中国科学院数学与系统科学研究院期刊网

15 October 2005, Volume 21 Issue 5
    

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  • Chun Lai ZHAO
    Acta Mathematica Sinica. 2005, 21(5): 961-976. https://doi.org/10.1007/s10114-005-0576-7
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    Let D=p1 p2pm,where p1,p2,…, pm are distinct rational primes with p1p2≡3(mod 8),pi≡1(mod 8)(3≤im),and m is any positive integer.In this paper,we give a simple combinatorial criterion for the value of the complex L-function of the congruent elliptic curve at s=1,divided by the period ω defined below,to be exactly divisible by 22m-2,the second lowest 2-power with respect to the number of the Gaussian prime factors of D.As a corollary,we obtain a new series of non-congruent numbers whose prime factors can be arbitrarily many.Our result is in accord with the predictions of the conjecture of Birch and Swinnerton-Dyer.
  • Nikolaos S. PAPAGEORGIOU, Nikolaos YANNAKAKIS
    Acta Mathematica Sinica. 2005, 21(5): 977-996. https://doi.org/10.1007/s10114-004-0508-y
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    This is the first part of a work on second order nonlinear,nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x(t) and x (t).In this first part we prove existence and relaxation theorems.We consider the case of an usc,convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C1(T,H).Also we examine the lsc,nonconvex case and again we prove the existence of solutions.In addition we establish the existence of extremal solutions and by strengthening our hypotheses,we show that the extremal solutions are dense in C1(T,H) to the solutions of the original convex problem (strong relaxation).An example of a nonlinear hyperbolic optimal control problem is also discussed.
  • Zuo LIU, Zhen De WU
    Acta Mathematica Sinica. 2005, 21(5): 998-1000. https://doi.org/10.1007/s10114-004-0403-6
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    Let k be non-negative integer.The unoriented bordism classes,which can be represented as [RP(ξk)] where ξk is a k-plane bundle,form an ideal of the unoriented bordism ring MO*.A group of generators of this ideal expressed by a base of MO* and a necessary and sufficient condition for a bordism class to belong to this ideal are given.
  • Nguyen BUONG
    Acta Mathematica Sinica. 2005, 21(5): 1001-1004. https://doi.org/10.1007/s10114-005-0530-8
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    A class of a posteriori parameter choice strategies for the operator version of Tikhonov regularization (including variants of Morozov's and Arcangeli's methods) is proposed and used in investigating the rate of convergence of the regularized solution for ill-posed nonlinear equation involving a monotone operator in Banach space.
  • Geng Sheng WANG
    Acta Mathematica Sinica. 2005, 21(5): 1005-1014. https://doi.org/10.1007/s10114-004-0410-7
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    This work is concerned with Pontryagin's maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations.A type of approach to the non-well-posed optimal control problem is given.
  • Wei Gao GE, Wei Ping SUN
    Acta Mathematica Sinica. 2005, 21(5): 1015-1026. https://doi.org/10.1007/s10114-005-0565-x
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    By the use of continuation theorems and the duality principle it's proved that for both homogeneous and nonhomogeneous Sturm-Liouville boundary value problems with Laplacian type operators,relative superlinearity implies the existence of infinitely many solutions under a few weakly added conditions.
  • Liang Yu LUAN, Xian WU
    Acta Mathematica Sinica. 2005, 21(5): 1027-1034. https://doi.org/10.1007/s10114-005-0449-0
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    In the present paper,some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.
  • Shuang Ping TAO, Shang Bin CUI
    Acta Mathematica Sinica. 2005, 21(5): 1035-1044. https://doi.org/10.1007/s10114-004-0446-8
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    This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation.∂u/∂t+αu2∂u/∂x+β∂3u/∂x3+γ∂5u/∂x5=0,(x,t)∈R2.We first establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem.Then we apply such estimates to prove local and global existence of solutions for the initial value problem of the modified nonlinear Karahara equation.The results show that a local solution exists if the initial function u0(x)∈Hs(R) with s≥1/4,and a global solution exists if s≥2.
  • Guang Gui DING
    Acta Mathematica Sinica. 2005, 21(5): 1045-1048. https://doi.org/10.1007/s10114-004-0443-y
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    In this paper we give the suffcient and necessary condition for the existence of any almost isometric operator from C(Ω) into C00).As a corollary,we show that there is no ∈-isometry from any abstract M space with a strong unit into C0(Γ) if 0<∈<1/9.
  • Shang Quan BU, Jin Myong KIM
    Acta Mathematica Sinica. 2005, 21(5): 1049-1056. https://doi.org/10.1007/s10114-004-0453-9
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    We establish operator-valued Fourier multiplier theorems on periodic Triebel spaces,where the required smoothness of the multipliers depends on the indices of the Triebel spaces.This is used to give a characterization of the maximal regularity in the sense of Triebel spaces for Cauchy problems with periodic boundary conditions.
