中国科学院数学与系统科学研究院期刊网

15 March 2007, Volume 50 Issue 2
    

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    论文
  • Shuan Ping(1); TAO Shan Zhen L
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 241-254. https://doi.org/10.12386/A2007sxxb0029
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    In this paper we study the local solvability of the initial-boundary problem for the modified Kawahara equation on the half line.By setting up some Strichartz-type estimates of the Duhamel forcing terms for a corresponding forced initial value problem, we prove that the initial-boundary problem of the modified Kawahaxa equation on the half line is locally solvable if the initial function belongs to H~8 (R_x~+) and the boundary function belongs to g~(x+2/5)(R_t~+) with 1/4■s<2.
  • Xian Meng MENG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 255-260. https://doi.org/10.12386/A2007sxxb0030
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    Let P_k denote any integer with no more than k prime factors,counted according to multiplicity.It is proved that for almost all sufficiently large even integers n■2 (mod 6),the equation n=P_1+P_2 has a solution in prime variables P_1,P_2 such that P_2+2=P_3.For every sufficiently large odd integer N■1 (mod 6),the equation N=p_1+p_2+p_3 has a solution in prime variables P_1,P_2,P_3 such that p_2+2=P_3,P_3+2=P_2.
  • Tai Shan YI Li; Hong HUANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 261-270. https://doi.org/10.12386/A2007sxxb0031
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    In this paper,we study the convergence of solutions of a class of delay differ- ential equations.These equations have important practical applications and generalize those on which Bernfeld and Haddock conjectured that each solution of the equations tends.to a constant.We first give an example to point out the errors in several existing works on the convergence of solutions of the equations as well as their generalizations. Then we confirm the Bernfeld-Haddock conjecture under weaker conditions.Our re- sult corrects and improves the existing ones.An appendix by Professor Tongren Ding is also given to correct the mistakes in one of his works.
  • Articles
  • Hao CHEN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 271-276. https://doi.org/10.12386/A2007sxxb0032
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    In this paper,we discuss the natural action of symmetric group on the moduli space of n-marked Riemannian spheres.We calculated out all the fixed points of this action and all the symmetric types of n-marked Riemannian sphere.We also discussed the dynamic property of the action of SL(2,C) on Riemannian sphere,so as to give a description of the periodic property of this action.Basing on this,we give a description of the singularity of the moduli space of n-punctured Riemannian sphere.
  • 论文
  • Ming Xue LIU(1); Pei De LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 277-280. https://doi.org/10.12386/A2007sxxb0033
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    In this paper,we show that the lattice of invariant subspaces for a class of subdecomposable operators is rich.Moreover,we provide a counter-examples on a Hilbert space in which the operator T has infinitely many invariant subspaces while the invariant subspace lattice Lat(T) for T is not rich.
  • Zhi Bin ZHU(1); Ke Cun ZHANG(2
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 281-290. https://doi.org/10.12386/A2007sxxb0034
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    In this paper,a feasible sequential equality constrained quadratic program- ming algorithm is proposed to solve the nonlinear inequality constrained optimization. Per single iteration,it is only neccessary to sovle three equality constrained quadratic programmings with the same scale(or in addition,a linear programming),so the com- putational effort is reduced.The theoretical analysis shows that the algorithm is global and superlinear convergence under some suitable conditions.Numerical results show that the method in this paper is effective.
  • Min Fang; Nan Jing HUANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 291-298. https://doi.org/10.12386/A2007sxxb0035
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    In this paper,we introduce and study a new system of generalized mixed vector quasi-equilibrium problems in product FC-spaces.By using the maximal element theorem,some existence results of solutions for the system of generalized mixed vector quasi-equilibrium problems in product FC-spaces are given.The results presented in this paper improve and extend some known results in the literature.
  • Yue Shan WANG; Yue Xiang HE
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 299-310. https://doi.org/10.12386/A2007sxxb0036
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    The aim of this note is to study the local regularity of solutions in Morrey spaces to the elliptic equation in divergence form-(a_(ij)u_(x_i))_(x_j)+b_iu_(x_i)-(d_ju)_(x_j)+cu= (f_j)_(x_j),a.e.x∈Ω.Where a_(ij)∈VMO∩L~∞(Ω),and the lower order terms belong to suitable Morrey spaces.
  • Rui Ying WANG(1); Zhi Fang JI(
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 311-318. https://doi.org/10.12386/A2007sxxb0037
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    In this paper,we introduce T_0-,T_1-,T_2-,T_3-,T_4-separation axioms in the framework of I-fuzzy topology,and give some of their equivalents as well as the relations with one another of these axioms.
