An (F)-spaceE is said to be locally midpoint constricted (in short,Imp-constricted) if there exists some δ>0 such that D(A/2)<D(A) for every subset A of E with 0<D(A)≤δ,where D(A) denotes the diameter of A.Our main result goes as follow:Let E be an Imp-constricted (F)-space and U an open connected subset of E.Assume that T:U|→F is an isometry (i.e.,a distance-preserving map) which maps U onto an open subset of the (F)-spaceF.Then T can be extended to an affine homeomorphism from E toF.Also,some other results about the question whether each isometry between two (F)-spaces is affine are obtained.

In this paper we classify infinite soluble minimal non-nilpotent-groups,detemine the basic structure of infinite soluble minimal non-Baer-groups,and using famed Heineken-Mohamed-groups we construct an example of minimal non-Baer-group which is not minimal non-nilpotent-group.

In this paper,we study the Dirichlet problems for the following quasilinear second order sub-elliptic equation,

whereX={X₁,...,X_m} is a system of real smooth vector fields which satisfies the Hörmander's condition,A_i,j,B_j,C∈C^∞(Ω×R) and (A_i,j (x,z)) is a positive definite matrix.We have proved the existence and the maximal regularity of solutions in the "non-isotropic" Hölder space associated with the system of vector fieldsX.

Hypothesis testing for arbitrarily varying source (AVS),which is to decide between the two hypotheses for the varying behavior of the distribution of AVS,is considered in this paper.We determine the best asymptotic exponent of the second kind of error probability when the first kind of error probability is fixed.This result generalizes the well-known lemma of Stein in statistics.As a corollary,Strassen's coding theorem for AVS is obtained.

Assume K is a rotor in a regular simplex of heihgt 1 in an n-dimensional Euclidean space.Let K^* denote the polar dual of K.Then the volume V(K^*) satisfies the inequality

where ω_n denotes the volume of an n-dimensional unit ball.Equality holds if and only if K is a ball centered at the centroid of the simplex.

In this paper we shall describe some algebraic concepts of Ockham algebras.We show that,if L,M∈K_1,1 then H(S(L),S(M)) S(H(L,M)).

The equivalence among bounded homeomorphisms of a surface,reducible homeomorphisms of the surface,bounded automorphisms of the surface group,induced or exchange automorphisms of the surface group,and the stabilizer of the translation length function of the tree action is established.

In this paper,we consider a two-parameter family of systems E_ε in which E_ε has a contour consisting of a saddle point and two hyperbolic periodic orbits,i.e.,the situation is similar to that described by the Lorenz equations for parameters b=8/3,Σ=10,r=r₁≈24.06.For the generic unfolding E_ε of E_ε,we find three kinds of infinitely many bifurcation curves and establish the correspondence of the trajectories which stay forever in a sufficiently small neighborhood of the contour with symbolic systems of finite or countably infinite symbols;these results can be used to explain the turbulence behaviors appearing at the critical value r=r₁≈24.06 observed on computer for Lorenz equations in a precise mathematical way.

Let f:X→X be a selfmap of a compact connected polyhedron,and A a nonempty closed subset of X.In this paper,we shall deal with the question whether or not there is a map g:X→X homotopic to f such that the fixed point set Fixg of g equals A.We introduce a necessary condition for the existence of such a map g.It is shown that this condition is easy to check,and hence some sufficient conditions are obtained.

Let f be analytic in a hyperbolic region Ω.The Bloch constant β_f of f is defined by ,where λ_Ω(z)|dz| is the Poincar émetric in Ω.Suppose Δ is hyperbolic and where .Then for allf withf(Ω)⊆Δ,we have β_f≤1/λ(Δ).In this paper we study the extremal functions defined by β_f=1/λ(Δ) and the existence of those functions.

In this paper,we apply the asymptotic methods to the study of the evolution and vanishing of limit cycles of a one parameter family of differential equations.Some sufficient conditions are given to guarantee the existence of duck solutions and duck cycles.The abruptness of this evolution is illustrated by a computer-analysis study.