  • Wei HUANG, Ye JIANG, Li Xin ZHANG
    Acta Mathematica Sinica. 2005, 21(5): 1057-1070. https://doi.org/10.1007/s10114-004-0452-x
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    Let {X,Xn; n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn = k=1n Xk, Mn = maxk ≤n |Sk|, n ≥ 1. Suppose limn→∞ ESn2/n =: σ2 > 0 and n=1 ρ2/d(2n) < ∞, where d = 2 if 1 ≤ r < 2 and d > r if r ≥ 2. We prove that if E|X|r < ∞, for 1 ≤ p < 2 and r > p, then

    where Z has a normal distribution with mean 0 and variance σ2.
  • Shang Bin CUI (Shangbin CUI)
    Acta Mathematica Sinica. 2005, 21(5): 1071-1082. https://doi.org/10.1007/s10114-004-0483-3
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    In this paper,we study a free boundary problem arising from the modeling of tumor growth.The problem comprises two unknown functions:R=R(t),the radius of the tumor,and u=u(r,t),the concentration of nutrient in the tumor.The function u satisfies a nonlinear reaction diffusion equation in the region 0<r<R(t),t>0,and the function R satisfies a nonlinear integrodi fferential equation containing u.Under some general conditions,we establish global existence of transient solutions,unique existence of a stationary solution,and convergence of transient solutions toward the stationary solution as t→∞.
  • Xing Zhong XU, Qi Guang WU
    Acta Mathematica Sinica. 2005, 21(5): 1083-1086. https://doi.org/10.1007/s10114-004-0458-4
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    Suppose YN(β,σ2In),where β∈Rn and σ2>0 are unknown.We study the admissibility of linear estimators of mean vector under a quadratic loss function.A necessary and suffcient condition of the admissible linear estimator is given.
  • Ping WANG, Jiong Sheng LI
    Acta Mathematica Sinica. 2005, 21(5): 1087-1092. https://doi.org/10.1007/s10114-004-0485-1
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    Let G be a finite simple graph with adjacency matrix A,and let P(A) be the convex closure of the set of all permutation matrices commuting with A.G is said to be compact if every doubly stochastic matrix which commutes with A is in P(A).In this paper,we characterize 3-regular compact graphs and prove that if G is a connected regular compact graph,G-v is also compact,and give a family of almost regular compact connected graphs.
  • Song Chol HAN, Hong Xing LI
    Acta Mathematica Sinica. 2005, 21(5): 1093-1098. https://doi.org/10.1007/s10114-004-0497-x
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    Inclines are the additively idempotent semirings in which products are less than or equal to either factor.In this paper,some necessary and sufficient conditions for a matrix over L to be invertible are given,where L is an incline with 0 and 1.Also it is proved that L is an integral incline if and only if GLn(L)=PLn(L) for any n (n≥2),in which GLn(L) is the group of all n×n invertible matrices over L and PLn(L) is the group of all n×n permutation matrices over L.These results should be regarded as the generalizations and developments of the previous results on the invertible matrices over a distributive lattice.
  • Yi Jun HU
    Acta Mathematica Sinica. 2005, 21(5): 1099-1106. https://doi.org/10.1007/s10114-004-0487-z
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    In this paper,we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process,and is no longer a linear function.For this more realistic risk model,Lundberg type limiting results for the finite time ruin probabilities are derived.Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.
  • Aleksander GRYTCZUK, Jaroslaw GRYTCZUK
    Acta Mathematica Sinica. 2005, 21(5): 1107-1112. https://doi.org/10.1007/s10114-005-0544-2
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    We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h(d) of the real quadratic field Q(√d).In particular,we give a new proof of the result of Hasse,asserting that in this case h(d)=1 is possible only if d is of the form p,2q or qr,where p,q,r are primes and qr≡3(mod 4).
  • Li Jun HEI, Jian Hua WU
    Acta Mathematica Sinica. 2005, 21(5): 1113-1120. https://doi.org/10.1007/s10114-004-0467-3
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    By discussing the properties of a linear cooperative system,the necessary and sufficient conditions for the existence of positive solutions of an elliptic cooperative system in terms of the principal eigenvalue of the associated linear system are established,and some local stability results for the positive solutions are also obtained.
  • Xiao Qian WANG, Shi Hong CHENG
    Acta Mathematica Sinica. 2005, 21(5): 1121-1130. https://doi.org/10.1007/s10114-004-0486-0
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    In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed.The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.
  • Xue Wen LI
    Acta Mathematica Sinica. 2005, 21(5): 1131-1136. https://doi.org/10.1007/s10114-005-0577-6
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    A Cayley graph Γ=Cay(G,S) of a group G with respect to S is called a circulant digraph of order pk if G is a cyclic group of the same order.Investigated in this paper are the normality conditions for arc-transitive circulant (di)graphs of order p2 and the classification of all such graphs.It is proved that any connected arc-transitive circulant digraph of order p2 is,up to a graph isomorphism,either ,G(p2,r),or G(p,r)[pK1],where r|p-1.
  • Shui Cao ZHENG, Huo Nan LIN, Di He HU
    Acta Mathematica Sinica. 2005, 21(5): 1137-1148. https://doi.org/10.1007/s10114-004-0521-1
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    In this paper,we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes,and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes.We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is φ(r)=rN-d/α(log log 1/r) d/α when >d.In addition,we obtain a sharp lower bound for the Hausdorff measure of level sets of general (N,d,α) strictly stable processes.
