中国科学院数学与系统科学研究院期刊网

23 November 2015, Volume 43 Issue 3
    

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  • Hong Zhou WANG,Li Hu DENG,Wei
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 385-390. https://doi.org/10.12386/A2000sxxb0051
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    By using fixed-point theorem in cones, we will study existence of positive solutions of a class of singular boundary value problem, which is relating to x.
  • Ping Zhi YUAN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 391-398. https://doi.org/10.12386/A2000sxxb0052
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    In this paper, by using Siegel-Tatuzawa Theorem, we prove that: if n > 1.2 × 10~11, then there is at most two positive integers n such that xy+yz+zx=n has no solutions with (x,y,z) = 1 and 0 < x < y < z. And we obtain a result related to the quadratic fields of class number 2 and the polynomials denoting primes.
  • Fang LI
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 399-414. https://doi.org/10.12386/A2000sxxb0053
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    In this paper, five equivalence relations on a coalgebra are defined, which are the Green's equivalence, i.e. G, D, C, R, H. About these equivalences, some properties are shown and some structures are characterized. A partial order relation is introduced on each of the sets C/L, C/R, C/H, C/G and the structures of semilattices and lattices are studied for the partial orders. The structures of subcoalgebras (resp. left, right coideals) is characterized as consisting of G-(resp. L-, R-)classes. The Green's equivalences are researched on tensor product. The Green's preserving and lifting properties of coalgebra morphisms are discussed. As applications, we obtain a condition such that the tensor product of two irreducible coalgebras is irreducible and show that the image of an irreducible coalgebra is irreducible under a G-preserving coalgebra morphism,
  • Jin ZHOU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 415-420. https://doi.org/10.12386/A2000sxxb0054
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    This paper gives new sufficient conditions for the boundedness of solutionsof the following a second-order nonlinear differential system (S')and obtains a necessary and sufficient condition for ail solutions of (S') to be bounded and to converge to zero. These results can be applied to the Lienard-type equation x + fi(x)x + f_2(x)x~2 + g(x) = e(t), (E)which substantially extends and improves some important results associated with the same problems in the literatures[1,2]et.al.
  • Ren Xing NI(1),Chong LI(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 421-426. https://doi.org/10.12386/A2000sxxb0055
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    The well posedness of farthest and simultaneous farthest problems in Banach spaces X are investigated. Under the Hausdorff metric of subsets, for closed convex subset D and bounded closed, relatively weakly compact K in X, we proved that the set of all points in D such that the farthest problem ma-c{x, K} is well posed is a dense Ge subset in D provided that D is both strictly convex and Kadec with respect to K. As an application, we also obtain the corresponding results for the simultaneous farthest problems.
  • Yan Ling SHAO(1),Yu Bin GAO(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 427-434. https://doi.org/10.12386/A2000sxxb0056
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    A digraph D of order n is called primitive if there exists a positive integer k such that for each ordered pair of vertices u and v, there is a walk of length k from u to v. If D is a symmetric digraph, then D is primitive if and only if its corresponding graph is connected and contains at least one odd cycle. In [2], we have determined the largest value of the k~(th) upper generalized exponents over the set of primitive symmetric digraphs whose shortest odd cycle length is a fixed number T. In this paper, we give a complete characterization for the extremal digraphs.
  • Kai Tai LI,Yan Ren HOU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 435-444. https://doi.org/10.12386/A2000sxxb0057
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    Inertial Manifold with Delay (IMD) is the recent development of the Inerial Manifold (IM) and Approximate Inertial Manifold (AIM) for the dissipative systems, which is based on the more precise observation of the interaction between large and small eddies, that is we believe this kind of interaction is related with the history of the system instead of implicitly regarding it is instantaneous as in IM and AIM. In this paper, we present a proof of the existence of IMD with respect to a certain sort of dissipative system. Becasue the so-called "spectral gap condition" is hot necessary for the existence of IMD, it exists widely. Then we introduce a kind of discrete IMD and construct a family of IMD. Their error estimations for approximating IMD show that this kind of method can provide a possible way to construct stable and accurate algorithms.
  • Hai Yi JIANG(1),Li Feng XI(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 445-456. https://doi.org/10.12386/A2000sxxb0058
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    The aim of this article is to prove a conjecture posed by A.Norton. The question of how complicated images of sets of rank r will be is answered by relating its Hausdorff dimension to the differentiability of the map.
  • Xiao Long JIANG(1),Yong Hua XU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 457-462. https://doi.org/10.12386/A2000sxxb0059
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    In this paper, we consider the isomorphic classes of H-Galois extensions with the normal basis property over a fixed comutative ring B for a finite Hopf algebra H. The result is that when H is cocommutative, then the above isomorphic classes and the 2-th cohomology group. H~2(L~*, U) are isomorphic as groups under the product defined in this paper, where L=B H, L~* == Hom_B(L, B).
