中国科学院数学与系统科学研究院期刊网

15 November 2005, Volume 48 Issue 6
    

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  • Bin Wu HE(1), Xiao Yan LI(2),
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0149
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    A metric method for homothetic deviation of m (m≥2) geometric bodies (star bodies or conevx bodies) is provided. By the metric mthod, and utilzing a refinement of H(?)lder's inequality we establish a new stablity version for the dual Aleksandrov-Fenchel inequality.
  • De Xiang MA(1), Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0150
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    In this paper, we get positive solutions of the following nonlinear multi-point singular boundary value problem with p-Laplaeian operator where f(t, u) may be singular at u=0 and q(t) may be singular at t=0 or t=1.
  • Yong Xiang LI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0146
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    This paper discusses the existence of solutions of initial value problem for semilinear evolution equation with noncompact semigroup u'(t)+Au(t)=f(t, u(t)), t≥0; u(0)=x_0 in a Banach space E, where -A is the infinitesimal generator of an equicontinuous C_0-semigroup, and f: [0, ∞)×E→E is continuous. In the case where f satisfies a weaker noncompactness measure condition, the existence results of saturated mild solutions are obtained. Particularly, an existence result without using noncompactness measure condition is present in ordereded and weakly sequentially complete Banach spaces. This result is very convenient for application.
  • Jing Xian SUN(1), Guo Wei ZHAN
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0147
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    The singular nonlinear Sturm-Liouville problem is considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where (L_φ)(x)=(p(x)φ'(x))'+q(x)φ(x) and h(x) is allowed to be singular at both x=0 and x=1. The existence results of positive solutions are given by means of the cone theory and the fixed point index. The conclusions in this paper essentially extend and improve the main results in [1-9].
  • Lei LI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0148
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    In this paper, we consider the isometry extension problem in the general real Banaeh spaces (not only in classical Banach spaces), and using the norming set, we give some sufficient conditions, under which the surjective isometry between unit spheres can be extended to a linear isometry on the whole space.
  • Xi Nian FANG(1), Jian Hua WANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0143
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    In this paper, we study the linear extension of isometries between the unit sphere S_1(E) of a real normed space E and the unit sphere S_1(F) of a real normed space F. We obtain that if T: S_1(E)→S_1(F) is a surjective isometry and for every x, y∈S_1(E), and real λ, we have ‖T(x)-|λ|T(y)‖≤‖x-|λ|y‖, then T can be extended to a real linear isometry on the whole space.
  • Xiao Bao SHU, Yuan Tong XU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0144
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    We obtain sufficient conditions for the existence of at least three positive solutions for the boundary value problem of a second order functional differential equation this is an application of a new fixed point theorem introduced by Avery and Peterson.
  • Fei XU, Yan HOU, Zhi Gui LIN
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0145
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    In this paper, a two-species predator-prey system is discussed, the dynamics of coupled system of semilinear parabolic equations with time delays is investigated using upper and lower solutions and the associated monotone iterations. The asymptotic behavior of solutions and the negative effect of stage structure on the permanence of populations are given.
  • Li FANG, Qi Hui LI, Hong Ke DU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0139
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    For A∈B(H), let σ(A) and W(A) denote the spectrum of A and the numerical range of A respectively. In the present paper we show two important results: one is that if σ(A)∩(-∞, 0]=φ then A has a unique n-th root B∈B(H) with σ(B)(?), and the other is that if (?)∩(-∞, 0]=φ then A has a unique n-th root B∈B(H) with (?), where S_(1/n)={λ∈C‖argλ|≤1/2nπ} and S_(1/n)~0 denotes the interior of the set S_(1/n).
  • Jing HUI(1), Lan SUN(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0140
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    With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solution of an impulsive equation with a distributed delay in a periodic environment. At the same time, effective sufficient conditions are found for stability via the approach of piece-wise continuous Lyapunov function introduced.
  • Xiao Yi ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0141
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    We study the self-similar solution of semi-linear wave equation with powerlike nonlinearity |u|~αu. The global existence of self-similar solution has been obtained when a is a generic positive real number (with suitable restrictions) by using the paraproduct decomposition. This is a problem left open by Planchon in his previous work.
  • Jian Yong WANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0142
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    In this paper, for 0<β<1, we study the structure and representation problems of the conjugate cones of complex locally β-convex spaces l~β and L~β[0, 1], obtain (l~β)_β~*(?)mM_β~+(T), (L_β[0, 1])_β~*(?)L~∞M_β~+(I×T), called the subrepresentation theorems of (l~β)_β~* and (L~β[0, 1])_β~*.
  • Xiu Zhong YANG, Zhi Bin HOU, X
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0135
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    In this paper, we obtain the general results on extension of isometries: Let E, F be normed (or β-strictly convex β-normed) spaces. If V_0: S_1(E)→S_1 (F) is an isometry and for all x, y∈S_1(E) we have ‖V_0x-|λ|V_0y‖≤‖x-|λ|y‖, (?)λ∈R, then V_0 can be extended to be an isometry (or linear isometry) on the whole space. In particular, if E, F are a normed spaces, V_0 is surjective or F is strictly convex, then V_0 can be extended to be a linear isometry on the whole space, thus generalizing the corresponding results in [3-5].
