15 June 1998, Volume 14 Issue 3

    

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  Quantum and Non-Causal Stochastic Calculus

  Liang Zongxia, Zheng Mingli

  Acta Mathematica Sinica. 1998, 14(3): 289-294. https://doi.org/10.1007/BF02580431

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  In this paper,using the Guichardet space technique,the relationship between Fermion quantum stochastic calculus and non-causal calculus in Segal space L2(H) is discussed,and an anticipating quantum stochastic calculus is naturally given.
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  Algebraic Independence by Approximation Method

  Zhu Yaochen

  Acta Mathematica Sinica. 1998, 14(3): 295-302. https://doi.org/10.1007/BF02580432

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  By the use of approximation method a general criterion of algebraic independence of complex numbers is established.As its application the algebraic independence of values of certain gap series at algebraic and transcendental points is given.
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  Edgeworth Expansion in Partial Linear Models

  Shi Jian

  Acta Mathematica Sinica. 1998, 14(3): 303-314. https://doi.org/10.1007/BF02580433

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  In this paper,under some fairly general conditions,a first-order Edgeworth expansion for the standardized statistic of β in partial linear models is given,then a non-residual type of consistent estimation for the error variance is constructed,and finally an Edgeworth expansion for the corresponding studentized version is presented.
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  The Behavior of Super-Brownian Motion near Extinction

  Guo Junyi, Wu Rong

  Acta Mathematica Sinica. 1998, 14(3): 315-320. https://doi.org/10.1007/BF02580434

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  We start from a super-Brownian motion with the branching mechanism presented by Dawson and Vinogradov.Its behaviour near extinction is studied in this paper,and the main result is that the diameter of the support tends to zero almost surely at the time of extinction.
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  Some Pairs of Adjoint Functors Involving Track Homotopy Categories

  Chen Jixiang

  Acta Mathematica Sinica. 1998, 14(3): 321-326. https://doi.org/10.1007/BF02580435

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  K.A.Hardie and K.H.Kamps investigated the track homotopy category H_B over a fixed space B ([1]).They have introduced two pairs of adjoint functors:P_B——|N_B and m_*——|m*,where P_B:H_B→HB,and m_*:H_A→H_B for a fixed map m:A→B.We have introduced a split fibration of categories L:H_b→H_B and proved L J,J——|L in [2].This paper first extends P_B——|N_B to for any fixed map b:B→B.Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categories H_b and H b where H b is the dual of H_b.One of our results is N_b——|P_b.This differs from P_B——|N_B.
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  Bessel (Riesz) Potentials on Banach Function Spaces and Their Applications Ⅰ Theory

  Wang Baoxiang

  Acta Mathematica Sinica. 1998, 14(3): 327-340. https://doi.org/10.1007/BF02580436

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  In this paper,we shall introduce the concept of the Bessel (Riesz) potential Köthe function spaces Xs and give some dual estimates for a class of operators determined by a semi-group in the spaces Lq (-T,T;Xs) (Lq(-T,T;)).Moreover,some time-space Lp -Lp' estimates for the semi-group exp(emt(-Δ)m/2) and the operator A:=∫₀t exp(i(t-τ)(-Δ)m/2)·dτ in the Lebesgue-Besov spaces Lq(-T,T;) are given.On the basis of these results,in a subsequent paper we shall present some further applications to a class of nonlinear wave equations.
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  Problems in Homoclinic Bifurcation with Higher Dimensions

  Zhu Deming

  Acta Mathematica Sinica. 1998, 14(3): 341-352. https://doi.org/10.1007/BF02580437

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  In this paper,a suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems.Then the Poincarémap is established to solve various problems in homoclinic bifurcations with codimension one or two.Bifurcation diagrams and bifurcation curves are given.
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  On Some Nonlinear Integral and Discrete Inequalitites Related to Ou-Iang’s Inequality

  Yang Enhao

  Acta Mathematica Sinica. 1998, 14(3): 353-360. https://doi.org/10.1007/BF02580438

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  Nonlinear integral and discrete inequalities are obtained,which are related to some recent results of B.G.Pachpatte in [1] given therein as generalizations of Ou-Iang's integral inequality [2].As special cases,some new inequalities with the power nonlinearity are derived from the main results.To show the contribution of our results,boundedness of solutions to certain nonlinear difference equation is also considered.
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  Conformal Deformations for Prescribing Scalar Curvature on Riemannian Manifolds with Negative Curvature