This article reveals the topological impact of full y-λ-bases in locally convex spaces where λ carries either the traditional normal topology or the fairly generalized Σμ-topology of Ruckle.It has been established that the generalized nuclearity of λ plays a significant role in influencing the topology of the space.Further,the equivalence of normal topology and the topology arising out of the full y-λ-base (λ being equipped with normal topology or Σμ-topology) has been investigated.

For an odd function 1/2(x) defined only on a finite interval, this paper deals with the existence of periodic solutions and the number of simple periodic solutions of the differential delay equation (DDE) x . By use of the method of qualitative analysis combined with the constructing of special solutions a series of interesting results are obtained on these problems.

A conjugacy between C^1+α Σ-hyperbolic circle covering maps is C^1+α if it has a positive derivative on some point in the Σ-set.

Let M be a compact minimal surface in S³. Y. J. Hsu^[5] proved that if ∥S∥₂≤2√2π, then M is either the equatorial sphere or the Clifford torus, where S is the square of the length of the second fundamental form of M,‖·‖₂ denotes the L²-norm on M. In this paper, we generalize Hsu's result to any compact surfaces in S³ with constant mean curvature.

In this paper, we investigate the generalized Sublaplacian. We give the expression of the restriction operators explicitly. By introducing the generalized λ-twisted convolutions, we obtain the estimates of the restriction operators in the mixed L^p spaces. Finally, we get a restriction theorem associated with the generalized Sublaplacian.

In this paper it is proved that

wherer=4,q is a prime power,χ and ψ are multiplicative and additive characters modulo q respectively, withχ nontrivial.

It has been conjectured that there is a hamiltonian cycle in every finite connected Cayley graph. In spite of the difficulty in proving this conjecture, we show that almost all Cayley graphs are hamiltonian. That is, as the order n of a group G approaches infinity, the ratio of the number of hamiltonian Cayley graphs of G to the total number of Cayley graphs of G approaches1.

In this paper we disscus the relative index for the Atiyah-Patodi-Singer type elliptic boundary value problems, as an application we give a new approach to the pairing between the relative K-homology and K-cohomology.

We show that for any differentiable involution on an r-dimensional manifold (M, T) whose fixed point set F is a disjoint union of real projective spaces of constant dimension 2n, we have:if r=4n then (M,T) is bordant to (F×F, twist), if 2n<r≠4n then (M,T) bounds.

In this paper we study surfaces in S⁴ and their twistor Gauss maps. Some necessary and sufficient conditions that the twistor Gauss map is harmonic are given. We find many examples of nonisotropic harmonic maps from a surface to CP³.

We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f εB if and only if |D^β f(z)|^p (1-|z|²)^βp-1 dm(z) is a generalized Carleson measure;f εB ₀ if and only if |D^β f(z)|^p (1-|z|²)^βp-1 dm(z) is a generalized vanishing Carleson measure, where D^β f(β > 0) is the fractional derivative of analytic function f of order Β, m denotes the normalised Lebesgue measure.

Symmetry properties of self-conjugate minimal surfaces, i.e. minimal surfaces which are congruent with their conjugate ones in R³ are studied.

This paper proves the following result:Let f(z) be a meromorphic function in the z-plane with a deficient value, and δ(θ _k )(k=1,2, ...,q;0≤θ₁<θ₂<...<θ _q<θ_q+1=θ₁+2π) be q rays (1≤q<∞) starting at the origin, and let n≥3 be an integer such that for any given positive numberε,0<ε<π/2,

where Ν is a constant independent of ε. If Μ<∞, then we have

where Μ and λ denote the lower order and order of f(z), respectively,Ω=minθ_k+1-θ_k;1≤k≤q, and n(E, f=a) is the number of zeros of f(z)-a in E with multiple zeros being counted with their multiplicities.

In this paper we construct the suitable weak solution for the initial-boundary value problem of the Boussinesq equations and obtain some properties for these solutions. Also in the case of a two dimensional space the uniqueness of weak solution is proved.

By using a general scheme for decomposing a zero-curvature equation into two commuting x- and t_n -finite-dimensional integrable Hamiltonian systems (FDIHS), a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint representation of the two auxiliary linear problems is presented. The Darboux transformation for these FDIHSs is derived.

