CHARACTERISTICS OF SUBDIFFERENTIALS OF FUNCTIONS

ＣＨＡＲＡＣＴＥＲＩＳＴＩＣＳＯＦＳＵＢＤＩＦＦＥＲＥＮＴＩＡＬＳＯＦＦＵＮＣＴＩＯＮＳ（郭兴明）ＣＨＡＲＡＣＴＥＲＩＳＴＩＣＳＯＦＳＵＢＤＩＦＦＥＲＥＮＴＩＡＬＳＯＦＦＵＮＣＴＩＯＮＳ￥ＧｕｏＸｉｎｇｍｉｎｇ（ＲｅｃｅｉｖｅｄＪｕｎｅ１６，１９９５...     

CHARACTERIZATION OF POWDER FLOWABILITY USING MEASUREMENT OF ANGLE OF REPOSE

In response to the need in industry for a quick and reproducible method of measuring the flowability of powders in processes involving transport and storage, the apparently simple idea of measuring angle of repose has been revived. The simple tester first used has evolved over a number of years into the present version which is shown to be capable of handling quite small samples of powders that are even slightly cohesive. Experimental data are presented and results shown to compare consistently with the better known Hausner ratio.     

TORSIONAL RIGIDITY OF SHELLS OF REVOLUTION

In this paper,the general equations of equilibrium for axisymmetrical deformationincluding the torsional deformation of revolutional shells are derived.It is shown that theshearing stress distribution due to torsion is independent of other stress componentsincluding those of membrane stress and bending stress.In this paper,the torsional deformation is considered to be represented by membraneaction only,and also by the combined action of bending membrane deformation.It is shownthat the main contribution of torsional rigidity is that related to membrane action.     

THE THEORY OF SIMILARITY AND THE PROFILE OF VERTICAL DISTRIBUTION OF CONCENTRATION OF SAND PARTICLES

In this article,we treat the problem of two-dimensionaluniform steady channel flow of turbid water with theory ofsimilarity.Under the condition of similarity of turbulentfluctuation velocity and fluctuation of concentration ofsand particles,we obtain the profile of the vertical dis-tribution of concentration of sand particles.This profileof vertical distribution of concentration of sand particlesis slightly different from that obtained by diffusion theory,and departs from that obtained by gravitational theory.     

THEORY OF ELASTICITY OF AN ANISOTROPIC BODY FOR THE BENDING OF BEAMS

A theory of elasticity for the bending of orthogonal anisotropic beams has been developed by analogy with the special case, which can be obtained by applying the theory of elasticity for bending of transversely isotropic plates to the problems of two deminsions. In this paper, we present a method to solve the problems of bending of orthogonal anisotropic beams and a new theory of the deep-beam whose ratio of depth to length is larger. It is pointed out that Reissner's theory to account for the effect of transverse shear deformation is not very approximate in the components of stress,     

ANALYSIS OF THE MOTION OF A GYRO-THEODOLITE

With the method of analytical mechanics,this paper studies the motions of a gyro-theodolite under the action of (1) the torque of gravity only,(2)the torque applied by theband suspension.(3)the torque of the band suspension with air damping considered,theequations of motion are then established and their solutions are found.Furthermore,analysis of the law of motion and the behaviour of gyro-theodolite during the orientation ismade.     

APPLICATION 0F THE THEORY OF BRANCHING OF SOLUTIONS OF NONLINEAR EQUATIONS IN THE ESTIMATION OF POLE PERTURBANCE OF LINEAR CLOSED-LOOP SYSTEMS

When the state and input matrices of a multivariable lineartime-invariant system are perturbed.the problem of the es-timation of pole perturbance of closed-loop system is con-sidered by making use of the theory of branching of solutionsfor nonlinear equations.     

COMPUTER SIMULATION OF THE MOTION OF THE BULLET BELT OF AIRPLANE GUN

ＣＯＭＰＵＴＥＲＳＩＭＵＬＡＴＩＯＮＯＦＴＨＥＭＯＴＩＯＮＯＦＴＨＥＢＵＬＬＥＴＢＥＬＴＯＦＡＩＲＰＬＡＮＥＧＵＮＺｈａｎｇＤｉｎｇｇｕｏ（章定国）（ＲｅｃｅｉｖｅｄＭａｒｃｈ１７，１９９５；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＷｕＲｕｉｆｅｎｇ）Ａｂｓｔｒ...     

BLOW-UP OF SOLUTIONS OF NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS OF GENERALIZED NERVE CONDUCTION TYPE

This paper deals with the two type of mixed problems with respect to Neumannboundary and Dirichlet boundary for nonlinear pseudo-hyperbolic equations of generalizednerve conduction typeu_1-△u_1=F(x,t,u,(?)u,u_t,(?)i_t)when the nonlinear part F(x.t,u,(?)u,u_t,(?)u_t)and the initial values satisfy someconditions,the blow-up properties of the solutions are obtained.     

EFFECT OF POLYETHYLENEIMINE ON THE PROPERTIES OF CONCENTRATED SUSPENSIONS OF TITANIUM DIOXIDE MICROBEADS

The effect of polyethyleneimine (PEI) concentration on the properties of titanium dioxide (TiO2) suspensions is studied with or without the addition of an electrolyte (barium acetate). Measurements of the apparent viscosity and the stability of TiO2 suspensions showed that PEI is an effective dispersant for TiO2 particles in suspension in the absence of an electrolyte, not only reducing the viscosity of the suspension but also increasing its stability. In the presence of an electrolyte, however, small quantities of polyethyleneimine could neither disperse the TiO2 particles nor de-crease the viscosity of the TiO2 suspensions; only PEI concentrations beyond saturation adsorption could perceptively improve the stabilitv of TiO2 suspensions.     