  Hu Zejun

  Acta Mathematica Sinica. 1998, 14(3): 361-370. https://doi.org/10.1007/BF02580439

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  We study the conformal deformation for prescribing scalar curvature function S on Cartan-Hadamard manifold Mn (n≥3) with strongly negative curvature.By employing the supersubsolution method and a careful construction for the supersolution,we obtain the best possible asymptotic behavior for S near infinity so that the problem of complete conformal deformation is solvable.In more general cases,we prove an asymptotic estimation on the solutions of the conformal scalar curvature equation.
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  The Keldys-Fichera Obstacle Problem

  Chen Zuchi, Yan Xiaodong

  Acta Mathematica Sinica. 1998, 14(3): 371-380. https://doi.org/10.1007/BF02580440

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  In this paper we consider a quasilinear obstacle problem with coefficients of higher growth orders and the Keldys-Fichera boundary condition.
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  The Lifetime of Diffusion Processes with Application to Conditioned Diffusions

  Wang Fengyu

  Acta Mathematica Sinica. 1998, 14(3): 381-384. https://doi.org/10.1007/BF02580441

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  Let τ_D.denote the lifetime of a diffusion process on domain D⊂Rd.This paper presents a sufficient condition for the exponential moment of τ_D to be finite.Here,both of the domain and the diffusion operator are general.As an application,the main result of Gao (1995) for conditioned diffusions is improved on.
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  On Endomorphism Rings of Regular Modules

  Wu Tongsuo

  Acta Mathematica Sinica. 1998, 14(3): 385-390. https://doi.org/10.1007/BF02580442

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  In this paper,we study the endomorphism rings of regular modules.We give sufficient conditions on a regular projective module P such that End _R(P) has stable range one.
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  Free Boundary Problem for a Viscous Compressible Flow Associated with Oxidation of Silicon

  V. A. Solonnikov, Yi Fahuai

  Acta Mathematica Sinica. 1998, 14(3): 391-398. https://doi.org/10.1007/BF02580443

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  This paper is concerned with a free boundary problem describing the oxidation process of silicon.Its mathematical model is a compressible Navier-Stokes equations coupling a parabolic equation and a hyperbolic one.Surface tension is involved at the free boundary and density equation is non-homogeneous.It is proved that for arbitrary data satisfying only natural consistency conditions the problem is uniquely solvable on some finite time interval.
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  On the Two-Dimensional Cauchy Problem of a Hyperbolic System

  Huang Feimin

  Acta Mathematica Sinica. 1998, 14(3): 399-410. https://doi.org/10.1007/BF02580444

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  In this paper,we prove the global existence of generalized solutions to a two-dimensional Cauchy problem of a hyperbolic system by introducing a new definition of generalized solution.Moreover,the solution may involve delta-wave.
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  Semilinear Elliptic Resonant Problems at Higher Eigenvalue with Unbounded Nonlinear Terms

  Su Jiabao

  Acta Mathematica Sinica. 1998, 14(3): 411-418. https://doi.org/10.1007/BF02580445

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  In this paper we study the existence of nontrivial solutions of a class of asymptotically linear elliptic resonant problems at higher eigenvalues with the nonlinear term which may be unbounded by making use of the Morse theory for a C2-function at both isolated critical point and infinity.
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  Asymptotic Behavior of Solutions for a Class of Retarded Difference Equations

  Huang Lihong, Yu Jianshe, Dai Binxiang

  Acta Mathematica Sinica. 1998, 14(3): 419-422. https://doi.org/10.1007/BF02580446

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  Consider the retarded difference equation
  x_n -x_n-1 =F(-f(x_n)+g(x_n-k)), (*)
  where k is a positive integer,F,f,g:R→R are continuous,F and f are increasing on R,and uF(u)>0 for all u≠0.We show that when f(y)≥g(y) (resp.f(y)≤g(y)) for y∈R,every solution of (*) tends to either a constant or -∞ (resp.∞) as n→∞.Furthermore,if f(y)≡g(y) for y∈R,then every solution of (*) tends to a constant as n→∞.
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  Partial Regularity for Two Dimensional Landau-Lifshitz Equations

  Chen Yunmei, Ding Shijin, Guo Boling

  Acta Mathematica Sinica. 1998, 14(3): 423-432. https://doi.org/10.1007/BF02580447

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  It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points,provided that the weak solution has finite energy.