中国科学院数学与系统科学研究院期刊网

05 March 2007, Volume 23 Issue 3
    

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  • Xiu Gui LIU
    Acta Mathematica Sinica. 2007, 23(3): 385-392. https://doi.org/10.1007/s10114-005-0548-y
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    In this paper, some groups ExtAs,t (Zp,Zp) with specialized s and t are first computed by the May spectral sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q-5S which is represented (up to a nonzero scalar) by (Zp,Zp) in the Adams spectral sequence, where p≥5 is a prime number, n≥3, 0≤s<p-3, q=2(p-1).
  • Hong Xia LIU, Tao PAN
    Acta Mathematica Sinica. 2007, 23(3): 393-410. https://doi.org/10.1007/s10114-005-0638-x
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    This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includes the following new interaction type: an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution is bounded by O1/2) in L1-norm; otherwise, as in the initial value problem, the L1-error bound is O(ε|lnε|).
  • Moo Young SOHN, Sang Bum KIM, Young Soo KWON, Rong Quan FENG
    Acta Mathematica Sinica. 2007, 23(3): 411-416. https://doi.org/10.1007/s10114-005-0607-4
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    In the present paper, the regular planar graphs with diameter two are classified.
  • Tian Ze LI
    Acta Mathematica Sinica. 2007, 23(3): 417-422. https://doi.org/10.1007/s10114-005-0715-1
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    For a group G and a subgroup M of G, we say that a subgroup A of G is a supplement to M in G, if G=MA. We prove that a finite group in which every Sylow normalizer admits a nilpotent supplement is solvable. In particular we confirm a conjecture of Buchthal. Moreover we investigate finite groups in which Sylow normalizers admit solvable supplements.
  • Guo Jian LIN, Rong YUAN
    Acta Mathematica Sinica. 2007, 23(3): 423-438. https://doi.org/10.1007/s10114-005-0588-3
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    Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In addition, the stability properties of these solutions are characterized by the construction of manifolds of initial data.
  • Bao Quan YUAN
    Acta Mathematica Sinica. 2007, 23(3): 439-448. https://doi.org/10.1007/s10114-005-0864-2
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    In this paper we consider the Cauchy problems of Burgers' equations and the Deybe system. Their existence and uniqueness of the time-global solutions for small initial data in some pseudomeasure spaces are obtained. The asymptotic stability of small solutions is proved. As an immediate result the existence and uniqueness of the self-similar solutions are also obtained provided the initial data satisfy the self-similar structures.
  • Xiao Li FU, Guo En HU, Da Chun YANG
    Acta Mathematica Sinica. 2007, 23(3): 449-456. https://doi.org/10.1007/s10114-005-0723-1
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    Let μ be a Radon measure on Rd which may be non-doubling. The only condition satisfied by μ is that μ(B(x, r))≤Crn for all x∈Rd, r>0 and some fixed 0<nd. In this paper, the authors prove that the boundedness from H1(μ) into L1,∞(μ) of a singular integral operator T with Calderón-Zygmund kernel of Hörmander type implies its L2(μ)-boundedness.
  • Zi Li CHEN, A. W. WICKSTEAD
    Acta Mathematica Sinica. 2007, 23(3): 457-466. https://doi.org/10.1007/s10114-005-0783-2
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    We present here that (E,F), the space of all r-compact operators from E into F, is a generalised sublattice of  (E,F) for arbitary Banach lattices E and F, and that the characterization of the regular norm on (E,F) is order continuous. Some conditions for (E,F) to be a KB-space or a band in   (E,F) are also provided.
  • Jing Ping YANG, Shi Hong CHENG, Xiao Qian WANG
    Acta Mathematica Sinica. 2007, 23(3): 467-478. https://doi.org/10.1007/s10114-005-0722-2
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    This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1(a, b) family, bivariate recursive equations for the joint distribution of the cedent's aggregate claims and the reinsurer's aggregate claims are obtained.
  • S. BERHANU, F. CUCCU, G. PORRU
    Acta Mathematica Sinica. 2007, 23(3): 479-486. https://doi.org/10.1007/s10114-005-0680-8
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    For γ ≥ 1 we consider the solution u=u(x) of the Dirichlet boundary value problem Δu+u-γ=0 in Ω, u=0 on ∂Ω. For γ=1 we find the estimate
    u(x)=p(δ(x))[1+A(x)(log1/δ(x)-∈],
    where p(r)r2log(1/r near r=0, δ(x) denotes the distance from x to ∂Ω, 0<∈<1/2, and A(x) is a bounded function. For 1<γ< 3 we find
    u(x)=((r+1)/√2(r-1)δ(x))[1+A(x)(δ(x))2(r-1)/(r+1)].
    For γ=3 we prove that
    u(x)=(2δ(x))1/2[1+A(x)δ(x)log1/δ(x)].