Chen Jingrun was born on 22 May,1933 in Fu Zhou in Fu Jian province of China.Chen's father Chen Yuanjun was a clerk in postoffice and his mother was passed away in 1947.Chen's family was comparatively poor since the income of his father was lower and the population of his family was comparatively large.

This paper mainly deals with minimal algebraic surfaces of general type with K²=2p_g-1. We prove that for p_g≥7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces with p_g=5, 6. Lastly we show that when p_g≥13 all these surfaces are simply-connected.

In this paper, we obtain the following main theorem for a free quadratic bialgebra J:

(a) For p≠0,J is a pointed cosemisimple coalgebra. For p=0,J is a hyperalgebra.

(b) For p≠0 and q≠0,J has antipode S iff p·q+2=0 and S(x)=x. For p=0 or q=0,J has antipode and S(x)=x.

(c) All left J^*-modules are rational.

Also, we give some applications in homological theory and algebraic K-theory.

In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that if L_i ∈MS(i=1, 2,…,n) then the Braided product of L_i(i=1, 2,…,n) exists if and only if L₁,…,L_n have isomorphic skeletons.

In this paper the regularity of the Lagrangians f(x, ξ)=|ξ|^α(x)(1<α₁≤α(x)≤α₂< +∞) is studied. Our main result: If α(x) is Holder continuous, then the Lagrangian f(x, ξ)=|ξ|^α(x) is regular. This result gives a negative answer to a conjecture of V. Zhikov.

Let G(k) denote the smallest number s such that every sufficiently large natural number is the sum of, at most,s k-th powers of natural numbers. In this paper, we give new bounds for G(12),G(13) and G(19).

In this paper we calculate the orbits of flag manifolds of the complex classical groups under the action of the sets of fixed points of Cartan involutions, and determine all the geometric parameters corresponding to representations of the classical groups with integral infinitesimal characters, which are used to discuss Arthur conjecture and the Langlands classification of the irreducible admissible representations of real classical groups(see[1]).

For every torsion free Fuchsian group Γ with Poincaré's Θ-operator norm ||Θ_Γ||=1, it is proved that there exists an extremal Beltrami differential of Γ which is also extremal under its own boundary correspondence. It is also proved that the imbedding of the Teichmüller space T(Γ) into the universal Teichmüller space T is not a global isometry unless Γ is an elementary group.

If in the linear model (1) the random errors e₁, e₂,… satisfy assumption (B) (See Section 1), then a necessary condition for the consistency of the LAD estimate of β₀ is .

This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.

In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems we prove the existence of global attractors for the initial value problem of Cahn-Hilliard equations. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are also obtained.

In this paper, a strongly consistent estimation of the optimal trimming proportion in trimmed mean is found by the random weighting method. In addition, using the same method a strongly consistent estimation for the distribution of some adaptive estimator is also obtained.

The study of the convergent rate (spectral gap) in the L²-sense is motivated from several different fields: probability, statistics, mathematical physics, computer science and so on and it is now an active research topic. Based on a new approach (the coupling technique) introduced in[7] for the estimate of the convergent rate and as a continuation of[4],[5],[7-9],[23] and[24], this paper studies the estimate of the rate for time-continuous Markov chains. Two variational formulas for the rate are presented here for the first time for birth-death processes. For diffusions, similar results are presented in an accompany paper[10]. The new formulas enable us to recover or improve the main known results. The connection between the sharp estimate and the corresponding eigenfunction is explored and illustrated by various examples. A previous result on optimal Markovian couplings[4] is also extended in the paper.

This paper establishes criteria for the existence and non-existence of nonzero periodic solutions of the generalized Liénard equation +g(x)=0. The main goal is to study to what extent the dampingf can be small so as to guarantee the existence of nonzero periodic solutions of such a system. With some standard additional assumptions we prove that if for a small |x|,∫^±∞|f(x,y)|^-1 dy=±∞, then the system has at least one nonzero periodic solution, otherwise, the system has no nonzero periodic solution. Many classical and well-known results can be proved as corollaries to ours.