A Matrix Operator Formalism for Investigating Spatially Bounded Multicomponent Liquid Systems

We consider a multicomponent spatially bounded liquid system and propose a method that allows analyzing such systems formally. We illustrate the application of the method with an approximate calculation of pair correlators and an analysis of the shifts of critical parameters due to the spatial bounds of the system.     

Method for diagonalizing pair correlation functions for a multicomponent liquid system

We consider the method for finding pair correlation functions for a multicomponent liquid system based on diagonalizing the initial system of integral equations for the pair correlation functions, which allows solving this system. We obtain asymptotic solutions for the correlation functions and analyze the introduced approximations from the physical standpoint. We interpret the obtained results physically.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 3, pp. 569–576, March, 2005.     

Critical Asymptotic Behavior of Correlations in a Simple Liquid

We consider a representation of the total and the direct correlation functions in a liquid in terms of the corresponding spectral densities. Analysis of the spectral density properties reveals a mechanism responsible for changing the analytic properties of the Fourier transform of the correlation function and its asymptotic behavior in the critical domain. We show that the well-known restrictions imposed on possible values of the critical asymptotic exponent follow from this mechanism.     

Correlation functions in the anomalous-dimension approximation for a multicomponent liquid

We analyze the features of solutions for pair correlation functions in the case of a multicomponent liquid. We obtain these solutions based on the Ornstein-Zernike equation. In the anomalous-dimension approximation, we find expressions for pair correlation functions in the case of a spatially unbounded multicomponent liquid. We show that all pair correlation functions for a system in the close vicinity of the critical state are described by a general expression similar to the expression for a pair correlation function in the case of a one-component liquid. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 124–129, October, 2007.     

Thermodynamics and Hydrodynamics (Statistical Foundations): 4. Kinetic Processes in Multicomponent Systems

We use the BBGKY hierarchy and the mass, momentum, and intrinsic energy conservation laws, which are consequences of this hierarchy, to obtain the hydrodynamic equations for multicomponent systems and the diffusion equations. We formulate several restrictions on the thermodynamic equations for irreversible processes.     

Lorentz-Minkowski空间中给定主曲率函数的旋转超曲面

给出(n,1)型orentz-Minkowski空间中给定主曲率函数的旋转类空超曲面的位置向量场,通过计算超曲面的主曲率,证明了这类超曲面的存在性.     

ASYMPTOTIC EXPANSION OF DIRAC-TYPE DISTRIBUTION ASSOCIATED WITH A CLASS OF HYPERSURFACES WITH DEGENERATED CRITICAL POINTS

1IntroductionTheformeran.thorgivesin[4]ageneralizationofHadamardgstheoryoffundamentalsolutionstothecaseofberthorderlinearholomorphicPDEandproveditsidentitywiththedistributionalfundamentalsolution.TheessenceofHadamard'sprocedure[6]istofindfundamentalsolutionintheformofwherek(x)=0istheequationofthecharacteristicconoidwithx=0asthevertex,andk(x)isholomorphicnearx=0.Whentheequationisnon-degenerated,k(x)hasalsoanondegeneratedHessianatx=0.ReplacehAin(1)byhi,(1)givesadistributionwithAasaparameter.…     

Quasi—Einstein Hypersurfaces in a Hyperbolic Space

§1.　IntroductionLetRijbethecomponentsofRiccitensorofann-dimensionalRiemannianmanifoldM.IfRij=Agij Bξiξj,　(i,j=1,2,…,n)(1.1)whereξisanunitvectorfield,thenMiscalledaquasi-EinsteinmanifoldanddenotedbyQE(ξ).Ifξisanisotropicvectorfield,thenMiscalledageneralizedquasi-Einsteinmanifold.Intheequality(1.1),AandBarescalarfunctions.WeknowQE(ξ)manifoldisEinsteinwhenB≡0.Especially,if〈ξ,ξ〉=e=±1,thenQE(ξ)iscalledanormalquasi-Einsteinmani-fold.Itiseasytoknowfrom[1]and[2]:Rij=R-Tn-1…     

The Slow Wave in an Anisotropic Liquid Layer Modeling a Reservoir

The velocity and attenuation of the slow wave propagating in an anisotropic liquid layer sandwiched between two elastic half-spaces are described. The liquid layer is composed of alternating liquid layers: water-oil, water-gas, and oil-gas. The problem is solved in the low-frequency approximation in the case where the wavelength is larger than the thickness of the layer. Bibliography: 8 titles.     

