdivision 方法的一个推广及其收敛性

给出了ＳｔａｔｉｏｎａｒｙＳｕｂｄｉｖｉｓｉｏｎ方法的一个推广——矩阵Ｙ－剖分方法。利用泛函分析及样条函数给出了矩阵Ｙ－剖分方法的一个重要的收敛性质。并证明了它的收敛性。

岩石爆破基础理论研究进展与展望Ⅲ——波纹关系

岩石爆破“三大关系(本构、动静、波纹)”是爆破理论研究的重要内容,爆炸应力波与裂纹的相互作用是影响岩石破碎效果的关键因素.本文围绕“炸药爆炸能量释放与爆炸裂纹扩展的精细控制原理”这一关键科学问题,聚焦爆炸应力波与静止裂纹(岩体中既有缺陷)的相互作用、爆炸应力波与爆炸裂纹的相互作用、爆炸应力波作用下裂纹间的相互作用、地应力与爆炸应力波耦合作用下的裂纹扩展等四个方面,深入探讨了不同爆炸应力波的传播方向和强度对裂纹扩展行为(包括裂纹扩展方向、速度和长度)的影响规律.现有研究发现爆炸应力波在静止裂纹处发生反射和衍射,产生“双马赫锥”现象,致使爆炸能量较多地积聚在静止裂纹周围,诱导静止裂纹周围产生损伤和破坏;爆炸膨胀波对迎面爆炸裂纹的扩展有抑制作用,剪切波对其扩展有促进作用,而在爆炸应力波与同向爆炸裂纹的相互作用过程中,爆炸膨胀波和剪切波对裂纹扩展速度的影响则相反;爆炸荷载下相向扩展的两条裂纹互为自由面,产生“咬合效应”,形成相互勾连的形状;地应力场能够促进平行最大主应力方向的爆炸裂纹扩展,抑制垂直最大主应力方向的爆炸裂纹扩展,且地应力场的主应力差值越大,爆炸裂纹沿最大主应力方向的扩展长度越长.研究成果可为优化爆破炮孔间距、延期时间等参数,实现精细调控爆炸裂纹扩展提供理论依据.

MULTIPLE STATIONARY SOLUTIONS OF EULER-POISSON EQUATIONS FOR NON-ISENTROPIC GASEOUS STARS

The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity of the stationary solutions of Euler-Poisson system.

A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL

A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.

Structural Scheme Optimization Design for the Stationary Platen of a Precision Plastic Injection Molding Machine

The current development of precision plastic injection molding machines mainly focuses on how to save material and improve precision, but the two aims contradict each other. For a clamp unit, clamping precision improving depends on the design quality of the stationary platen. Compared with the parametric design of stationary platen, structural scheme design could obtain the optimization model with double objectives and multi-constraints. In this paper, a SE-160 precision plastic injection molding machine with 1600 kN clamping force is selected as the subject in the case study. During the motion of mold closing and opening, the stationary platen of SE-160 is subjected to a cyclic loading, which would cause the fatigue rupture of the tie bars in periodically long term operations. In order to reduce the deflection of the stationary platen, the FEA method is introduced to optimize the structure of the stationary platen. Firstly, an optimal topology model is established by variable density method. Then, structural topology optimizations of the stationary platen are done with the removable material from 50%, 60% to 70%. Secondly, the other two recommended optimization schemes are given and compared with the original structure. The result of performances comparison shows that the scheme II of the platen is the best one. By choosing the best alternative, the volume and the local maximal stress of the platen could be decreased, corresponding to cost-saving material and better mechanical properties. This paper proposes a structural optimization design scheme, which can save the material as well as improve the clamping precision of the precision plastic injection molding machine.

The Role of Stationary and Transient Planetary Waves in the Maintenance of Stratospheric Polar Vortex Regimes in Northern Hemisphere Winter

Using 1958-2002 NCEPNCAR reanalysis data, we investigate stationary and transient planetary wave propagation and its role in wave-mean flow interaction which influences the state of the polar vortex （PV） in the stratosphere in Northern Hemisphere （NH） winter. This is done by analyzing the Eliassen-Palm （E-P） flux and its divergence. We find that the stationary and transient waves propagate upward and equatorward in NH winter, with stronger upward propagation of stationary waves from the troposphere to the stratosphere, and stronger equatorward propagation of transient waves from mid-latitudes to the subtropics in the troposphere. Stationary waves exhibit more upward propagation in the polar stratosphere during the weak polar vortex regime （WVR） than during the strong polar vortex regime （SVR）. On the other hand, transient waves have more upward propagation during SVR than during WVR in the subpolar stratosphere, with a domain of low frequency waves. With different paths of upward propagation, both stationary and transient waves contribute to the maintenance of the observed stratospheric PV regimes in NH winter.

