中国科学院数学与系统科学研究院期刊网

15 July 2008, Volume 51 Issue 4
    

  • Select all
    |
    论文
  • Ai Fang QU
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 625-632. https://doi.org/10.12386/A2008sxxb0074
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We give the fundamental solution of the Tricomi operator Tu=y(u_(x_1x_1)+u_(x_2x_2))+u_(yy)=0.(Ⅰ) It has stronger singularity than Tu=yu_(xx)+u_(yy)=0.We indicate that it is necessary to introduce the principal part of Cauchy integral to define the fundamental solution in the theory of distribution.
  • Song Ping ZHOU(1); Dan Sheng YU2); Ping ZHOU(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 633-646. https://doi.org/10.12386/A2008sxxb0075
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We generalize some classical results in convergence and integrability for the trigonometric series with non-negative coefficients to the series with varying coefficients (they may change signs),by introducing the so-called piecewise bounded variation sequences (PBVS).
  • Rui Feng ZHANG(1); Bo Long GUO(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 647-654. https://doi.org/10.12386/A2008sxxb0076
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    A class of generalied Long-Short wave equations in an unbounded domain is studied.By introducing the weighted space,applying interpolation inequality and a priori estimate in weighted space,the existence of global solution for the Long- Short wave equations is obtained.Moreover,the existence of global attractor for these equations is established.
  • Song Xiao LI
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 655-662. https://doi.org/10.12386/A2008sxxb0077
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let φ(z)=(φ_1(z),…,φ_n(z)) be a holomorphic self-map of D~n andψ(z) a holomorphic function on D~n,where D~n is the unit polydisk of C~n.This paper investigates the essential norm of the weighted composition operatorψC_φ on Bloch spaces.
  • Zhou Xin LI; Yao Tian SHEN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 663-670. https://doi.org/10.12386/A2008sxxb0078
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We consider the p-Laplacian-like equation with critical exponent:-div (a(|Du|~p)|Du|~(p-2)Du)=|u|~(p~(*-2))u+λf(x,u),u∈W_0~(1,p)(Ω),whereΩ∈R~N (N≥2) is a bounded smooth domain and a is a smooth function from R~+ to R.The solutions are obtained by variational methods,the analysis of Palais-Smale sequences requires suitable generalizations of the techniques involved in the study of the corresponding quasilinear problem with lack of compactness.Using the concentration compactness principle of Lions,the result that the associated functional I_λsatisfies the (PS)_c con- dition is proved.Applying the Clark's critical theory and the properties of genus,the existence of infinitely many solutions of the problem is obtained.Furthermore,the existence of a special eigenfunction whenλ>0 small enough is proved.
  • Shao Rong WANG; Ze Heng YANG; Ming XIONG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 671-676. https://doi.org/10.12386/A2008sxxb0079
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In the paper,we obtain some iterative approximation theorems of fixed points for asymptotically quasi-nonexpansive type mapping and asymptotically nonexpansive type mapping with error member in uniformly convex Banach space without the con- dition"for ■ε>0,■n_0∈N_+,■n≥n_0 and ■x∈D,suth that‖T~nx-T~(n+1)x‖<ε."our results improve and extend some recent results.Also improve for the theorem of methods of proof.
  • Mao Hua LE
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 677-684. https://doi.org/10.12386/A2008sxxb0080
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let r be a positive odd integer with r>1,and let m be a positive even integer.Further move let a=|V(r)|,b=|U(r)| and c=m~2+1,where V(r)+ U(r)(-1)~(1/2)=(m+(-1)~(1/2))~r.In this paper we prove that if r≡5 (mod 8) and either m>r~2,r<11500 or m>2r/π,r>11500,then the equation a~x+b~y=c~z has only the positive integer solution (x,y,z)=(2,2,r).
  • Chang Xiong NIE; Chuan Xi WU
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 685-692. https://doi.org/10.12386/A2008sxxb0081
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We research into the conformal geometry in Lorentzian space forms,and classify the space-like hypersurfaces with parallel conformal second fundamental forms in the conformal space.
  • Xu Dan FU(1); Xia ZHOU(2); Xiao Dong ZHAO(1)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 693-698. https://doi.org/10.12386/A2008sxxb0082
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this note,we prove Lucas' congruence on q-binomial coefficient with the help of a result on partition of integers moduls a prime.Furthermore,we aim at studying Lucas' and Babbage's congruences on generalized binomial coefficient defined in terms of second order recurrent sequences with initial values 0 and 1.
  • Ying WANG(1); Chun Lai MU(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 699-710. https://doi.org/10.12386/A2008sxxb0083
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We are concerned with the blow-up of solution and the instability of the ground state solution for a class of nonlinear Boussinesq equation.Furthermore,we obtain the global bounded solutions with initial data in different regions.
  • Jun Sheng ZHAO(1); Hong Zhi LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 711-720. https://doi.org/10.12386/A2008sxxb0084
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study the Cauchy problem of nonlinear Klein-Gordon equation u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0; u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n. By introducing a family of potential wells we obtain a threshold result of global existence and nonexistcnce of solutions.
  • Bo HE
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 721-726. https://doi.org/10.12386/A2008sxxb0085
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let a and b be positive integers.In this paper,we prove that the simulta- neous Pell equations x~2-ay~2=1,y~2-bz~2=1 possess at most two positive integer solutions (x,y,z).This result follow from a combination of the techniques including simultaneous Padéapproximation to binomial functions.It improves the previous work of Bennett (1998) and Yuan (2004).