Normal connections induced by a framed hypersurface in the conformal space

We find two normal connections induced by the normal framing of a hypersurface V _{n ? 1} in the conformal space C _n , and establish relationship between these connections and a Weyl connection which is also induced by the normal framing of V _{n ? 1}. We study two normal connections induced by a complete framing of a hypersurface V _{n ? 1} in C _n . We establish relationship between geometries of a framed hypersurface V _{n ? 1} of the conformal space C _n and a quadratic hyperband of the projective space P _{n + 1} associated with V _{n ? 1}.     

Fermionic construction of the partition function for multimatrix models and the multicomponent Toda lattice hierarchy

We use p-component fermions, p = 2, 3,..., to represent (2p−2)N-fold integrals as a fermionic vacuum expectation. This yields a fermionic representation for various (2p−2)-matrix models. We discuss links with the p-component Kadomtsev-Petviashvili hierarchy and also with the p-component Toda lattice hierarchy. We show that the set of all but two flows of the p-component Toda lattice hierarchy changes standard matrix models to new ones. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 265–277, August, 2007.     

Singularities of de Sitter Gauss map of timelike hypersurface in Minkowski 4-space

We study the singularities of de Sitter Gauss map of timelike hypersurface in Minkowski 4-space through their contact with hyperplanes.     

Looking at a Gaussian process through a window

We show that an observer recording only the presence or absence of a Gaussian process in a window can reconstruct its correlation function.     

基于S型隶属度函数的模糊网络计划关键线路分析

在众多研究三角或梯形模糊网络计划的基础上,分析了S型隶属函数下模糊网络计划的可行性.针对在模糊网络计划中以总时差为零来判断关键线路可能遇到的问题,引出相关面积的概念,以最接近总工期的线路对工程工期影响最大的原则,得出关键线路的求法.     

一类浸入在半黎曼卷积空间的完备超曲面

We deal with complete hypersurfaces immersed in a semi-Riemannian warped product of the type eI×f M~n,where M~n is a connected n-dimensional oriented Riemannian manifold.When the fiber M~n is complete with sectional curvature-k≤K_M for some positive constant k,under appropriate restrictions on the norm of the gradient of the height function h,we proceed with our technique in order to guarantee that complete hypersurface immersed in a semi-Riemannian warped product is a slice.Our approach is based on the well known generalized maximum principle and another suitable maximum principle at the infinity due to Yau.     

Atomic and Subatomic Decompositions in Anisotropic Function Spaces

This work deals with decompositions in anisotropic function spaces. Defining anisotropic atoms as smooth building blocks which are the counterpart of the atoms from the works of M. Frazier and B. Jawerth , it is shown that the study of anisotropic function spaces can be done with the help of some sequence spaces in a similar way as it is done in the isotropic case. It is also shown that the subatomic decomposition theorem for isotropic function spaces, recently proved by H. Triebel , can be extended to the anisotropic case if the mean smoothness parameter is sufficiently large.     

On spectral characterizations of Willmore hypersurfaces in a sphere

Let M be a closed Willmore hypersurface in the sphere S^n＋1（1） （n ≥ 2） with the same mean curvature of the Willmore torus Wm,n-m, if SpecP（M） = Spec^P（Wm,n-m ） （p = 0, 1,2）, then M is Wm,n-m.     

The inverse partial correlation function of a time series and its applications

The concept of the inverse correlation function of a stationary process was introduced by Cleveland (Technometrics14 (1972), 277–293). The inverse partial correlation function of a stationary process may intuitively be thought of as the corresponding extension of the concept of the partial correlation function. A precise mathematical definition of this function is given. Its importance in describing the structure of a moving average of finite order h is discussed. Having observed X₁,…,X_T, the autoregressive method of estimating the inverse correlations is employed for constructing sample estimates of the inverse partial correlations. For the hth-order moving average process, the estimates beyond h are, as T → ∞, asymptotically independent normally distributed with 0 mean and variance T^?1. Their use for estimating h and for testing hypotheses concerning h is examined.