COMPREHENSIVE MATHEMATICAL MODEL OF MICROCIRCULATORY DYNAMICS (Ⅰ)——BASIC THEORY

Under the basis of physiological data, a nonlinear and unsteady comprehensive mathematical model of microcirculatory dynamics with distributed parameters is developed. Hemodynamics, interstitium dynamics, lymph dynamics, dynamics of protein transport, oxygen dynamics, dynamics of heat transfer, and myogenic and metabolic regulation procedures are included. The interactions between these factors were comprehensively exhibited. The influences of arteriolar vasomotion and nonlinear viscoelasticity of blood in arteriole are considered. A simplified vessel network consisting of arteriole, open and reserved capillaries, venule, initial lymphatics and arteriole-venule anastomose is adopted as the geometrical model. This kind of comprehensive mathematical model is helpful in analyzing clinical data and developing a “numerical experiment method” in microcirculation research.     

COMPREHENSIVE MATHEMATICAL MODEL OF MICROCIRCULATORY DYNAMICS(Ⅱ)—ALCULATION AND THE RESULTS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｍｐｒｅｈｅｎｓｉｖｅｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｄｅｖｅｌｏｐｅｄｉｎｔｈｅｆｉｒｓｔｐａｒｔｏｆｔｈｉｓｐａｐｅｒ[1]ｃｏｎｔａｉｎｓｄｏｚｅｎｓｏｆｃｏｕｐｌｅｄｅｑｕａｔｉｏｎｓｔｈａｔｆｏｒｍａｌａｒｇｅｎｏｎｌｉｎｅａｒｅｑｕａｔｉｏｎｓｙｓｔｅｍ.Ｈｅｒｅｗｅｃｏｍｂｉｎｅａｎａｌｙｔｉｃａｌａｎｄｎｕｍｅｒｉｃａｌｍｅｔｈｏｄｓｔｏｓｏｌｖｅｉｔａｎｄｄｉｓｃｕｓｓａｎｄａｎａｌｙｚｅｓｏｍｅｉｍｐｏｒｔａｎｔｐｒｏｂｌｅｍｓｉｎｍｉｃｒｏｃ…     

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 (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.     

EIGEN THEORY OF VISCOELASTIC DYNAMICS BASED ON THE KELVIN-VOIGT MODEL

Using the eigen theory of solid mechanics, the eigen properties of anisotropic viscoelastic bodies with Kelvin-Voigt model were studied, and the generalized Stokes equation of anisotropic viscoelastic dynamics was obtained, which gives the three-dimensional pattern of viscoelastical waves. The laws of viscoelastical waves of different anisotropical bodies were discussed. Several new conclusiones are given.     

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...     

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅰ)—BASIC IDEAS AND THEORY

This paper suggests a hydrodynamic stability theory of distorted laminar flow,andpresents a kind of distortion profile,of mean velocity in parallel shear flow.With suchdistortion profiles,the new theory can be used to investigate the stability behaviour ofparallel shear flow,and thus suggests a new possible approach to instability.     

NOETHER’S THEORY OF VACCO DYNAMICS

In this paper,we first study the latent relation between the conservative quantityand the symmetry of nonholonomic dynamical systems without any additionalrestrictive conditions to its virtual displacement,and then establish Noether’s theoremand Noether’s inverse theorem of Vacco dynamics.Lastly,we give two examples toillustrate the application of result of this paper.     

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

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｒｉｃｅｏｆｇｏｏｄｓｖａｒｙｉｎｇａｒｏｕｎｄｉｔｓｖａｌｕｅｉｓｃｏｎｓｉｄｅｒｅｄｔｏｂｅａｂａｓｉｃｒｕｌｅｏｆｇｏｏｄｓ,ｉ.ｅ .,ｔｈｅｌａｗｏｆｖａｌｕｅｏｆｇｏｏｄｓ.Ａｓｔｏｃｋｉｓａｋｉｎｄｏｆｇｏｏｄｓ ,ｉｔｎａｔｕａｌｌｙｏｂｅｙｓｔｈｅｌａｗｏｆｖａｌｕｅｏｆｇｏｏｄｓ.Ｓｏｔｈａｔｔｈｅｐｒｉｃｅｏｆｓｔｏｃｋｖａｒｉｅｓａｒｏｕｎｄｉｔｓｖａｌｕｅ.Ｔｏｄｅｔｅｒｍｉｎｅｔｈｅｖａｌｕｅｏｆｓｔｏｃｋｉｓｖｅｒｙｉｍｐｏｒｔａｎｔｆｏｒｔｈ…     

THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC—PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS(Ⅰ)

In this paper:(A) We cast aside the traditional quaternion theory and build up the theory offunctions of a complex variable under Dirac-Pauli representation. Thus the multivariateand multidimensional problems become rather simple problems.(B) We simplify the Navier-Stokes equation of incompressible viscous fluid dynamicsand the equations group of isentropic aerodynamics by theory of functions of a complexvariable under Dirac-Pauli representation. And the above-equations, as central problems offluid dynamics, are classified as the nonlinear equation with only one complex unknownfunction.So the changes are the Great Pole, and give birth to the Two Bearings; the TwoBearings give birth to the Four Quadrants, and the Four Quadrants give birth to the EightDiagrams.——Commentaries on Changes,Copula(Ⅰ)     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅰ)──GENERAL THEORY

1.Intr0ductionInrecentyears,multilayersandwichshells,duetotheirhighrigidityandlightweight,havefoundwideapplicationinaeronautical,astronauticalandnavalengineerings.Withpropermaterialsforfacingsandcores,theshellsmaypossessshock-mitigating,thermal-insulating…     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅰ)──GENERAL THEORY

In this paper, a nonlinear theory is given for multilayer sandwich shells undergoing small strains and moderate rotations. Then a simplified theory for the shells undergoing moderate or moderate/small rotations are obtained.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain,water andgas.In this paper,the consolidation problem of unsaturated soil is investigated basedon the theory of mixture.A theoretical formula of effective stress on anisotropicporous media and unsaturated soil is derived.The principle of effective stress and theprinciple of Curie symmetry are taken as two fundamental constitutive principles ofunsaturated soil.A mathematical model of consolidation of unsaturated soil isproposed,which consists of25 partial differenfial equations with25 unknowns.Withthe help of increament linearizing method,the model is reduced to5 governingequations with5 unknowns,i.e.,the three displacement components of solid phase,thepore water pressure and the pore gas pressure.7 material parameters are involved inthe model and all of them can be measured using soil tests.It is convenient to use themodel to engineering practice.The well known Biot’s theory is a special case of themodel.