  • Yu Rong ZHOU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 463-470. https://doi.org/10.12386/A2000sxxb0060
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    In this paper, the method of comparision integral of divergence is improved in many ways. By this new method we give some more effective conditions which judge that the Lienard system has at most one or two limit cycles.
  • Chang Xiang RUI(1),Jian Fei CH
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 471-480. https://doi.org/10.12386/A2000sxxb0061
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    In this paper, we give a structure theorem of fundamental weakly regular *-semigroups. As a special case of the theorem, we present a new construction of fundamental regular *-semigroups.
  • Zhong WANG(1),Jiong SUN(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 481-486. https://doi.org/10.12386/A2000sxxb0062
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    In this paper, we give some sufficient conditions for a class of J-symmetric differential operators to be the limit-point (its deficiency index is equal to n or 1 for second order) by the method of Naimark M. A.[1].
  • De Ze MO
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 487-494. https://doi.org/10.12386/A2000sxxb0063
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    By Theorems 1, 2 and 3, it becomes a simple matter to solve any equation a~x-6~y=n, a~xb~y±a~z±b~w±1 = 0 or a~x±b~y±a~z±b~w=0 (x,y, z,w w∈≥0) where a and b are relatively prime positive integers with 2≤a, b≤50 and n is some positive integer integer with n≤80000.
  • Jian Miao CEN(1),Jin Qi LI(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 495-502. https://doi.org/10.12386/A2000sxxb0064
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    In this paper, Lie coalgebras in triangular Hopf algebra representation cate gory are studied. We give mainly the structures of the universal coenveloping coalgebras of Lie coalgebras in triangular Hopf representation category.
  • Jiao MO
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 503-516. https://doi.org/10.12386/A2000sxxb0065
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    This paper deals with the non-degenerate Lie algebras on the field C of complex numbers. They are associated with the orthogonal algebras B_l and D_l, then some of their properties can be obtained. We also discuss a certain kind of non degenerate nilpotent Lie ajgebras and describe them intensively.
  • Jin Ping ZHANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 517-524. https://doi.org/10.12386/A2000sxxb0066
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    In this paper, we studied n-parameter d-dimension radom walk marked by RW~d_n. Its various multiparameter Maxkov properties、Single-point and wide-past transition functions were discussed. A weak law of large numers of RW~1_n (B~1(p, q)) was obtained.
  • Xian WU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 525-530. https://doi.org/10.12386/A2000sxxb0067
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    In the paper, we first prove a improved version of the Fan-Ha's section theorem and some corresponding equivalent versions, and next as their applications, a minimax theorem, some coincidence theorems and a maximal element theorem are obtained.
  • Yong Kun LI,Gui Tong XU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 531-534. https://doi.org/10.12386/A2000sxxb0068
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    We are concerned with the oscillation of all bounded solutions of some even order neutral delay nonlinear differential equation [x(t)-p(t)x(t-τ)]-q(t)h(x(t - σ))=0 and its corresponding linear equation [x(t)-p_0(t)x(t-τ)]-q-0(t)x(t-σ) = 0 for their oscillations. Our result improves a result which is obtained by Ladas and Qian.
  • Ming Xian PANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 535-544. https://doi.org/10.12386/A2000sxxb0069
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    In this paper, discussed the problem of spectral inclusion regions for par titioned matrices, obtained two spectral inclusion regions and spectral distribution theorems, these results generalized and improved corresponding results in paper [1-9].
  • Bao SHI
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 545-554. https://doi.org/10.12386/A2000sxxb0070
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    In this paper, we consider the existence and uniqueness of positive solutions and bounded positive solutions of systems of Volterra reaction-diffusion equations with infinite delay by making use of the theories of C_h space, BC_h space and the method of lower and upper solutions. In the final, we give an example.
  • Guang Xing SONG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 555-560. https://doi.org/10.12386/A2000sxxb0071
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    In this paper, by use of some new differential and integral inequalities, the unique solution and iterative approximation of the two-point boundary value problem for integro-differential equations in Banach spaces are investigated.
  • Shu Qin WANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 561-568. https://doi.org/10.12386/A2000sxxb0072
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    This paper proves the following result: A kind of nilpotent Lie algebres g with nondegenerate invariant bilinear form satisfies: Theory 1. (i) c(g) = g~N, (ii) dim c(g) = l, N is index of nilpotent, l is the number of generaters of g. And Theory 3 proves the sufficient and necessary Conditions for the Construction of this kind of Lie algebras.
  • Qing Nian PAN(1),Zhi Feng HAO(
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 569-576. https://doi.org/10.12386/A2000sxxb0073
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    Double crossproducts D(X, A) of Skew-Hopf pairs (X, A) were constructed, which includes Drinfeld quantum double as special case, and which implies several important Hopf algebras exist double crossproducts.