BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅲ)—BASIC THEORIES

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BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅰ)——BASIC EQUATIONS

This paper studies computational stock market by using network model and similar methodology used in solid mechanics. Four simultaneous basic equations, i.e., equation of interest rate and amount of circulating fund, equations of purchasing and selling of share, equation of changing rate of share price, and equation of interest rate, share price and its changing rate, have been established. Discussions mainly on the solution and its simple applications of the equation of interst rate and amount of circulating fund are given. The discussions also involve the proof of tending to the equilibrium state of network of stock market based on the time discrete form of the equation by using Banach theorem of contraction mapping and the influence of amount of circulating fund with exponential attenuation due to the decreasing of banking interest rate.     

BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅰ)──BASIC EQUATIONS

IntroductionComputationaleconomicwillbethetendencyofmodemeconomicanalysis,nevedhelessthereisalongwaytoachievethelevelofcomputationalmathematicsandcomputationalmechanicsatpresent.Stockmarketisasensiblebarometermeasuredtheweatherofmarketeconomicactivities.Althoughtherearemanypapersoncomputationaleconomic(forexampleRefs.[l,2])butpaperconcernedwithstockmarketisrarelyseen.InChina,mostpublicationsonstockmarket(forexampleRefs.[3~5])arequotationdata,predicationoftendency,skillsorexperiencesforgainin…     

BASIC EQUATIONS, THEORY AND PRINCIPLES OF COMPUTATIONAL STOCK MARKET (Ⅱ)——BASIC PRINCIPLES

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅａｒｅｍａｎｙｐｒｉｎｃｉｐｌｅｓｉｎｍｅｃｈａｎｉｃｓ,ｓｕｃｈａｓｔｈｅＳａｉｎｔ＿Ｖｅｎａｎｔ’ｓｐｒｉｎｃｉｐｌｅ,ｔｈｅＤ’Ａｌｅｍｂｅｒｔ’ｓｐｒｉｎｃｉｐｌｅ,ｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓ...     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅷ)—PRINCIPLE OF TOTAL WORK AND ENERGY

IntroductionRecently ,wehaverestudiedtheconventionalconservationlawofenergy ,whichhaswidelybeenusedandisusinginliteraturesofclassicalcontinuummechanicsathomeandabroad ,andpointedoutthatitistheoreticallyincompleteeveninthetraditionalframework .Thepresentsituationoftheconservationlawsofenergyforpolarcontinuaisthesameasthatforclassicalcontinuummechanics.Inordertochangethestatusquo ,itseemstobequitenecessarythatnewprinciplesoftotalworkandenergyshouldbeproposedtotaketheplaceoftheexistingconservatio…     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅷ)—PRINCIPLE OF TOTAL WORK AND ENERGY

Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Via total variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded. Contributed by DAI Tian-min, Original Member of Editorial Committe, AMM Project supported by the National Natural Science Foundation of China (Nos. 10472041, 10072024) and the Science Research Foundation of Liaoning Province (No. 990111001)     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived. Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931≈)     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

IntroductionThispaperisadirectcontinuationofRef.[1 ] .InitthecoupledconservationlawofenergypresentedinRef.[2 ]wasextendedandtherathercompletesystemsofbasicbalancelawsandequationsformicropolarcontinuumtheoryhavebeenconstitutedbycombiningtherenewedresultsandthetraditionalconservationlawsofmassandmicroinertiaandtheentropyinequality .Thepurposeofthispaperistorestablishthesystemsofbasicbalancelawsandequationsformicromorphiccontinuumtheoryandcouplestresstheoryviadirecttransitionsandreductionsfromth…     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅰ)

This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space) are given and the characterizations of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to study the linear operator theory and fixed point theory on PM-spaces. Projects supported by the Science Fund of the Chinese Academy of Sciences.     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES(Ⅱ)

This paper is a continuation of the author's previous paper [1], in which the characterizations of various probabilistically bounded sets are presented, and the linear operator theory and fixed point theory on probabilistic metric spaces are given, too.     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES(Ⅰ)

This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space ) are given and the characterizations of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to study the linear operator theory and fixed point theory on PM-spaces.     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅱ)

This paper is a continuation of the author’s previous paper [1], in which the characterizations of various probabilistically bounded sets are presented, and the linear operator theory and fixed point theory on probabilistic metric spaces are given, too.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅲ)—NOETHER''''S THEOREM

IntroductionThispaperisadirectcontinuationofthepreviouspapers [1 ,2 ] .ThefieldequationsoflinearcouplestresselasticityweredevelopedbyMindlinandTiersten[3].AgeneralcouplestresstheorywaspresentedbyToupin[4 ].Eringen[5 ,6 ]haspointedoutthatthecouplestresstheoriesofelasticmediafluidsmaybededucedfromthemicropolarelasticityandfluidmechanicswhenthemicrorotationsiandψiareconstrainedbytherotationvectorωiofclassicalelasticityandvorticityvectorrioffluidmechanics,respectively .AnexpressionoftheJ_int…     

EXTENSION OF POINCARE’S NONLINEAR OSCILLATION THEORY TO CONTINUUM MECHANICS (I)-BASIC THEORY AND METHOD

In this paper we extend Poincare’s nonlinear oscillation theory of discrete system to continuum mechanics. First we investigate the existence conditions of periodic solution for linear continuum system in the states of resonance and non-resonance. By applying the results of linear theory, we prove that the main conclusion of Poincare’s nonlinear oscillation theory can be extended to continuum mechanics. Besides, in this paper a new method is suggested to calculate the periodic solution in the states of both resonance and nonresonance by means of the direct perturbation of partial differential equation and weighted integration.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅲ) —NOETHER’S THEOREM

The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether’s theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics. The new concrete forms of various conservation laws of couple stress elasticity are derived. The precise nature of these conservation laws which result from the given invariance requirements are established. Various special cases are reduced and the results of micropolar continua may be naturally transited from the results presented in this paper.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅸ)— THERMOMECHANICS

The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES(Ⅸ)—THERMOMECHANICS

The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅵ)—CONSERVATION LAWS OF MASS AND INERTIA

The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented. Combining, these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum and energy may be obtained by the usual localization. Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931≈)     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅵ)—CONSERVATION LAWS OF MASS AND INERTIA

IntroductionThisworkisadirectcontinuationandasupplementofRefs .[1～8] .InRefs.[1～8]thecoupledbalancelawsandequationsofmomentum ,angularmomentumandenergyaswellasthenewHamiltonprinciple,principleofvirtualpowerandNoethertheoremhavebeenpresented .However,thecoupledconservationlawsofmassandinertiahavenotbeenreestablishedyet.Thepurposeofthispaperistoreestablishtheconservationlawsandequationsofmassandinertiaandtocombinethemwiththecoupledbalancelawsandequationsofmomentum ,angularmomentum ,energyand…