TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(φ)=(1+k)sinφ/ 1+kcosφ.     

THE RELATIONSHIP BETWEEN THE STABILITY AND THE OPTIMALITY OF LINEAR SYSTEMS(Ⅱ)

Different from the inverse problem put forward by R.E.Kalman, another kind ofinverse problem of linear optimal control is proposed and discussed in[1] as follows:Givenan asymptotically stable linear constant system and a nonnegative quadratic performanceindex, when can a state-feedback be separated from the stable system so that this state-feedback control law is optimal for the given index? In this paper this problem is extended.Similar conclusions are obtained for linear discrete systems and linear time-variablesystems. According to these conclusions we can say that the correspondence between theasymptotically stable system and the optimal feedback system is the inherent character ofall kinds of linear systems.     

ON THE STRUCTURE OF SOLUTIONS OF LINEAR PARTIAL DIFFERENTIAL EQUATION sum from (i j≤n) (a_(ij)p~iq~j(■))=0 WITH TWO INDEPENDENT VARIABLES AND CONSTANT COEFFICIENTS

This paper is a continuation of [1].In this paper,the solutions of the more generallinear partial differential equation (?) with two independent variables andconstant coefficients are discussed in detail.The general solution which can be used in theapproximation to the conditions of the definite solution of the practical problems ispresented.To illustrate the use of the results obtained in this paper,some practicalexamples in mechanics are given.     

THERMODYNAMIC ENTROPY MODELS OF THE FROZEN-WALL SYSTEM(I)

In this paper,the author describes,and comments on the traditional thermal theory onartificial ground freezing,and points out its important significance and shortcomings.Thefrozen-wall is analysed by system analysis methods.According to matter levels,the frozen-wall is divided into three sub-systems:frozen colloid system,frozen soil system and frozen-wall system.They correspond to different characteristics.The frozen-wall system is a largeopen system with multi-levels and multi-aspects.The problems of stability of the system andits control are the key problems in the techniques of artificial ground freezing.Based onnon-equilibrium thermodynamics and dissipative structure theory methods,the authordiscusses and reveals the problems of the formation and stability of the frozen-wall systemand its thermodynamic nature,and proposes the thermodynamic entropy models of thesystem.The result is a great satisfaction.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE Ⅰ CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅱ)—THE ANALYSES OF THE STRESS STRUCTURE

Based on[1],the stress structures of the smooth region and shear lip of thespecimens have been investigated in the paper.The characteristics of the stress structure inthe smooth region have been found that the variable z can separated out;the stressesin the midsection can be obtained by the plane strain FEM results or HRR structuremodified by the stress triaxiality.The effects of load level and thickness on the stressstructure can be reflected by the distribution of CTOD along the thickness direction.The obtained expressions of the stresses are very simple and visualized.The analysesof the stress structure in the shear lip show that the stresses can be obtained bydifferent methods of interpolation to a certain precise degree.A new degree parameter of the plane strain state has been put forward andstudied.The parameter can reflect relatively well the variation of the kind andthickness of the specimen as well as the load level.The fracture parameter has alsobeen investigated to be sure that it can be obta     

THERMODYNAMIC ENTROPY MODELS OF THE FROZEN-WALL SYSTEM (Ⅱ)

This paper is a further research of reference [1]. At first, the author analyzes the forceenergetics basis of the frozen-wall system. By quantitative discussion of Model (Ⅰ) in reference [1], we get a thermal stability entropy model of the frozen-wall system (called Model (Ⅱ)). At last, we check the models by the field observed data in Anhui Province. P.R.C. The result is greatly satisfactory.     

THERMODYNAMIC ENTROPY MODELS OF THE FROZEN-WALL SYSTEM(Ⅱ)

This paper is a further research of reference [1]. At first, the author analyzes the force-energetics basis of the frozen-wall system. By quantitative discussion of Model(Ⅰ)in reference [1], we get a thermal stability entropy model of the frozen-wall system(called Model(Ⅱ)). At last, we check the models by the field observed data in Anhui Province. P.R.C. The result is greatly satisfactory.     

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅲ)—CANTILEVER RECTANGULAR PLATES

In this paper,applying the method of the reciprocal theorem,we give the stationarysolutions of the forced vibration of cantilever rectangular plates under uniformly distributedharmonic load and concentrated harmonic load acting at any point of the plates,the figuresand tables of number value of bending moment and the deflection amplitudes as well.     

THE EFFECTS OF ROUGHNESS CHANGE ON THE SURFACE LAYER OF THE ATMOSPHERE(Ⅰ)—THE VARIATIONS OF WIND SPEED AND SHEAR STRESS

A general four-layer structure linear theory for predicting the effects of arbitrarilydistributed roughness change on the variations of wind speed and shear stress in the surfacelayer of3D and2D atmospheres was presented.The results derived by the theory wereagreeable to the previous ones.     

