ON THE CRITICAL POINTS OF THE MAP Fp:X→‖AXB-C‖pp

Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A^- such that (AA^-)^*=AA^- and B has a generalized inverse B^- such that (B^-B)^*=B^-B,the general characteristic forms for the critical points of the map F_p:X^→‖AXB-C‖_p^p(1p=2. Similarly, the same question has been discussed for several operators.     

DISCUSSION ON THE SIF FOR POINTS ON BORDER OF ELLIPTICAL FLAT CRACK INSIDE INFINITE SOLID UNDER UNIFORM TENSION

Using the results of crack surface displacement field in Green-Sneddon’s solution and coordinate transformation,this paper hasderived an expression K_1(x_1,z_1,α)for SIF at any point and at anyorientation on the border of elliptical flat crack inside infinitesolid under uniform tension.As a complement of Irwin’s work,it is shown that for any pointed point on the elliptical border theSIF defined on normal plane takes the maximum value.And it shouldbe pointed out that in some works some idea concerning Irwin’s con-tents is open to question.An expression K_I in terms of polarangle which is more intuitional than centrifugal angle is proposedfor SIF at any point on the elliptical border.     

ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED POINTS FOR ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒｗｅａｓｓｕｍｅｔｈａｔＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅ ,Ｅ ｉｓｔｈｅｄｕａｌｓｐａｃｅｏｆＥ ,ＤｉｓａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆＥａｎｄＪ:Ｅ → 2 Ｅ ｉｓｔｈｅｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ∈Ｅ :〈ｘ ,ｆ〉 =‖ｘ‖·‖ｆ‖ ,　‖ｆ‖ =‖ｘ‖ (ｘ∈Ｅ) .　　Ｄｄｆｉｎｉｔｉｏｎ 1 1　ＬｅｔＴ :Ｄ →Ｄｂｅａｍａｐｐｉｎｇ1 )Ｔｉｓｓａｉｄｔｏｂｅａｓｙｍｐｔｏｔｉｃａｌｌｙｎｏ…     

FIRST INTEGRAL AND STABILITY OF MOTION IN THE CRITICAL CASES

In this paper. we indicate that after the Liapunov function by using linear combinationof mechanical first integral was suggested by Chetayev in 1946.He and his students solvedstability of conservative system by means of this method. But he had trouble to solve theproblems by means of cut and try.Moreover,the condition of stability is imperfect.Solution by this method is limited for problems of purely imaginary roots.The cases of zeroroots have not been considered Condition of stability secured is more strict.This paper suggests that the differential equation can be transformed into standardform by method of cancellation of cyclic coordinates(method of lowering degree of order),and condition of stability can be determined by energy integral.By this method not only thecomputation is clear and concise.But also zero roots can be considered.Therefore theproblems of two cyclic coordinates can be transformed into second-order system,and we getnew conclusion of the condition of stability simply .As for problem     

THE CREEP EFFECTS ON THE BUCKLING OF SHALLOW SHELLS

An analysis of the creep effects on the buckling of concreteshallow shells is presented in this paper.Based on the non-linear theory of thin elastic shells.it is found that forthose of the elliptical paraboloidal type.the upper cri-tical load of the load-deflection curve will decrease whilethe lower limit Will increase with time.As to the problemof local buckling of the shell.the critical load is de-pendent only upon the modulus of elasticity at the instantit occurs.     

ON THE POSITIVE DEFINITENESS OF A CLASS OF OPERATORS

In this paper,a proof of the positive definiteness for a class of operators is given.Theoperators considered are general enough to include those in two-and three-dimensionalelasticity,thin plates and shells as their special cases.     

