THE ASYMPTOTIC EXPRESSION OF THE SOLUTION OF THE CAUCHY’S PROBLEM FOR A HIGHER ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION WHEN THE LIMIT EQUATION HAS SINGULARITY

ＴＨＥＡＳＹＭＰＴＯＴＩＣＥＸＰＲＥＳＳＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮＯＦＴＨＥＣＡＵＣＨＹ’ＳＰＲＯＢＬＥＭＦＯＲＡＨＩＧＨＥＲＯＲＤＥＲＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＨＥＮＴＨＥＬＩＭＩＴＥＱＵＡＴＩＯＮ...     

ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS VIA THE INTRINSIC METHOD

ＯＮＴＨＥＢＯＵＮＤＥＤＮＥＳＳＡＮＤＴＨＥＳＴＡＢＩＬＩＴＹＲＥＳＵＬＴＳＦＯＲＴＨＥＳＯＬＵＴＩＯＮＯＦＣＥＲＴＡＩＮＦＯＵＲＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＶＩＡＴＨＥＩＮＴＲＩＮＳＩＣＭＥＴＨＯＤＣｅｍｉｌＴＵＮＣ;Ａ...     

THE APPLICATION OF MULTI－SCALE PERTURBATION METHOD TO THE STABILITY ANALYSIS OF PLANE COUETTE FLOW

ＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＭＵＬＴＩ－ＳＣＡＬＥＰＥＲＴＵＲＢＡＴＩＯＮＭＥＴＨＯＤＴＯＴＨＥＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＰＬＡＮＥＣＯＵＥＴＴＥＦＬＯＷＺｈｏｕＺｈｅ－ｗｅｉ（周哲玮）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｌｙ;Ｓｈａｇ...     

THE DIFFERENTIAL SOLUTION TO THE FLYING LOCUS EQUATION OF THE SHOT AND ITS APPLICATION

ＴＨＥＤＩＦＦＥＲＥＮＴＩＡＬＳＯＬＵＴＩＯＮＴＯＴＨＥＦＬＹＩＮＣＬＯＣＵＳＥＱＵＡＴＩＯＮＯＦＴＨＥＳＨＯＴＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＬｉｕＸｉａｏ－ｘｉａｎｇ（刘小湘）　　（ＸｉａｎｇｔａｎｉｎｓｔｉｔｕｉｅｏｆＭａｃｈｉｎｅｒｙａｎｄ...     

THE REMAINDER－EFFECT ANALYSIS OF FINITE DIFFERENCE SCHEMES AND THE APPLICATIONS

ＴＨＥＲＥＭＡＩＮＤＥＲ－ＥＦＦＥＣＴＡＮＡＬＹＳＩＳＯＦＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＡＮＤＴＨＥＡＰＰＬＩＣＡＴＩＯＮＳＬｉｕＲｕ－ｘｕｎ（刘儒勋）ＺｈｏｕＺｈａｏ－ｈｕｉ（周朝晖）（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｕｎｉｖｅｒｓｉｔｙｏ...     

A COMPARATIVE STUDY OF THE OPENING AND CLOSING PROCESS OF TWO TYPES OF MECHANICAL HEART VALVES USING ALE FINITE ELEMENT METHOD

ＡＣＯＭＰＡＲＡＴＩＶＥＳＴＵＤＹＯＦＴＨＥＯＰＥＮＩＮＧＡＮＤＣＬＯＳＩＮＧＰＲＯＣＥＳＳＯＦＴＷＯＴＹＰＥＳＯＦＭＥＣＨＡＮＩＣＡＬＨＥＡＲＴＶＡＬＶＥＳＵＳＩＮＧＡＬＥＦＩＮＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＡＣＯＭＰＡＲＡＴＩＶＥＳＴＵＤＹＯＦ...     