  • J. M. ALDAZ, Juan L. VARONA
    Acta Mathematica Sinica. 2007, 23(3): 487-490. https://doi.org/10.1007/s10114-005-0682-6
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    We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1, 1) inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension.
  • Wen Ming WU, Li Guang WANG
    Acta Mathematica Sinica. 2007, 23(3): 491-496. https://doi.org/10.1007/s10114-005-0850-8
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    In this note, we give complete descriptions of the structure of the monotone product of two von Neumann algebras and two C*-algebras. We show that the monotone product of two simple von Neumann algebras and C*-algebras aren't simple again. We also show that the monotone product of two hyperfinite von Neumann algebras is again hyperfinite and determine the type of the monotone product of two factors.
  • Li Wen XU, Song Gui WANG
    Acta Mathematica Sinica. 2007, 23(3): 497-506. https://doi.org/10.1007/s10114-005-0794-z
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    In this paper, the authors address the problem of the minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general normal linear model with random effects. Under a quadratic loss function, the minimax property of linear estimators is investigated. In the class of all estimators, the minimax estimator of estimable functions, which is unique with probability 1, is obtained under a multivariate normal distribution.
  • Jean-Paul PENOT, Robert RATSIMAHALO
    Acta Mathematica Sinica. 2007, 23(3): 507-520. https://doi.org/10.1007/s10114-005-0763-6
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    In this work, we study some subdifferentials of the distance function to a nonempty nonconvex closed subset of a general Banach space. We relate them to the normal cone of the enlargements of the set which can be considered as regularizations of the set.
  • Eberhard MALKOWSKY, M. MURSALEEN, Suthep SUANTAI
    Acta Mathematica Sinica. 2007, 23(3): 521-532. https://doi.org/10.1007/s10114-005-0719-x
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    Let p=(pkk=0) be a bounded sequence of positive reals, m∈N and u be s sequence of nonzero terms. If x=(xk)k=0 is any sequence of complex numbers we write Δ(m)x for the sequence of the m-th order differences of x and Δu(m)X={x=(x)k=0:uΔ(m)xX} for any set X of sequences.We determine the α-,β- and γ-duals of the sets Δu(m)X for X=c0(p),c(p),l(p) and characterize some matrix transformations between these spaces Δ(m)X.
  • Xing Xiao LI, Feng Yun ZHANG
    Acta Mathematica Sinica. 2007, 23(3): 533-548. https://doi.org/10.1007/s10114-005-0919-4
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    For an immersed submanifold x: MmSn in the unit sphere Sn without umbilics, an eigenvalue of the Blaschke tensor of x is called a Blaschke eigenvalue of x. It is interesting to determine all hypersurfaces in Sn with constant Blaschke eigenvalues. In this paper, we are able to classify all immersed hypersurfaces in Sm+1 with vanishing Möbius form and constant Blaschke eigenvalues, in case (1) x has exact two distinct Blaschke eigenvalues, or (2) m=3. With these classifications, some interesting examples are also presented.
  • Lynn ERBE, Christopher C. TISDELL, Patricia J. Y. WONG
    Acta Mathematica Sinica. 2007, 23(3): 549-556. https://doi.org/10.1007/s10114-005-0901-1
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    Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.
  • De Li LI, Fu Xing ZHANG, Andrew ROSALSKY
    Acta Mathematica Sinica. 2007, 23(3): 557-562. https://doi.org/10.1007/s10114-005-0823-y
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    Let {X, Xn; n≥1} be a sequence of i.i.d. Banach space valued random variables and let {an; n≥1} be a sequence of positive constants such that
    .
    Set Sn=∑em=1n Xem, n≥1. In this paper we prove that

    if and only if
    .
    This result generalizes the Baum-Katz-Spitzer complete convergence theorem. Combining our result and a corollary of Einmahl and Li, we solve a conjecture posed by Gut.
  • Yi Ran HE, Xiu Zhen MAO, Mi ZHOU
    Acta Mathematica Sinica. 2007, 23(3): 563-570. https://doi.org/10.1007/s10114-005-0918-5
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    Strict feasibility is proved to be an equivalent characterization of (dual) variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinitedimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.
  • Daniele Ettore OTERA
    Acta Mathematica Sinica. 2007, 23(3): 571-576. https://doi.org/10.1007/s10114-005-0900-2
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    A non-compact polyhedron P is Tucker if, for any compact subset KP, the fundamental group π1(P-K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru's theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.