NEW POINTS OF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS(Ⅲ)——RE-DISCUSS THE LINEAR THEORY OF NONLOCAL ELASTICITY

In this paper, it is proven that the balance equation of energy is the first integral of the balance equation of momentum in the linear theory of nonlocal elasticity. In other words, the balance equation of energy is not an independent one. It is also proven that the residual of nonlocal body force identically equals zero. This makes the transform formula of the nonlocal residual of energy much simpler. The linear nonlocal consitutive equations of elastic bodies are deduced in details, and a new formula to calculate the antisymmetric stress is given. Foundation item: the Natural Science Foundation of Jiangsu Province, China (BK97063)     

ON THE CRITERION FOR THE ABSOLUTE STABILITY OF THE CONTROL SYSTEM

In this paper,firstly we give the criterion for the absolutestability of the second canonical form for the control system,in-cluding.the equation of the longitudinal motions of a plane as aparticular example.The corresponding result in[8],[9]is a par-ticular example given in this paper.Secondly,we give the criteriafor the absolute stability of the first canonical form in the usualcase and in the critical case.Finally,we give some criteria forthe absolute stability of the general form for the direct controlsystem.All the results in this paper merelg depend upon the relationsbetween the parameters of the system itself to give an explicit al-gebraic discriminant.     

ON THE EXISTENCE OF LIMIT CYCLES OF LIENARD EQUATION

In this paper,we have proved several theorems which guarantee that the Lienardequation has at least one or n limit cycles without using the traditional assmuption G(±∞)= ∞.Thus some results in[3 -5]are extended.The limit cycles can be located by ourtheorems.Theorems3 and4 give sufficient conditions for the existence of n limit cycleshaving no need of the conditions that the function F(x)is odd or“nth order compatible witheach other”or“nth order contained in each other”.     

THE EFFECT OF THE VASOMOTION ON THE MASS TRANSFER IN MICROCIRCULATION

This paper deals with the mass transfer in the microcirculation with vasomotion. The effect of the vasomotion on the mass transfer is analysed. It is shown that the vasomotion is of great importance to accelerate the mass transfer.     

REMABKS ON THE STRUCTURE OF EVOLUTION EQUATIONS

ＲＥＭＡＢＫＳＯＮＴＨＥＳＴＲＵＣＴＵＲＥＯＦＥＶＯＬＵＴＩＯＮＥＱＵＡＴＩＯＮＳＪ．Ｂａｄｕｒ；ＳｕｎＢｏｈｕａ（孙博华）（Ｒｕｈｒ－ＵｎｉｒｅｒｓｉｔＢｏｃｈｕｍ，ＬｅｈｒｓｔｕｈｌｆｒＡｌｌｇｅｍｅｉｎｅＭｅｃｈａｎｉｋＤ－４４７８０Ｂｏｃｈｕ...     

ON THE METHOD OF RECIPROCAL THEOREM TO FIND SOLUTIONS OF THE PLANE PROBLEMS OF ELASTICITY

In this paper the method of reciprocal theorem is extended to find solutions of planeproblems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with fouredges built-in as the basic system and then find displacement expressions of the actualsystem by using the reciprocal theorem between the basic system and actual system withvarious edge conditions.When only displacement edge conditions exist,obtaining displacement expressions bymeans of the method of reciprocal theorem is actual.But in other conditions,when staticforce edge conditions or mixed ones exist,the obtained displacements are admissible.Inorder to find actual displacement,the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple,convenient andgeneral one for the solution of plane problems of elasticity of the rectangular plates withvarious edge conditions.Evidently,it is a new method.     

ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＭａｎｙｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｓｃａｎｂｅｖｉｅｗｅｄａｓｌｉｎｅａｒＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓ.Ｗｈｅｎｗｅｓｔｕｄｙｔｈｅｅｆｆｅｃｔｓｏｆｓｙｓｔｅｍｐａｒａｍｅｔｅｒｓｏｎｔｈｅｂｅｈａｖｉｏｒｏｆｔｈｅｓｙｓｔｅｍｓ,ｔｈｅｓｙｓｔｅｍｃａｎｂｅｒｅｇａｒｄｅｄａｓｔｈｅｓｙｓｔｅｍｄｅｐｅｎｄｉｎｇｏｎｐａｒａｍｅｔｅｒｓ.Ｖｅｒｙｉｍｐｏｒｔａｎｔｓｙｓｔｅｍｐａｒａｍｅｔｅｒｓ ,ｓｕｃｈａｓｃｒｉｔｉｃａｌｌｏａｄ ,ｃｒｉｔｉｃａｌａｎｇ…     