THE THEORETICAL COST OF SEQUENTIAL AND PARALLEL ALGORITHMS FOR SOLVING LINEAR SYSTEMS OF EQUATIONS

ＴＨＥ　ＴＨＥＯＲＥＴＩＣＡＬ　ＣＯＳＴ　ＯＦ　ＳＥＱＵＥＮＴＩＡＬ　ＡＮＤ　ＰＡＲＡＬＬＥＬ　ＡＬＧＯＲＩＴＨＭＳ　ＦＯＲ　ＳＯＬＶＩＮＧ　ＬＩＮＥＡＲ　ＳＹＳＴＥＭＳ　ＯＦ　ＥＱＵＡＴＩＯＮＳＳａｌｍａｎＨ．Ａｂｂａｓ（ＲｅｃｅｉｖｅｄＭａｙ２４...     

A COMPLETE EXPRESSION OF THE ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION WITH A N－TH ORDER TURNING POINT

ＡＣＯＭＰＬＥＴＥＥＸＰＲＥＳＳＩＯＮＯＦＴＨＥＡＳＹＭＰＴＯＴＩＣＳＯＬＵＴＩＯＮＯＦＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＡＮ－ＴＨＯＲＤＥＲＴＵＲＮＩＮＧＰＯＩＮＴＺｈａｎｇＪｕ－ｌｉｎｇ（张居铃）（ＳｉｃｈｕａｎＩｎｓｔｉｔｕｔｅｏ...     

AN ITERATIVE METHOD FOR THE DISCRETE PROBLEMS OF A CLASS OF ELLIPTICAL VARIATIONAL INEQUALITIES

ＡＮＩＴＥＲＡＴＩＶＥＭＥＴＨＯＤＦＯＲＴＨＥＤＩＳＣＲＥＴＥＰＲＯＢＬＥＭＳＯＦＡＣＬＡＳＳＯＦＥＬＬＩＰＴＩＣＡＬＶＡＲＩＡＴＩＯＮＡＬＩＮＥＱＵＡＬＩＴＩＥＳＺｈｅｎｇＴｉｅ－ｓｈｅｎｓ（郑铁生）ＬｉＬｉ（李立）ＸｕＱｉｎｇ－ｙｕ（许庆余）（Ｄ...     

THE LAW OF THE ITERATED LOGARITHM OF RANDOM WEIGHTING APPROXIMATION FOR MEAN ERROR──NON．I．I．D．SITUATION

ＴＨＥＬＡＷＯＦＴＨＥＩＴＥＲＡＴＥＤＬＯＧＡＲＩＴＨＭＯＦＲＡＮＤＯＭＷＥＩＧＨＴＩＮＧＡＰＰＲＯＸＩＭＡＴＩＯＮＦＯＲＭＥＡＮＥＲＲＯＲ──ＮＯＮ．Ｉ．Ｉ．Ｄ．ＳＩＴＵＡＴＩＯＮＷａｎｇＢｉｎｇｚｈａｎｇ（王炳章）ＰｅｎｇＪｉａｎｐｉｎｇ（彭建平...     

On the criterion for the absolute stability of the control system

In this paper, firstly we give the criterion for the absolute stability of the second canonical form for the control system, including the equation of the longitudinal motions of a plane as a particular example. The corresponding result in [8], [9] is a particular example given in this paper. Secondly, we give the criteria for the absolute stability of the first canonical form in the usual case and in the critical case. Finally, we give some criteria for the absolute stability of the general form for the direct control system.All the results in this paper merely depend upon the relations between the parameters of the system itself to give an explicit algebraic discriminant.     

捷联式惯性导航系统惯性元件的设置与可靠性

本文对惯性元件的最佳冗余设置及其在飞行器上的布局与可靠性之间的关系进行了研究，建立了相应的可靠性数学模型，探讨了３／６（Ｇ）冗余惯性元件出现第三个故障时故障的检测与识别的方法。所得结果可供惯性导航系统可靠性分析及工程上应用。     