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID(Ⅰ)

The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial value problem on hyper plane {t=0} in R⁴, and explain that the problem has more than one solution. Foundation item: the National Natural Science Foundation of China (19971054) Biography: Shen Zhen (1977−)     

On the formal solution of initial value problem of Navier-Stokes equation

Ｉｎｒｅｆｅｒｅｎｃｅ [1 ] ,ｗｅｄｉｓｃｕｓｓｅｄｔｈｅｉｎｓｔａｂｉｌｉｔｙｏｆＮａｖｉｅｒ＿ＳｔｏｋｅｓｅｑｕａｔｉｏｎｏｎＲ3×Ｒ ,ａｎｄ ,ｉｎｔｈｅｉｌｌｕｓｔｒａｔｉｏｎｏｆｉｔ,ｗｅｐｒｅｓｅｎｔｅｄｓｏｍｅｅｘａｍｐｌｅｓｉｎｔｈｅｆｏｒｍｏｆｅｘａｃｔｓｏｌｕｔｉｏｎ .Ｔｈｅｂａｓｉｓｏｆｔｈｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆｔｈｅｍｉｓｔｈｅ“ｅｑｕａｔｉｏｎｓｅｃｏｎｄａｉｒｅ”ｏｆｔｈｅｅｑｕａｔｉｏｎ .Ｉｎｆａｃｔ,ｔｈｅｓｅｅｘａｃｔｓｏｌｕｔｉｏｎｓａｒｅｓｏｍｅｌｉｍｉｔ…     

The asymptotic theory of initial value problems for semilinear pertubed wave equations in two space dimensions

The asymptotic theory of initial value problems for semilinear ware equations in two space dimensions was dealt with. The well-posedness and vaildity of formal approximations on a long time scale were discussed in the twice continuous classical space. These results describe the behavior of long time existence for the validity of formal approximations. And an application of the asymptotic theory is given to analyze a special wave equation in two space dimensions. Foundation item: Sichuan Youth Foundation (1999-09) Biography: LAI Shao-yong (1965−), Associate Professor     

The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations

A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. Foundation items: the National Natural Science Foundation of China (10071048); the “Hunfred Talents Project” by Chinese Academy of Sciences Biography: Mo Jia-qi (1937−)     

TheC k instability of navier-Stokes equation appending polynomials of unknown functions

Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation isdetermined. It is proved that such kind of equation has no C^k (k≥2) stable solution by the fact that the strate transversale is a null set. Foundation item: the National Natural Science Foundation of China (19971054), Shanghai Natural Science Foundation (99ZA14034) Biography: HE You-hua (1960-)     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION （Ⅰ）——THE CONTINUOUS-TIME CASE

An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal.     

Global solution of the inverse problem for a class of nonlinear evolution equations of dispersive type

The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin. Contributed by Chen Yu-shu Foundation item: the National Natural Science Foundation of China (Significance 199990510); the National Key Basic Research Special Foundation of China (G1998020316); Liuhui Center for Applied Mathematics, Nankai University & Tianjin University Biography: Chen Fang-qi (1963-)     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅰ)—MICROPOLAR CONTINUA

Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for micropolar continuum theory are presented. In these new systems not only the additional angular momentum, surface moment and body moment produced by the linear momentum, surface force and body force, respectively, but also the additional velocity produced by the angular velocity are considered. The new coupled balance laws of linear momentum, angular momentum and energy are reestablished. From them the new coupled local and nonlocal balance equations are naturally derived. Via contrast it can be clearly seen that the new results are believed to be rather general and complete. Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: Dupai Tian-min (1931≈)     

Similarity reductions for 2+1-dimensional variable coefficient generalized kadomtsev-petviashvili equation

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｒｉｎｇｔｈｅｓｔｕｄｙｏｆｓｈａｌｌｏｗｗａｔｅｒｗａｖｅｓ,ｐｅｏｐｌｅｏｂｔａｉｎｅｄｍａｎｙｗｅｌｌ＿ｋｎｏｗｎｃｏｍｐｌｅｔｅｌｙｉｎｔｅｇｒａｂｌｅｍｏｄｅｌｓ,ｓｕｃｈａｓＫｄＶｅｑｕａｔｉｏｎ,ｍＫｄＶｅｑｕａｔｉｏｎ,Ｂｏｕｓｓｉｎｅｓｑｅｑｕａｔｉｏｎ,Ｗｈｉｔｈａｍ＿Ｂｒｏｅｒ＿ＫａｕｐｅｑｕａｔｉｏｎａｎｄＫｈｏｋｈｌｏｖ＿Ｚａｂｏｌｏｔｓｋａｙａｅｑｕａｔｉｏｎｅｔｃ.[1～8].Ｆｏｒ2 1＿ｄｉｍｅｎｓｉｏｎａｌｖａｒｉａｂｌｅｃｏｅｆｆｉｃｉｅｎｔｇ…     

The 3-layered explicit difference scheme for 2-D heat equation

A 3-layered explicit difference scheme for the numerical solution of 2-D heat equation is proposed. Firstly, a general symmetric difference scheme is constructed and its optimal error is obtained. Then two kinds of condition for choosing the parameters for optimal error and stable difference scheme are given. Finally, some numerical results are presented to show the advantage of the schemes Foundation items: the Science Foundation of Chinese Postdoctoral (2002031224); the Science Foundations of Southeast University (9209011148, 3007011043) Biography: Liu Ji-jun (1965-)