  • Huai Xin CAO; Zheng Li CHEN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 319-324. https://doi.org/10.12386/A2007sxxb0038
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    Let A be a unital complex Banach algebra,Ωbe a region andγbe a rectifiable closed curve such that ins(γ)Ω.It is proved that the Riesz functional calculus f:x)f(x) is a Lipschitz operator from some A_δ~γinto A,i.e.,f∈L~1(A_δ~γ,A) and has the Lipschitz constant L_1 (f)■(M_f(γ)Γ)/(2πδ~2)As an application,Lipschitz propertites of the operator valued root-function TT 1/m and the absolute value function T|T| are disccussed.Lastly,it is proved that f∈L~1 (E,A) holds for every nonempty bounded subset E of A.
  • Yuan Zheng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 325-332. https://doi.org/10.12386/A2007sxxb0039
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    In this paper,we show that the only complete spacelike hypersurfaces with constant mean curvature in Lorentz-Minkowski space which are bounded be- tween two concentric hyperbolic cylinders are the hyperbolic cylinders,i.e.,the product R~k×H~(n-k).In the case of constant higher mean curvature,if the sectional curvature is bounded from below,then the only complete spacelike hypersurfaces in Lorentz- Minkowski space which are bounded between two concentric hyperbolic spaces are the hyperbolic spaces.
  • Jie LI
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 333-336. https://doi.org/10.12386/A2007sxxb0040
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    Let p be a prime,n be any positive integer.We define the Smarandache primitive function S_p(n) as the smallest positive integer such that S_p(n)! is divisible by p~n.In this paper,we use the elementary methods to study the solvability of the equation S_p(1)+S_p(2)+…+S_p(n)=S_p((n(n+1)/2)),and give all its solutions.
  • Zhen Long CHEN(1); San Yang LI
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 337-346. https://doi.org/10.12386/A2007sxxb0041
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    The problem of the capacity for N-parameter d-dimensional generalized Brownian sheet,which may satisfy neither scaling property nor stationary increments, is investigated.It is proved that the generalized Brownian sheet locally looks like a stationary process.The relationship between the hitting probabilities for generalized Brownian sheet and the capacity is obtained by means of Cairoli's maximal inequality and multiparameter martingales.An explicit capacity estimate for its hitting probabil- ities is provided.The conclusions about the Brownian sheet and the additive Brownian motion can be considered as special cases of our results.
  • Zhong Li WEI; Chang Ci PANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 347-356. https://doi.org/10.12386/A2007sxxb0042
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    In this paper,we study the existence and multiplicity of nontrivial solutions for the 2nth-order two-point boundary value problems.Making use of the theory of fixed point index in cone and Leray-Schauder degree,under general conditions on nonlinearity,we prove that there exist at least six different nontrivial solutions for the 2nth-order two-point boundary value problems.Furthermore,if the nonlinearity is odd,we obtain that there exist at least eight different nontrivial solutions.
  • Wei CAO
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 357-362. https://doi.org/10.12386/A2007sxxb0043
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    Let F_q be the finite field,and let N(V) denote the number of F_q-rational points on the variety defined by the diagonal polynomials over F_q:f_i(x)=a_(i1)x_1~(d_(i1))+…+a_(in)x_n~(d_(in))+C_i,i=1,...,m.By using the Newton polyhedra technique introduced by Adolphson and Sperber,we show that ord_qN(V)≥「1/(d_1)+…+1/(d_n)(?)-m with d_i=max{d_(1i),...,d_(mi)},which can improve the Ax-Katz theorem in many cases.This generalizes Wan's theorem for the case m=1.Moreover,we provide a different proof to Wan's theorem.
  • Zhi Lin YANG(1); Geng Ping WEI
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 363-372. https://doi.org/10.12386/A2007sxxb0044
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    We study the existence of positive solutions for a functional integral equation using a fixed point theorem of expansion and compression type in a cone.Finally the main results are used to establish some existence results for positive solutions of integral boundary value problems for ordinary differential equations.The results presented substantially generalize and improve some recent ones due to Ma et al.
  • Ping SUN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 373-384. https://doi.org/10.12386/A2007sxxb0045
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    We study in this paper certain series involving ■n(k),which are the partial sums of Riemann-zeta function ■(k),by the probabilistic and combinatorial methods, several important sums are evaluated.Specially the known result of Euler 5(?)(4)= 2■~2(2) can be derived directly from the three sums of 4-order,and therefore the eleven sums of 6-order evaluated in this paper imply that it is possible to obtain the value of ■(3) from searching for the nontrivial relation among certain series.