  • Chang Ci PANG, Zhong Li WEI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0136
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    This paper establishes the exact multiplicities of positive solutions for a class of differential equations involving p-Lapalacian operator by the shooting method.
  • Wen Yu ZHU(1), Qi SUN(), Xian
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0137
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    In this note, we suppose n is a composite, Z_n is a residue class ring mod n, r(x)∈Z_n[x] and r(x) is a monic irreducible polynomial of degree k (k>0) over Z_n. We give a definition for n is Generalized Carmichael Number of order k modulo r(x) and denote this by n∈C_(k,r(x)). So we give another definition: C_k={UC_(k,r(x))|r(x) are all monic irreducible polynomials of degree k (k>0) over Z_n}. Clearly, C_1 is the ordinary Carmichael number. We obtain a necessary and sufficient condition for n∈C_(k,r(x)). Moreover, we get hold of a necessary and sufficient condition for n∈C_k and an easily calculate necessary and sufficient condition for n∈C_2. In addition, we prove C_1(?)C_2 and |C_2|=∞.
  • Jian Qin ZHOU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0138
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    Based on the theory of L-shaped tile, utilizing Chinese remainder theorem, it is proved that we can generate some infinite families of k-tight (k>m) double loop networks with any integer m≥0. An algorithm to judge whether there is a k-tight (k≥0) double loop network with N nodes is also presented.
  • Shi Chang SHU, San Yang LIU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0130
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    In this paper, we study the Moebius characterization of submanifolds in S~n without umbilic points and with vanishing Moebius form and fiat normal bundle. We give some Moebius characterizations of submanifolds by making use of the rigidity relations among Moebius Ricci curvature, Blaschke tensor and Moebius normalized scalar curvature as well as the rigidity relations between Blaschke tensor and Moebius normalized scalar curvature. We obtain two classification theorems of submanifolds with flat normal bundle in S~n.
  • Huo Xiang WU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0131
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    This paper is devoted to the study of multiple Marcinkiewicz integrals along polynomial curves with kernels belonging to certain block spaces. It is showed that the multiple Marcinkiewicz integral operator is bounded on L~p for some 1
  • Dong Xiang CHEN(1), Jie Cheng
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0132
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    In this paper, the properties of multilinear maximal commutators for vectorvalued singular integrals are considered, and the weighted estimates and weighted weak type estimates are proved. As a corollary, it is deduced that the operator T_(q, b)~* is bounded on L~P(ω) when ω ∈ A_p and admits a corresponding weighted L(log L)~(1/r)-type estimate with ω ∈A_1.
  • Shao Yuan XU(1), Chao Yi ZENG(
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0133
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    In this paper, the definition of φ concave-(-ψ) convex operator is introduced and a class of mixed monotone operators are discussed. Without any compactness or continuity of the operators, the existence and uniqueness for the fixed points of the operators with such concavity and convexity, as α concavity-convexity, concavity- (-α) convexity, α concavity-Guo convexity, concavity-Guo convexity, e concavity-Guo convexity, e concavity-convexity, e concavity-(-α) convexity and α_1 concavity-(-α_2) convexity, is obtained. As corollaries, some new results about these operators are produced. In the end, the new results are applied to the Hammerstein integral equations on unbounded regions.
  • Bo Qing DONG(1), Yong Sheng LI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0134
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    In this paper the authors study the decay rate for weak solutions to a class of the incompressible non-Newtonian fluids in R~2, and prove that the weak solutions decay in L~2 norm at (1+t)~(-1/2). The estimate for the decay rate is sharp in the sense that it coincides with that of the solution to a linear heat equation.
  • Shi Feng DING, Hui Ling LI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0126
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    Let G be a finite group and H(?)G. If H≌~2B_2(q) or H≌~2G_2(q) or H≌PSU(3, q), then G can not be isomorphic to a point-transitive collineation group of any projective plane. The method used can be generalized to prove that a linear space admitting a point-transitive automorphism group isomorphic to some almost simple group is not a projective plane.
  • Yong Zhong HU(1), Ping Zhi YUA
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0128
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    Let a=|m(m~4-10m~2+5)|, b=5m~4-10m~2+1, c=m~2+1, where m is a positive even integer. We apply a new, deep result of Bilu, Hanrot & Voutier to show that the only positive integer solution of the exponential Diophantine equation a~x+b~y=c~z is (x, y, z)=(2, 2, 5).
  • Qing Zhong LI(1), Jian Bing SU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0129
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    The Busemann function plays a very important role in the study of topology and geometry of a complete Riemannian manifold. In this paper, the Busemann function on one of the non-exceptional irreducible Riemannian globly symmetric spaces of Type Ⅲ is obtained via an explicit formula.
  • Ke Dian LI(1), Shou LIN(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(6): . https://doi.org/10.12386/A2005sxxb0127
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    In this paper a sufficient and necessary condition in which a-spaces are preserved by pesudo-open and L-mappings is obtained, a mapping theorem on σ-spaces by Chaber in 1978 is improved, it is shown that pseudo-open and compact images of k-semistratifiable spaces are σ-spaces, which generalizes a mapping theorem on stratifiable spaces by Henry in 1971 and affirmatively answers a question on N-spaces posed by Shou Lin in 1990. In the final, some examples are given showing the theorems are nice pseudo-open mapping theorems on σ-spaces and k-semistratifiable spaces.