中国科学院数学与系统科学研究院期刊网

15 March 2009, Volume 25 Issue 3
    

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  • Li Ping ZHANG, Ji Ye HAN
    Acta Mathematica Sinica. 2009, 25(3): 343-354. https://doi.org/10.1007/s10114-008-7096-1
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    We generalize the D-gap function developed in the literature for variational inequalities toa general equilibrium problem(EP).Through the D-gap function,the equilibrium problem is cast asan unconstrained minimization problem.We give conditions under which any stationary point of theD-gap function is a solution of EP and conditions under which it provides a global error bound for EP.Finally,these results are applied to box-constrained EP and then weaker conditions are established toobtain the desired results for box-constrained EP.
  • Wen De LIU, Xiu Ying HUA, Yu Cai SU
    Acta Mathematica Sinica. 2009, 25(3): 355-378. https://doi.org/10.1007/s10114-008-6547-z
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    In this paper we mainly study the derivations for even part of the finite-dimensional oddHamiltonian superalgebra HO over a field of prime characteristic.We first give the generating set of theeven part g of HO.Then we compute the derivations from g into the even part W of the generalizedWitt superalgebra.Finally,we determine the derivation algebra and outer derivation algebra of gand the dimension formulas.In particular,the first cohomology groups H1(g;W)and H1(g;g)aredetermined.
  • F.CASTAÑO-IGLESIAS, N.CHIFAN, C.NÃSTÃSESCU
    Acta Mathematica Sinica. 2009, 25(3): 379-392. https://doi.org/10.1007/s10114-008-6027-5
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    Using categorical techniques we obtain some results on localization and colocalizationtheory in Grothendieck categories with a set of small projective generators.In particular,we givea suffcient condition for such category to be semiartinian.For semiartinian Grothendieck categorieswhere every simple object has a projective cover,we obtain that every localizing subcategory is aTTF-class.In addition,some applications to semiperfect categories are obtained.
  • Guo FENG, Gen Sun FANG
    Acta Mathematica Sinica. 2009, 25(3): 393-402. https://doi.org/10.1007/s10114-008-7308-8
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    In this paper,we consider some classes of 2π-periodic convolution functions Bp,and Kpwith kernels having certain oscillation properties,which include the classical Sobolev class as specialcase.With the help of the spectral of nonlinear integral equations,we determine the exact values ofBernstein n-width of the classes Bp,Kp in the space Lp for 1
  • Yun Zhang LI, Qiao Fang LIAN
    Acta Mathematica Sinica. 2009, 25(3): 403-418. https://doi.org/10.1007/s10114-008-7077-4
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    The periodic multiresolution analysis(PMRA)and the periodic frame multiresolutionanalysis(PFMRA)provide a general recipe for the construction of periodic wavelets and periodicwavelet frames,respectively.This paper addresses PFMRAs by the introduction of the notion of spec-trum sequence.In terms of spectrum sequences,the scaling function sequences generating a normalizedPFMRA are characterized;a characterization of the spectrum sequences of PFMRAs is obtained,whichprovides a method to construct PFMRAs since its proof is constructive;a necessary and su?cient con-dition for a PFMRA to admit a single wavelet frame sequence is obtained;a necessary and su?cientcondition for a PFMRA to be contained in a given PMRA is also obtained.What is more,it is provedthat an arbitrary PFMRA must be contained in some PMRA.In the meanwhile,some examples areprovided to illustrate the general theory.
  • Lan Dang YUAN, Qing De KANG
    Acta Mathematica Sinica. 2009, 25(3): 419-434. https://doi.org/10.1007/s10114-008-6615-4
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    In this paper,we introduce a new concept—overlarge sets of generalized Kirkman systems(OLGKS),research the relation between it and OLKT S,and obtain some new results for OLK T S.The main conclusion is:If there exist both an OLK F(6k)and a 3-OLGK S(6k-1,4)for all k {6,7,...,40}\{8,17,21,22,25,26},then there exists an OLKT S(v)for any v≡3(mod 6),v=21.As well,we obtain the following result:There exists an OLKT S(6u+3)for u=22n-1-1,7n,31n,127n,4r25s,where n≥1,r+s≥1.
  • Dong Sheng KANG
    Acta Mathematica Sinica. 2009, 25(3): 435-444. https://doi.org/10.1007/s10114-008-6450-7
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    SupposeΩ⊂RN(N≥3)is a smooth bounded domain,ξi∈Ω,0i<√μμ:=(N-2/2)2,0≤μi<(√μ-ai)2,aiii+1 and pi:=2N/N-2(1+ai-bi)are the weighted critical Hardy–Sobolev exponents,i=1,2,...,k,k≥2.We deal with the conditions that ensure the existenceof positive solutions to the multi-singular and multi-critical elliptic problemwith Dirichlet boundary condition,which involves the weighted Hardy inequality and the weighted Hardy–Sobolev inequality.The results depend crucially on the parameters ai,bi andμi,i=1,2,...,k.
  • Jing Hui QIU
    Acta Mathematica Sinica. 2009, 25(3): 445-454. https://doi.org/10.1007/s10114-008-6418-7
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    Applying the theory of locally convex spaces to vector optimization,we investigate therelationship between Henig proper effcient points and generalized Henig proper effcient points.Inparticular,we obtain a suffcient and necessary condition for generalized Henig proper effcient pointsto be Henig proper effcient points.From this,we derive several convenient criteria for judging Henigproper effcient points.
  • Jintana SANWONG, Boorapa SINGHA, R.P.SULLIVAN
    Acta Mathematica Sinica. 2009, 25(3): 455-466. https://doi.org/10.1007/s10114-008-6280-7
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    In 2006,Sanwong and Sullivan described the maximal congruences on the semigroupN consisting of all non-negative integers under standard multiplication,and on the semigroup T(X)consisting of all total transformations of an infinite set X under composition.Here,we determine allmaximal congruences on the semigroup Zn under multiplication modulo n.And,when Y⊆X,we dothe same for the semigroup T(X,Y)consisting of all elements of T(X)whose range is contained in Y.We also characterise the minimal congruences on T(X,Y).
  • Xi Li TAN, Xiao Yun YANG
    Acta Mathematica Sinica. 2009, 25(3): 467-480. https://doi.org/10.1007/s10114-009-6229-5
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    Let{εt;t∈Z}be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment.{aj;j∈Z}is a sequence of real numbers satisfying−j=-∞|aj|<∞.Define a moving average process Xt=−j=-∞aj+tεj,t≥1,and Sn=−nt=1Xt,n≥1.In this article,by using the weak convergence theorem of{Sn/√n;n≥1},we study the precise asymptotics of the complete convergence for the sequence{Xt;t∈N}.
  • Yang Rong LI, Bo Ling GUO
    Acta Mathematica Sinica. 2009, 25(3): 481-490. https://doi.org/10.1007/s10114-008-6226-0
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    We study the random dynamical system(RDS)generated by the Benald flow problem with multiplicative noise and prove the existence of a compact random attractor for such RDS.
  • Yong HUANG, Huai Yu, JIAN Ning SU
    Acta Mathematica Sinica. 2009, 25(3): 491-502. https://doi.org/10.1007/s10114-008-6010-1
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    In this paper,we prove an existence theorem for spacelike convex hypersurfaces of prescribed Gauss curvature in Minkowski space.
  • Ruixiang XING
    Acta Mathematica Sinica. 2009, 25(3): 503-518. https://doi.org/10.1007/s10114-008-5615-8
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    In this paper,we derive an upper bound estimate of the blow-up rate for positive solutionsof indefinite parabolic equations from Liouville type theorems.We also use moving plane method toprove the related Liouville type theorems for semilinear parabolic problems.