  • Fei Long CAO(1); Yong Quan ZHA
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 385-392. https://doi.org/10.12386/A2007sxxb0046
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    The problem of approximation for neural networks with single hidden layer is studied in this paper.With the best polynomial approximation as a metric,the rate of approximation of the neural networks with single hidden layer to a continuous function is estimated by using a constructive approach.The result obtained shows that for any continuous function defined a compact set,a neural network with single networks can be constructed to approximate the function,and the rate of approximation do not exceed the double of the best polynomial approximation of the function.
  • Xiao Song LIU(1); Tai Shun LIU
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 393-400. https://doi.org/10.12386/A2007sxxb0047
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    In this paper,we consider a normalized biholomorphic almost spirallike map- ping of typeβ(-π/2<β<π/2) and order a (0■α<1) or a normalized biholomorphic spirallike mapping of typeβ(-π/2<β<π/2) and order a (0<α<1) f defined on the unit polydisk of C~n and the unit ball in a complex Banach space,where x=0 is a zero of order k+1 of f(x)-x.We investigate its construction,and the refined estimation of homogeneous expansion for f(x)is obtained.Our result extends the corresponding known conclusions.
  • Yuan CHEN; Yun Ge XU
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 401-408. https://doi.org/10.12386/A2007sxxb0048
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    Let A be the quasi-hereditary algebra associated with the radical bimodule over a hereditary algebra of finite representation type.Based on the minimal pro- jective bimodule resolution constructed by Bardzell,the dimensions of all Hochschild cohomology groups of A are explicitly calculated.
  • Xiao Jun LIU; Xue Cheng PANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 409-412. https://doi.org/10.12386/A2007sxxb0049
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    In this paper,it is proved:Let ■ be a family of meromorphic functions on the unit disc△,and a_1,a_2 and a_3 be three distinct complex numbers.If for every f∈■,f and f′share the set S={a_1,a_2,a_3},then ■ is normal on△.
  • Qing De ZHANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 413-420. https://doi.org/10.12386/A2007sxxb0050
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    Let λ be a positive number,q_1 and q_2 be positive integers.Assume that E_1={arg z=θ_j|0■θ_1<θ_2<…<θ_(q1)<2π} and E_2={arg z=Φ_j|0■<φ_1<φ_2<…<φ_(q2)<2π} such that E_1∩E_2=■.Then (1) there exists a meromorphic function f(z) of order λ with E_1 ∪ E_2 as its T direction and E_2 as its Borel direction, (2) there exists a meromorphic function g(z) of order and lower order λ with E_1 ∪ E_2 as its Borel direction and E_2 as its T direction.
  • Xiao Hong ZHANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 421-442. https://doi.org/10.12386/A2007sxxb0051
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    Firstly,non-commutative R_0 t-norms (called PR_0 t-norms) are established, and based on PR_0 t-norms a new fuzzy logic formal system PL~* is constructed as a non-commutative generalization of the formal system L~*.The soundness theorem of PL~* is proved.Secondly,the notion of PL~*-algebra is introduced,and the filter theory of PL~*-algebra is constructed.By the normal prime filter theorem of PL~*-algebra, the completeness theorem of formal system PL~* is proved.Finally,the role of formal system PL~* in application field is explained.
  • Cheng Bin SI; Bo Qian SHEN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 443-450. https://doi.org/10.12386/A2007sxxb0052
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    An integral polynomial system with a central ring region is studied in this paper.After a little polynomial disturbance,we give a practical theorem to inquire the zero points of the Abel integral for this system,and give some practical examples.
  • Yi SHAO(1); Yu Lin ZHAO(2)
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 451-460. https://doi.org/10.12386/A2007sxxb0053
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    In this paper,we apply Abelian integrals and complete elliptic integrals of the first,second kinds to study an upper bound on the number of zeros of Abelian integrals for a class of the plane quadratic systems with two centres,under polynomial perturbation of arbitrary degree n.We obtain a smaller upper bound of zeros of Abelian integrals.
  • Xi Tao YANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 461-472. https://doi.org/10.12386/A2007sxxb0054
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    In this paper,we deal with the unique existence and asymptotic stability of almost periodic solution and pseudo-almost periodic solution for the systems of varying coefficient differential equations with piecewise constant argument by virtue of the exponential dichotomy for difference equations.Our results improve those in the literature.Moreover,we have obtained a sufficient condition which guarantees the exponential dichotomy for the difference equations.
  • Guo Lin HOU; Alatancang; Jun J
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 473-480. https://doi.org/10.12386/A2007sxxb0055
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    In this paper,the sufficient and necessary conditions are obtained for the existence of a bounded inverse operator for a linear operator appearing in the linear- quadratic optimal control problems in a Hilbert space and having a matrix representa- tion of the following form ■ where F_3,F_5 are self-adjoint operators,the effectiveness of this result has been shown on several test examples.