ON THE NEW FORMS OF THE DIFFERENTIAL EQUATIONS OF THE SYSTEMS WITH HIGHER-ORDER NONHOLONOMIC CONSTRAINTS

In this paper,the new forms of the differential equations of motion of the systems withhigher-order nonholonomic constraints are obtained at first,and then the equivalencebetween these equations and the known equations is demonstrated.Finally an example isgiven to illustrate the application of our new equations.     

ON THE DYNAMICAL STRUCTURE OF THE WIND FIELD OF JUPITER''''S GREAT RED SPOT

Based on the geographic approximation the two-dimensional dynamical structure of the wind fields of Jupiterls Great Red Spot and White Oval BC is obtained. The results of calculation are in good agreement with the observations. Thus, an explanation of the observed dispersion of the velocities along the horizontal streamline is given. The major physical mechanism of this dispersion is as follwos: The distance between two adjacent elliptical streamlines varies along the elliptical streamline; leading to the variance of the normal pressure gradient. Thus, the horizontal velocity V_T has to vary correspondingly so that the Coriolis force can approximately balance the normal pressure gradient Another less important factor, i.e., the change of the Coriolis force parameter with the latitude, is also taken into account. The distributions of the vorticities of GRS and White Oval BC are also calculated.     

THE CORRECTION OF "ON THE MOTTON OF FLYING PLATE UNDER EXPLOSIVE ATTACK

Chu Chao-hsiang and Jiang Da-he,On the Motion of Flying Plate under Ex-plosive Attack,Applied Mathematics and Mechanics,Vol.1,No.3 (1980).PP.293-304.1.Eq.(2.2)should be as follows:     

TRANSVERSE VIBRATION OF RECTANGULAR PLATES ELASTICALLY SUPPORTED AT POINTS ON EDGES

This paper studies transverse vibration of rectangular plates with two opposite edgessimply supported,other two edges arbitrarily supported and free edges elasticallysupported at paints.A highly accurate solution is presented for calculating inherentfrequencies and mode shape of rectangular plates elastically supported at points.Thenumber and location of these points on free edges may be completely arbitrary.This paperuses impulse function to represent reaction and moment at points.Fouricr series is used toexpand the impulse function along the edges.Characteristic equations satisfying allboundary conditions are given.Inherent frequencies and mode shape with any accuracy canbe gained.     

ON THE UNIFORM BOUNDEDNESS OF SOLUTIONS OF SOME NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｗｏｒｋ，ｗｅｓｔｕｄｙｔｈｅｐｒｏｂｌｅｍｓｏｆｔｈｅｂｏｕｎｄｅｄｎｅｓａｎｄｕｎｉｆｏｒｍｂｏｕｎｄｅｄｎｅｓｏｆｓｏｌｕｔｉｏｎｓｏｆｎｏｎ＿ａｕｔｏｎｏｍｏｕｓｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆ...     

NEW POINTS OF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS (Ⅰ)──FUNDAMENTAL THEORY

I.Intr0ductionNonlocallinearelasticitytheoryisp0ssible0fbuildingthebridgebetweenmicrostructuresofmaterialsandtheirmacrosc0picmechanicsbehaviorsduet0consideringthelong-rangeforcesamongmicroscopicparticles.SincenonIocalfieldtheorywasadvanced,aseriesresultsl…     

ON THE GENERAL EQUATIONS OF AXISYMMETRIC PROBLEMS OF IDEAL PLASTICITY

In this paper, introducing a velocity potential, we reduce the fundamental equations of axisymmetric problems of ideal plasticity to two nonlinear partiCal differential equations. From these equations we discuss compatibilitg of Harr-Kármán hypothesis with von Mises yield criterion and the associated flow law.