THE SINGULAR PERTURBATION METHOD APPLIED TO THE NONLINEAR STABILITY PROBLEM OF A SHALLOW SPHERICAL SHELL(Ⅱ)

In this paper we consider the nonlinear stability of a thin elastic circular shallowspherical shell under the action of uniform normal pressure with a clamped edge.When thegeometrical parameter k is large,the uniformly valid asymptotic solutions are obtained bymeans of the singular perturbation method.In addition,we give the analytic formula fordetermining the centre deflection and the critical load,and the stability curve is also derived.This paper is a continuation of the author’s previous paper[11].     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅱ)- CALCULATION FOR OMEGA-SHAPED BELLOWS

is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega-shaped bellows were calculated, and the present results were compared with those of the other theories and experiments. It is shown that the non-homogeneous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself, and be more effective than by the theory of slender ring shells; but if a lateral slide of the bellows support exists the non-homogeneous solution will no longer entirely satisfy the boundary conditions of the problem, in this case the homogeneous solution of (Ⅰ) should be included, that is to say, the full solution of (Ⅰ) can meet all the requirements.     

RESEARCH ON THE COMPLICATED DYNAMICAL BEHAVIORS OF NONLINEAR ECOSYSTEMS(Ⅱ)

This paper is a further study of reference[1].In this paper,we mainly discuss thecomplicated dynamical behaviors resulting from a simple one-dimensional model ofnonlinear ecosystems:fixed point motion,periodic motion and chaotic motion etc.,andbriefly discuss the universality of the complicated dynamical behaviors,which can bedescribed by the first and the,second M.Feigenbaun.constants.At last,we discuss the“one-side liowering phenomenon”due to near unstabilization when the nonlinear ecosystemapproaches bifurcation points from unbifurcation side.It is of important theoretical andpractical meanings both in the development and utilization of ecological resources and inthe design and management of artifitial ecosystems.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper,three dimensional analyses of some general constraintparameters and fracture parameters near the crack tip of Mode I CT specimens in twodifferent thicknesses are carried out by employing ADINA program.The results revealthat the constraints along the thickness direction are obviously separated into twoparts:the keeping similar high constraint field(Z_1)and rapid reducing constraintsone(Z_2).The two fields are experimentally confiremed to correspond to the smoothregion and the shear lip on the fracture face respectively.So the three dimensionalstress structure of Mode I specimens can be derived through discussing the two fieldsrespectively.The distribution of the Crack Tip Opening Displacement(CTOD)alongthe thickness direction and the three dimensional distribution of the void growth ratio(V_9 )near the crack tip are also obtained.The two fracture parameters are in similartrends along the thickness direction,and both of them can reflect the effect ofthickness and that of the loading l     

STUDY ON THE COMPLICATED DYNAMICAL BEHAVIORS OF NONLINEAR ECOSYSTEMS(Ⅲ)

This paper is a continuous study of references[1-2].At first,we introduce theconcept of assembles of ecosystems,and then discuss macro-and micro-synergeticalmethods for ecology study.Combining the two methods,by use of the macroscopic data(observable)outputted from the ecosystems,we can construct their GGLE,master theirinformation changes between,before and after the generalized phase changes(e.g.community successions),and find out the action mechanisms of microscopic factors onmacroscopic results.This may be a new approach to the study of action mechanisms ofcomplex ecosystems.     

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES W~(m,p)t(Ω)

In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreom for J(u)=0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL (Ⅰ) -THE UPPER BOUND ON THE EVOLUTION OF DISTURBANCE TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol’s second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅱ)

Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country’s macro-financial system: balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people’s understanding of the lever function of all kinds of financial policies.     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM (Ⅰ)

Based on the mathematical model of a kind of complicated financial system, all possible things that the model shows in the operation of our country’s macro-financial system were analyzed, such as balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcations,and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior were analyzed. This study will deepen people’s understanding of the lever function of all kinds of financial policies.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅱ)——THE LINEAR STABILITY ANALYSIS OF DISTORTED PARALLEL SHEAR FLOW

Based on the hydrodynamic stability theory of distorted laminar flow and the kind ofdistortion profiles on the mean velocity in parallel shear flow given in paper[1],this paperinvestigates the linear stability behaviour of parallel shear flow.presents unstable results ofplane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetricdisturbances for the first time,and obtains neutral curves of these two motions under certaindefinition.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅲ)—THE NONLINEAR STABILITY ANALYSIS OF DISTORTED PARALLEL SHEAR FLOW

Based on the hydrodynamic stability theory of distorted laminar flow and the kind ofdistortion profiles on the mean velocity in parallel shear flow given in paper[1].this paperinvestigates the nonlinear stability behaviour of parallel shear flow,carries on stabilitycalculation taking account of the perturbations of background turbulence noise undercertain assumption,and obtains some results in accordance qualitatively with those ofexperiment for plane Poiseuille flow and pipe Poiseuille flow.