分流河道淤积与洞庭湖萎缩对长江洪灾的影响

1998年长江流域的特大洪水灾害表明，目前长江流域防洪体系在面临特大洪水时仍然显得比较脆弱．以长江中下游荆江洞庭湖地区为背景，运用有限体积计算方法建立了一维河道和二维湖泊交错的复杂水系洪水演进数值模型，细致分析了由于分流河道淤积以及洞庭湖萎缩对长江洪灾的影响．得出长江分流河道和洞庭湖由于泥沙淤积产生的萎缩将造成长江干流河道洪水期间水位抬升，从而加重长江的洪水灾害．其结论可为长江中下游地区的洪水治理提出建设性意见．     

On the Controllability of the Hydrostatic Stokes Equations

This paper is devoted to present some results on the controllability of the hydrostatic Stokes equations. The first main result of this paper states that the approximate null controllability of this system holds. This is proved whatever the boundary conditions are. Then, we extend this result to an exact null controllability result when the boundary conditions are ∂ _z u = 0 (the vertical derivative of the horizontal velocity) at the bottom.      

On the effect of the nonparallelism of the boundary layer flow over a flat plate on its stability characteristics

The effect of the nonparallelism of the boundary layer flow over a flat plate on its stability characteristics has been investigated by several authors, and it was claimed that the results of the theoretical calculations are already in good agreement with the experimental observations. However, this is not true. In this paper, this problem is reinvestigated, using two different methods. It is found that within the framework of linear theory, the theoretical results are in fact not in good agreement with the experimental observations. To settle this problem, nonlinear effect must be taken into consideration. Projects Supported by the Science Fund of the Chinese Academy of Sciences     

On the anomalous pressure dependence of the viscosity of helium

Summary In contradiction to the general behaviour of gases, the viscosity of helium has been found experimentally to show an initial decrease with increase of pressure. In this paper it has been suggested that association may account for this anomalous behaviour of helium.     

The perturbation-iterative method applied to the problems of the large deflection of the elastic circular thin plates

In this paper, we present a perturbation-iterative method for solving certain boundary value problems encountered in the nonlinear theory of elastic circular thin plates. At the same time, with this method, we strictly prove the convergence of the solutions for the large deflection equations of circular plates subjected to certain distributed loads.     

Qualitative behaviors of the continuous-time chaotic dynamical systems describing the interaction of waves in plasma

In this paper, a new Lorenz-like chaotic system describing the interaction of three resonantly coupled waves in plasma is studied. Explicit ultimate boundedness and global attraction domain are derived according to stability theory of dynamical systems. The innovation of the paper is that this paper not only proves this chaotic system is globally bounded for the parameters of this system but also gives a family of mathematical expressions of global exponential attractive sets for this system with respect to the parameters of this system. Furthermore, the exponential rate of the trajectories is also obtained. Finally, numerical localization of attractor is presented.     

Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient

In this paper we examine the problem of minimizing the sup norm of the gradient of a function with prescribed boundary values. Geometrically, this can be interpreted as finding a minimal Lipschitz extension. Due to the weak convexity of the functional associated to this problem, solutions are generally nonunique. By adopting G. Aronsson's notion of absolutely minimizing we are able to prove uniqueness by characterizing minimizers as the unique solutions of an associated partial differential equation. In fact, we actually prove a weak maximum principle for this partial differential equation, which in some sense is the Euler equation for the minimization problem. This is significantly difficult because the partial differential equation is both fully nonlinear and has very degenerate ellipticity. To overcome this difficulty we use the weak solutions of M. G. Crandall and P.-L. Lions, also known as viscosity solutions, in conjunction with some arguments using integration by parts.     

A study on the period of the free lateral vibration of the beam bridge by the theory of the orthotropic rectangular plate

Conclusion The frequency of the right, simple beam bridges is discussed by the laboratory study on the model beam bridges and the field tests on existing beam bridges in this paper, but furthermore, the application to the skew beam bridge or to the continuous beam bridge and the problem of forced vibration should be studied.Even if more exact studies are necessary, it is made sure by the study in this paper that the theory of the orthotropic plate is proper to the analysis of the free lateral vibration of the beam bridge and sufficient enough for practical purpose, especially for the beam bridge of which the width is almost equal to the span.