中国科学院数学与系统科学研究院期刊网

05 August 2007, Volume 23 Issue 8
    

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  • Jian Ming ZHAN, Bijan DAVVAZ, K. P. SHUM
    Acta Mathematica Sinica. 2007, 23(8): 1345-1356. https://doi.org/10.1007/s10114-007-0951-7
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    We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in (Fuzzy Sets Syst., 117: 477- 484, 2001) and Bhakat and Das in (Fuzzy Sets Syst., 80: 359-368, 1996). The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued (α, β)-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued (α, β)-fuzzy sub-hypermodule is a generalization of the usual fuzzy sub-hypermodule. We shall study such fuzzy sub-hypermodules and consider the implication-based interval-valued fuzzy sub-hypermodules of a hypermodule.
  • Luz M. FERNÁNDEZ-CABRERA, Antón MARTÍNEZ
    Acta Mathematica Sinica. 2007, 23(8): 1357-1374. https://doi.org/10.1007/s10114-007-0948-2
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    We work with the abstract K and J interpolation method generated by a sequence lattice Γ. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal measure of the interpolated operator in terms of the ideal measures of restrictions of the operator. Formulae are given in terms of the norms of the shift operators on Γ.
  • Tai Shan YI, Li Hong HUANG
    Acta Mathematica Sinica. 2007, 23(8): 1375-1384. https://doi.org/10.1007/s10114-005-0932-7
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    The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t → ∞. Our results improve and extend some corresponding ones already known.
  • Chun Lan JIANG, Yong Fei JIN, Zong Yao WANG
    Acta Mathematica Sinica. 2007, 23(8): 1385-1390. https://doi.org/10.1007/s10114-007-0809-z
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    Let L be a complex seperable Hilbert space and L(L) denote the collection of bounded linear operators on L. For an operator in L(L), rad{A}' denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}'/rad{A}'. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.
  • Ming Zhi WANG, Guang Bin REN
    Acta Mathematica Sinica. 2007, 23(8): 1391-1404. https://doi.org/10.1007/s10114-007-0953-5
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    Polynomial approximation is studied on bounded symmetric domain Ω in Cn for holomorphic function spaces X, such as Bloch-type spaces, Bergman-type spaces, Hardy spaces, Ω algebra and Lipschitz space. We extend the classical Jackson’s theorem to several complex variables:
    Ek(f, X)ω(1/k,f,x),
    where Ek (f, X ) is the deviation of the best approximation of fX by polynomials of degree at most k with respect to the X-metric and ω(1/k, f, X) is the corresponding modulus of continuity.
  • Lian Zhong YANG, Hong Xun YI
    Acta Mathematica Sinica. 2007, 23(8): 1405-1412. https://doi.org/10.1007/s10114-005-0848-2
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    In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f(j) and g(j) have the same zeros and poles for j = 0, 1, 2. We provide some examples to show that our results are sharp.
  • Lun Chuan ZHANG
    Acta Mathematica Sinica. 2007, 23(8): 1413-1418. https://doi.org/10.1007/s10114-007-0867-2
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    In this paper we obtain a Douglas type factor decomposition theorem about certain important bounded module maps. Thus, we come to the discussion of the topological continuity of bounded generalized inverse module maps. Let X be a topological space, xTx : XL(E) be a continuous map, and each R(Tx ) be a closed submodule in E, for every fixed xX. Then the map xTx+: XL(E) is continuous if and only if ||Tx+|| is locally bounded, where Tx+ is the bounded generalized inverse module map of Tx . Furthermore, this is equivalent to the following statement: For each x0 in X, there exists a neighborhood U0 at x0 and a positive number λ such that (0, λ2)⊆∩x∈U0C\σ(TX*TX),where σ(T) denotes the spectrum of operator T.
  • Di Rong CHEN, Xu YOU
    Acta Mathematica Sinica. 2007, 23(8): 1419-1426. https://doi.org/10.1007/s10114-005-0880-2
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    In the problem of classification (or pattern recognition), given a set of n samples, we attempt to construct a classifier gn with a small misclassification error. It is important to study the convergence rates of the misclassification error as n tends to infinity. It is known that such a rate can't exist for the set of all distributions. In this paper we obtain the optimal convergence rates for a class of distributions D(λ,ω) in multicategory classification and nonstandard binary classification.