Glucose,cellobiose,lactose and raffinose used as chiral stationary phases in HPLC

This paper presents the enantioseparation using glucose, cellobiose, lactose and raffinose as chiral selector bonded to silica gel via an arm in HPLC. Surprisingly, they also possess high enantioseparation selectivity, may be used in normal-phase and reversed- phase mode, and there is a big chiral discriminating complementary. This work indicates that oligosaccharides could soon become very attractive as a new class of chiral stationary phase for HPLC.

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

Effect of Single-walled Carbon Nanotubes on Cellulose Phenylcarbamate Chiral Stationary Phases

Single-walled carbon nanotubes（SWNTs） have a high adsorption ability and nanoscale interactions. Cellulose trisphenylcarbamates possess high enantioseparation ability in high-performance liquid chromatography（HPLC）. Single-walled carbon nanotubes mixed with cellulose trisphenylcarbamate are coated on the silica gel as chiral stationary phases and higher enantioseparation factors are obtained. After a single-walled carbon nanotube is linked to the 6-pesition of cellulose 2,3-bisphenylcarbamate, its enantioseparation resolution increases compared to that of the cellulose trisphenylcarbamate. It is the first time that SWNTs have been applied to enantioseparation. The results indicate that the single-walled carbon nanotubes are good promoters of chiral recognition. This method can be used to improve the enantioseparation efficiency of the polysaccharide chiral stationary phases.

High performance liquid chromatographic separation of thirteen drugs collected in Chinese Pharmacopoeia 2010(Ch.P2010) on cellulose ramification chiral stationary phase

The enantiomers separation of thirteen drugs collected in Ch.P2010 was performed on chiral stationary phase of cellulose ramification (chiralpak OD and chiralpak OJ) by high performance liquid chromatographic (HPLC) methods, which included ibuprofen (C1), ketoprofen (C2), nitrendipine (C3), nimodipine (C4), felodipine (C5), omeprazole (C6), praziquantel (C7), propranolol hydrochloride (C8), atenolol (C9), sulpiride (C10), clenbuterol hydrochloride (C11), verapamil hydrochloride (C12), and chlorphenamine maleate (C13). The mobile phase consisted of isopropanol and n-hexane. The detection wavelength was set at 254 nm and the fiow rate was 0.7 mL/min. The enantiomers separation of these thirteen racemates on chiralpak OD column and chiralpak OJ column was studied, while the effects of proportion of organic additives, alcohol displacer and temperature on the separation were studied. And the mechanism of some of racemates was discussed. The results indicated that thirteen chiral drugs could be separated onchiral stationary phase of cellulose ramification in normal phase chromatographic system. The chromatographic retention and resolution of enantiomers could be adjusted by factors including column temperature and the concentration of alcohol displacer and organic alkaline modifier in mobile phase. It was shown that the resolution was improved with reducing concentration of alcohol displacer. When concentration of organic alkaline modifier was 0.2% (v/v), the resolution and the peak shape were fairly good. Most racemates mentioned above had better resolution at column temperature of 25 1C. When racemates were separated, the temperature should be kept so as to obtain stable separation results.

UNIQUENESS OF STATIONARY SOLUTIONS WITH VACUUM OF EULER-POISSON EQUATIONS

In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlinear transformation which is a function of density and entropy, the corresponding problem can be reduced to a semilinear elliptic equation with a nonlinear source term consisting of a power function, for which the classical theory of the elliptic equations leads the authors to the uniqueness result under some assumptions on the entropy function S(x). As an example, the authors get the uniqueness of stationary solutions with vacuum of Euler-Poisson equations for S(x) =|x|θandθ∈{0}∪[2(N-2),+∞).

Synthesis of novel chiral stationary phases for high-performance liquid chromatography

Three novel chiral selectors 4a-c were synthesized from （S）-amino acids and （R）-1-phenyl-2-（4-methylphenyl）ethylamine. 4a-c were connected to 3-aminopropylsilanized silica gel to be used as the chiral stationary phase for HPLC. Five amino acid derivatives and two pyrethroid insecticides were fairly resolved on these three new chiral stationary phases under normal phase condition.

THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM

In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.