中国科学院数学与系统科学研究院期刊网

15 March 2003, Volume 46 Issue 3
    

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  • Zong Guang LIU(1),Shan Zhen LU
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 417-426. https://doi.org/10.12386/A2003sxxb0058
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    In this paper, some estimates for the commutator, [b, T] on certain Hardy type spaces are established, where b ∈ BMO(Rn) and is uniformly continuous on Rn, and T is a strongly singular convolution operator.
  • Chang Mei TAN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 427-430. https://doi.org/10.12386/A2003sxxb0059
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    The main objective of this note is to study the boundedness of maximal operators in general Morrey spaces on homogeneous spaces. The results in this paper substantially improve and extend the known results.
  • Yu Wen WANG,Shao Rong PAN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 431-438. https://doi.org/10.12386/A2003sxxb0060
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    In this paper, the representation of the set-valued metric generalized inverse of closed linear operator with closed range in reflexive Banach space and its single selection are given. By the geometric property of the space, we prove that single selection of set-valued metric generalized inverse is a bounded homogeneous operator.
  • Lian Ping ZHANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 439-444. https://doi.org/10.12386/A2003sxxb0061
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    Four characteristic conditions for a C0 semigroup T(t) with continuity in the uniform operator topology for t > to (to≥0) on a Hilbert space are given.
  • Sheng Li XIE(1),Zhi Lin YANG(2
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 445-452. https://doi.org/10.12386/A2003sxxb0062
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    In this paper, under loose conditions, we investigate the existence of solutions to nonlinear impulsive Volterra integral equations and impulsive integro-differential equations in Banach spaces, establish the new existence theorems and essentially improve some known results.
  • Xiao Chun FANG,Rong CHENG,Bo Z
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 453-456. https://doi.org/10.12386/A2003sxxb0063
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    In this note, the mapping spectrum between C*-algebras of continuous trace is introduced, and proved to be a closed subset of the spectrum space of initial C*-algebras. Some properties similar to those of mappings between C*-algebras of the form C(X) Mn, such as lower semi-continuity, have been obtained.
  • Jun LUO(1),Zuo Ling ZOU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 457-462. https://doi.org/10.12386/A2003sxxb0064
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    For any F Rn, denote by dimF and HdimF(F) the Hausdorff dimension and the dim F-dimensional Hausdorff measure of F. Suppose T is the attractor of the IFS {f1,..., fm} consisting of similitudes. If fi(T) ∩ fj(T) = for i≠ j, then for any ε > 0 there exists some δ > 0 such that |Hdim T(T) -Hdim D(D)| < ε whenever D is the attractor of the IFS {g1,...,gm} where g1,...gm are similitudes with sup{||/fk(x) -gk(x)||: ||x|| ≤1,1≤k≤m}<ε.
  • Heng Shan GAO
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 463-468. https://doi.org/10.12386/A2003sxxb0065
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    Let WMг be the set of all formulae of MIPC* and г ∪{A} WMμ. The meaning of "г MIPC* A" is obvious, and "г M A" means that г M-implies A. In a previous paper, we proved that F M A гMIPC* A, i.e., MIPC* is strongly complete. In this note we show that its inverse is also true, namely, г MIPC* A гM A. In other words, the system MIPC* is sound.
  • Jue Xian LI(1),You Qing JI(2),
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 469-480. https://doi.org/10.12386/A2003sxxb0066
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    For an operator weighted shift S, the essential spectrum σe(S) and the indices associated with holes in σe(S) are described. Moreover, Banach reducibility of S is investigated and a condition for S* to be a Cowen-Douglas operator is characterized.
  • Hai HUANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 481-486. https://doi.org/10.12386/A2003sxxb0067
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    We prove that the forced pendulum-type equation x + Gx(x,t) = p(t), where G(x, t) ∈ C1(R2) with 1-periodicity in x, satisfies the conditions: sup(x,t)∈R2|Gx(x, t)| < +∞ and limsupt→∞{supx∈R } = 0, and possesses infinitely many unbounded solutions on cylinder S1×R for any almost periodic function p(t) with nonvanishing mean value.
  • Yan Ying WANG,Zhen De WU,Zhao
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 487-492. https://doi.org/10.12386/A2003sxxb0068
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    Special generators of the unoriented cobordism ring MO* are constructed to determine some groups of cobordism classes in MOn containing a representative Mn admitting a (Z2)k-action with the fixed point set of (n -li)-dimensional submanifolds of Mn.
  • Zhong Kui LIU(1),Yuan FAN(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 493-496. https://doi.org/10.12386/A2003sxxb0069
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    Let R be an associative ring not necessarily possessing an identity, and (S, ≤) a strictly totally ordered monoid which is also artinian and satisfies that 0 ≤ s for any s ∈ S. Assume that M is a left .R-module having property (F). It is shown that M is a co-Hopfian left R-module if and only if [MS,≤] is a co-Hopfian left [[RS,≤]]-module.
  • Yu Qun CHEN(1),K. P. SHUM(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 497-506. https://doi.org/10.12386/A2003sxxb0070
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    Recall that the semigroups S and R are said to be strongly Morita equivalent if there exists a unitary Morita context (S,R, sPR, RQs, <>, ) with <> and surjec-tive. For a factorisable semigroup S, we denote ζS = {(s1, s2)∈ S× S| ss1 = ss2, s ∈ S}, S' = S/ζs and U S-FAct= {SM ∈ S-Act | SM = M and SHoms(S, M)≌ M}. We show that, for factorisable semigroups S and R, the categories U S-FAct and U R-FAct are equivalent if and only if the semigroups S' and R' are strongly Morita equivalent. Some conditions for a factorisable semigroup to be strongly Morita equivalent to a sandwich semigroup, local units semigroup, monoid and group respectively are also given. Moreover, we show that a semigroup S is completely simple if and only if S is strongly Morita equivalent to a group and for any index set I, S SHoms(S, i∈I S)→ i∈I S, s t·f → (st)f is an S-isomorphism.
  • Jing Hu YU(1),Di He HU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 507-512. https://doi.org/10.12386/A2003sxxb0071
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    Let K be statistical self-similar set defined by Graf. In this paper, we construct a random measure p which is supported by K, and study the multifractal decomposition for K with ρ. Under such a decomposition, we obtain the expression of the spectrum function f(α).
  • Yuan Di WANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 513-522. https://doi.org/10.12386/A2003sxxb0072
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    Recently, much work has been devoted to nonlocal problems. However, very little has been accomplished in the literature for nonlocal initial problems with nonlinear boundary conditions. It is the purpose of this paper to prove existence results for solutions to a semilinear second parabolic PDE with linear homogeneous boundary conditions and to another with nonlinear boundary conditions provided that the ordered upper and lower solutions are given. Semigroup, fractional order function spaces, and generalized Poincare operators play an important role in proving the existence of solutions.
  • Hong Jun GAO(1),Ji Shan FAN(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 523-528. https://doi.org/10.12386/A2003sxxb0073
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    In this paper, under the Lorentz gauge, the global existence, local dissipativity and attractors of the evolutionary superconductivity problem which is a parabolic-hyperbolic system are obtained.
  • Jun Ning ZHAO(1),Pei Dong LEI(
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 529-538. https://doi.org/10.12386/A2003sxxb0074
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    We study the solvability of the Cauchy problem (1.1)-(1.2) for the largest possible class of initial values, for which (1.1)-(1.2) has a local solution. Moreover, we also study the critical case related to the initial value u0, for 1 < p < ∞.
  • Wei Chuan LIN(1),Lian Zhong YA
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 539-544. https://doi.org/10.12386/A2003sxxb0075
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    In this paper, we prove the following result that improves Miranda's Normal Criteria for a family of holomorphic functions. Let F be a family of functions which are holomorphic in a domain G, a, b (≠ 0) be two finte constants, n be an integer, and let, f∈ F, f and f(n) share the pair of values (a,b) IM, and f' = f(n+1) = b when f = a. Then F is normal on G.
  • Xin Song WANG,Wei Xing ZHENG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 545-554. https://doi.org/10.12386/A2003sxxb0076
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    In this paper, we introduce the concepts of distance, modulus of smoothness and derivative on SL(2,R). Hence we arrive at the direct approximation theorems of Jackson type on SL(2, R) by function classes Tn and Bσ,n respectively, and obtain the relation between the smoothness and the best approximations on SL(2,R).
  • Run Sheng YANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 555-560. https://doi.org/10.12386/A2003sxxb0077
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    Let X be a compact metric space and f : X →X a continuous onto map. f is called topologically ergodic if for any nonempty open sets U, V of X, {n > O | fn(U)∪ V ≠} is a set of positive upper density. Topological double ergodicity means that f@f is topologically ergodic. In this paper, we shall use the results in [2] to study the properties of topologically ergodic maps and topologically double ergodic maps.
  • Bao Lin LI(1),Cong Xin WU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 561-570. https://doi.org/10.12386/A2003sxxb0078
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    The existence theorem of the bounded Φ-variation solution to Kurzweil equations is established by using the function of bounded Φ-variation that was introduced by Musielak-Orlice in [10]. This result is an essential generalization of the existence theorem of the bounded variation solution to Kurzweil equations in [6].
  • Ping Yan CHEN(1),Qing Ping CHE
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 571-580. https://doi.org/10.12386/A2003sxxb0079
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    In this paper, we discuss the Chover's law of iterated logarithm (LIL) for the partial sum of sequence of identically distributed -mixing random variables with corn-mom distribution in the domain of attraction of stable (non-Gaussian) distribution. In particular, if the distribution is in the domain of normal attraction of stable distribution, then we obtain a more exact result, i.e. the integral test, for the partial sum and forward delayed sum, whence the corresponding Chover's LIL is derived immediately.
  • Ke Ying CHEN,Ai Nong FANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 581-590. https://doi.org/10.12386/A2003sxxb0080
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    In this paper, we characterize the quasisymmetric maps by modulus inequalities of rings in Q-regular Loewner spaces. Furthermore, we establish the Grotzsch-Teichmuller type modulus inequality for quasisymmetric maps between Q-dimensional Ahlfors-David regular spaces, which is expressed in terms of the integral mean value of dilatation coefficients.
  • Chun Hui QIU
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 591-600. https://doi.org/10.12386/A2003sxxb0081
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    In this paper, we obtain a weighted homotopy formula of the (r, s) differential forms and a weighted continuous solution to the -equation of type (r, s) on a local q-convex wedge in a complex manifold. A new weighted homotopy formula without boundary integral of the (r, s) differential forms and a new weighted continuous solution to the -equation of type (r, s), which are different from the classical ones, are given. The new weighted formulas are especially suitable for the case of a local q-convex wedge with non-smooth boundary, so one can avoid complex estimates of the boundary integrals, and the density of integral may not be defined on the boundary but only in the domain. Moreover, the weighted integral formulas have much freedom in applications such as in the interpolation of functions.
  • Shi Ping LU(1),Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 601-610. https://doi.org/10.12386/A2003sxxb0082
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    By using the coincidence degree principle, the authors study periodic solutions for the second order n-dimensional neutral differential system (d2)/(dt2)(x(t)- Cx(t-)) + d/(dt)gradF(x(t))+gradG(x(t-τ(t))) = p(t). Some sufficient conditions to guarantee the existence of periodic solutions to the system are obtained. Meanwhile, our results improve and extend the corresponding ones already known.
  • Bao Huai SHENG(1),San Yang LIU
    Acta Mathematica Sinica, Chinese Series. 2003, 46(3): 611-620. https://doi.org/10.12386/A2003sxxb0083
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    The concepts of α-order Clarke tangent derivative, α-order adjacent tangent derivative and α-order contingent derivative for a set-valued map are introduced, and their properties are discussed. Hence the derivative type Kuhn-Tucker optimality condition for constrained vector set-valued optimization with Benson proper efficiency solutions is established.