  • Sheng Jun FAN
    Acta Mathematica Sinica. 2007, 23(8): 1427-1434. https://doi.org/10.1007/s10114-007-0943-7
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    In this paper, under the most elementary conditions on a backward stochastic differential equation (BSDE for short) introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of "process", based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved.
  • Hua WANG, Shang Bin CUI, Dong Gao DENG
    Acta Mathematica Sinica. 2007, 23(8): 1435-1446. https://doi.org/10.1007/s10114-007-0959-z
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    We first prove that the Cauchy problem of the Kawahara equation, ∂tu+uxu+β∂x3u+γ∂x5u = 0, is locally solvable if the initial data belong to Hr(R) and r ≥-7/5, thus improving the known local well-posedness result of this equation. Next we use this local result and the method of "almost conservation law" to prove that global solutions exist if the initial data belong to Hr (R) and r >1/2.
  • Bao Qiang YAN, Donal O'REGAN, Ravi P. AGARWAL
    Acta Mathematica Sinica. 2007, 23(8): 1447-1456. https://doi.org/10.1007/s10114-005-0822-z
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    This paper presents a lower and upper solution technique for singular second order boundary value problems on the half line.
  • Vijay GUPTA
    Acta Mathematica Sinica. 2007, 23(8): 1457-1462. https://doi.org/10.1007/s10114-005-0776-1
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    In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.
  • Zhao Yong HUANG
    Acta Mathematica Sinica. 2007, 23(8): 1463-1474. https://doi.org/10.1007/s10114-005-0891-z
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    Let Λ and Γ be artin algebras and ΛUΓ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of k-Gorenstein modules with respect to ΛUΓ and then characterize it in terms of the U-resolution dimension of some special injective modules and the property of the functors Ext em (Extem(-, U), U) preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of ΛUΓ with finite left or right injective dimension.
  • Xiao Huan MO, Li Bing HUANG, Yuan Zheng ZHANG
    Acta Mathematica Sinica. 2007, 23(8): 1475-1484. https://doi.org/10.1007/s10114-005-0896-7
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    We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from Rm\{0} to Rn. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3(m + 1)-harmonic morphism Φ : Rm\{0} → Rn where m = 2(n-1).
  • Wei Dong WANG, Gang Song LENG
    Acta Mathematica Sinica. 2007, 23(8): 1485-1494. https://doi.org/10.1007/s10114-005-0894-9
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    Recently, Lutwak, Yang and Zhang posed the notion of Lp -projection body and established the Lp -analog of the Petty projection inequality. In this paper, the notion of Lp -mixed projection body is introduced—the Lp -projection body being a special case. The Petty projection inequality, as well as Lutwak's quermassintegrals (Lp -mixed quermassintegrals) extension of the Petty projection inequality, is established for Lp -mixed projection body.
  • De Ming ZHU, Ying SUN
    Acta Mathematica Sinica. 2007, 23(8): 1495-1504. https://doi.org/10.1007/s10114-005-0746-7
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    In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic (resp. 2-homoclinic) orbit Γ, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic (resp. 2-periodic) and accumulate onto Γ. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits.
  • D. O'REGAN, N. HUSSAIN
    Acta Mathematica Sinica. 2007, 23(8): 1505-1508. https://doi.org/10.1007/s10114-007-0935-7
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    The existence of common fixed points and invariant approximations for pointwise R-subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class of noncommuting mappings.
  • Sehie PARK
    Acta Mathematica Sinica. 2007, 23(8): 1509-1526. https://doi.org/10.1007/s10114-007-0947-3
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    Let B be the class of ‘better' admissible multimaps due to the author. We introduce new concepts of admissibility (in the sense of Klee) and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of Φ-spaces, sets of the Zima-Hadžić type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.
  • Fu Qing GAO
    Acta Mathematica Sinica. 2007, 23(8): 1527-1536. https://doi.org/10.1007/s10114-007-0941-9
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    Let {Xn;n ≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X1) and let {N(t);t ≥ 0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {Xn;n ≥ 1}. In this paper, asymptotic expressions of P((X1+…+XN(t))-λ(t)μ >x) uniformly for x ∈[γb(t),∞) are obtained, where γ >0 and b(t) can be taken to be a positive function with limt→∞ b(t)/λ(t) = 0.