  • Ya Li GUO; Chuan Yi ZHANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 727-734. https://doi.org/10.12386/A2008sxxb0086
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We investigate the existence and uniqueness of asymptotically almost pe- riodic solutions for the first-order differential system:u′+F(u)=h(t),where F is a strictly monotone map on R~N.Particularly,we discuss the necessary and sufficient conditions for the existence and uniqueness of asymptotically almost periodic solutions for the first-order differential equation u′+▽Φ(u)=h(t),where▽Φdenotes the gradi- ent of the convex functionφon R~N.Then we extend the results to some second-order equations.
  • Xue Liang ZHENG(1); Shen Zhou ZHENG(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 735-748. https://doi.org/10.12386/A2008sxxb0087
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    It's established that the bounded weak solution of a class of nonlinear degenerate elliptic equations with the natural growth belongs to the Hlder space with some Hlder exponent by way of Moser-Nash's iterating argument and a density lemma. Then,we further obtain that each bounded weak solution is of sharp Hlder exponent with anyγ:0≤γ
  • Ling JIA(1); Fang LI(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 749-754. https://doi.org/10.12386/A2008sxxb0088
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The authors give the properties of almost split sequences for group algebras. Our aim is to generalize some of the results under the setting of cocommutative weak Hopf algebras.
  • Ya Jun MA; Ji Tao SUN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 755-760. https://doi.org/10.12386/A2008sxxb0089
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper focuses on the stability in terms of two measures of delay impul- sive systems on time scales.We introduce a new concept of (h_0,h) stability for delay impulsive systems on time scales.By using Lyapunov functions and analysis method, some sufficient conditions for the stability to hold axe given.An example is presented to illustrate the efficiency of results proposed in this paper.
  • Feng Hui WANG(1); Chang Sen YANG(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 761-768. https://doi.org/10.12386/A2008sxxb0090
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The estimate of the weakly convergent sequence coefficient concerning the coefficient R(1,X) and the generalized von Neumann-Jordan (James) constant is es- tibalished.These estimates enable us to obtain two sufficient conditions for normal structure,which extend and improve some known results.
  • Xiao Guang LI; Jian ZHANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 769-778. https://doi.org/10.12386/A2008sxxb0091
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We show the existence of blow-up solutions for a coupled nonlinear wave system with critical power in dimension two.Furthermore,we study the qualitative property of the blow-up solutions,and prove that the blow-up solutions have L~2 con- centration property.
  • Yan Feng HE; Xiao Wei PAN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 779-786. https://doi.org/10.12386/A2008sxxb0092
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    For any positive integer n,the famous Smarandache LCM function SL(n) is defined as the smallest positive integer k such that n|[1,2,…,k],where [1,2,…,k] denotes the least common multiple of 1,2,…,k.The main purpose of this paper is to use the elementary methods to study the solutions of an equation involving the Smarandache LCM function SL(n),and obtain all positive solutions of this equation.
  • Xian Yang ZHU(1); Gang Song LENG(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 787-794. https://doi.org/10.12386/A2008sxxb0093
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Recently,Lutwak,Yang and Zhang posed the notion of new geometric bodyΓ_(-p)K and got some results.In this paper,the notion of mixed new geometric bodyΓ_(-p,i)K is introduced,new geometric body being a special case.Some properties and inequalities are established for the mixed new geometric bodyΓ(-p,i)K.
  • Qing Jun LUO
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 795-802. https://doi.org/10.12386/A2008sxxb0094
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In the present paper,some basic properties of MP filters and prime filters in R_0-algebra M are studied.By introducing some topological structures on the set of all prime filters and the set of all maximal filters respectively,we conclude that the set of all prime filters is a compact To topological space and the set of all maximal filters is a compact Hausdorff space.
  • Wen Ming WU(1); Wei Yuan(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 803-808. https://doi.org/10.12386/A2008sxxb0095
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Letαbe an action of the semi-direct product G ■_σH of countably discrete groups G and H on von Neumann algebra M.Thenβ_h=α_(e,h)  AdU_h is an action of H on the von Neumann algebra crossed product M■_αG.We show that M■_α(G■_σH) is ~*-isomorphic to (M ■_αG)■_βH,therefore the crossed product of von Neumann algebras has the associative law.
  • Zhi Wei LIU
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 809-814. https://doi.org/10.12386/A2008sxxb0096
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let D be a positive integer with D>1,and let p be a prime with p (?) D.In this paper we prove that if D=3a~2+1,and p=4a~2+1,where a is a positive integer, then the equation x~2+D~m=p~n has only two positive integer solutions (x,m,n) = (a,1,1) and (8a~3+3a,1,3),except for (D,p)=(4,5).By the above mentioned result, the best upper bound for the number of solutions of this equation is given.
  • Jia Jin WEN; Chao Bang GAO
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 815-832. https://doi.org/10.12386/A2008sxxb0097
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We define the noncentral 2-surround system S~(m){Γ,A,A_+,l} and the cen- tered 2-surround system S~(2) {P,Γ,A,A_+,l}.For S~(2) {P,Γ,A,A_+,l},by means of the theories of the isoperimetric inequality,we establish a class of geometric inequalities as follws