  • Shi Ping LU, Wei Gao GE, Zu Xiu ZHENG
    Acta Mathematica Sinica. 2005, 21(5): 1149-1158. https://doi.org/10.1007/s10114-005-0533-5
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    In this paper,the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows:
    (x(t)-cx(t-τ))"=g(t,x(t-μ(t)))+e(t),
    in the critical case|c|=1.By employing Mawhin's continuation theorem and some analysis techniques,some new results are obtained.
  • P. K. SAHOO
    Acta Mathematica Sinica. 2005, 21(5): 1159-1166. https://doi.org/10.1007/s10114-005-0551-3
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    In this paper,we determine the general solution of the functional equation f1 (2x+y)+f2 (2x-y)=f3 (x+y)+f4 (x-y)+f5 (x) without assuming any regularity condition on the unknown functions f1,f2,f3,f4,f5:RR.The general solution of this equation is obtained by finding the general solution of the functional equations f(2x+y)+f(2x-y)=g(x+y)+g(x-y)+h(x) and f(2x+y)-f(2x-y)=g(x+y)-g(x-y).The method used for solving these functional equations is elementary but exploits an important result due to Hosszú.The solution of this functional equation can also be determined in certain type of groups using two important results due to Székelyhidi.
  • Zhao Fang BAI, Jin Chuan HOU
    Acta Mathematica Sinica. 2005, 21(5): 1167-1182. https://doi.org/10.1007/s10114-005-0503-y
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    Let X be a (real or complex) Banach space with dimension greater than 2 and let B0 (X) be the subspace of B(X) spanned by all nilpotent operators on X.We get a complete classification of surjective additive maps Φ on B0 (X) which preserve nilpotent operators in both directions.In particular,if X is infinite-dimensional,we prove that Φ has the form either Φ(T)=cATA-1 or Φ(T)=cAT'A-1,where A is an invertible bounded linear or conjugate linear operator,c is a scalar,T' denotes the adjoint of T.As an application of these results,we show that every additive surjective map on B(X) preserving spectral radius has a similar form to the above with|c|=1.
  • Bin Heng SONG, Huai Yu JIAN
    Acta Mathematica Sinica. 2005, 21(5): 1183-1190. https://doi.org/10.1007/s10114-005-0573-x
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    We establish the existence of fundamental solutions for the anisotropic porous medium equation,uti=1n(umi)xixi in Rn×(0,∞),where mv1,m2,…,and mn are positive constants satisfying min1≤in{mi}≤1,Σi=1nmi>n-2,and max 1≤in{mi}≤1/n (2+Σi=1nmi).
  • Zhao Hui HUO, Bo Ling GUO
    Acta Mathematica Sinica. 2005, 21(5): 1191-1196. https://doi.org/10.1007/s10114-005-0574-9
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    The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered,and low regularity and limit behavior of the solutions are obtained.For k=1,local well- posedness is obtained for data in Hs(R)(s >-3/4).For k=2,local result for data in Hs(R)(s≥1/4) is obtained.For k=3,local result for data in Hs(R)(s>-1/6) is obtained.Moreover,the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero.
  • Da Chun YANG
    Acta Mathematica Sinica. 2005, 21(5): 1209-1218. https://doi.org/10.1007/s10114-004-0451-y
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    Let Γ be a compact d-set in R n with 0<dn,which includes various kinds of fractals.The author establishes an embedding theorem for the Besov spaces Bpqs(Γ) of Triebel and the Sobolev spaces W1,p(Γ,d,μ) of Hajlasz when s>1,1<p<∞ and 0<q≤∞.The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces Bpq0(Γ) and Fpq0(Γ).
  • Mei Yue JIANG
    Acta Mathematica Sinica. 2005, 21(5): 1219-1228. https://doi.org/10.1007/s10114-004-0459-3
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    In this paper,we give a Landesman-Lazer type theorem for periodic solutions of the asymmetric 1-dimensional p-Laplacian equation
    (|x'|p-2x')=λ|x|p-2x++μ|x|p-2x-+f(t,x)
    with periodic boundary value.
  • Hui Ying WANG
    Acta Mathematica Sinica. 2005, 21(5): 1229-1240. https://doi.org/10.1007/s10114-004-0515-z
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    We study the zero-dissipation problem for a one-dimensional model system for the isentropic flow of a compressible viscous gas,the so-called p-system with viscosity.When the solution of the inviscid problem is a rarefaction wave with finite strength,there exists unique solution to the viscous problem with the same initial data which converges to the given inviscid solution as εgoes to zero.The proof consists of a scaling argument and elementary energy analysis,based on the underlying wave structure.
  • Lin Sen XIE
    Acta Mathematica Sinica. 2005, 21(5): 1241-1248. https://doi.org/10.1007/s10114-004-0425-0
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    We establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth Ditzian-Totik modulus of smoothness ωΦr(f,t) where Φ is an admissible step-weight function.An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained.