中国科学院数学与系统科学研究院期刊网

15 December 2013, Volume 29 Issue 12
    

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  • Ai Ju DONG, Dong WANG
    Acta Mathematica Sinica. 2013, 29(12): 2219-2232. https://doi.org/10.1007/s10114-013-3087-y
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    We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.
  • Guo Chun WEN
    Acta Mathematica Sinica. 2013, 29(12): 2233-2244. https://doi.org/10.1007/s10114-013-2805-9
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    In this article, we first transform the general uniformly elliptic systems of first order equations with certain conditions into the complex equations, and propose the discontinuous Riemann- Hilbert problem and its modified well-posedness for the complex equations. Then we give a priori estimates of solutions of the modified discontinuous Riemann-Hilbert problem for the complex equations and verify its solvability. Finally the solvability results of the original discontinuous Riemann-Hilbert boundary value problem can be derived. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.
  • Sheng YANG
    Acta Mathematica Sinica. 2013, 29(12): 2245-2250. https://doi.org/10.1007/s10114-013-2220-2
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    Let G be a finite group and let p be a fixed prime number. Let B be a p-block of G with defect group D. In this paper, we give results on 3-blocks with abelian defect groups isomorphic to Z3m ×Z3n. We are particularly interested in the number of irreducible ordinary characters and the number of irreducible Brauer characters in the block. We calculate two important block invariants k(B) and l(B) in this case.
  • Artūras DUBICKAS
    Acta Mathematica Sinica. 2013, 29(12): 2251-2260. https://doi.org/10.1007/s10114-013-1059-x
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    Let u be a sequence of positive integers which grows essentially as a geometric progression. We give a criterion on u in terms of its distribution modulo d, d = 1, 2,..., under which the set of positive integers expressible by the sum of a prime number and an element of u has a positive lower density. This criterion is then checked for some second order linear recurrence sequences. It follows, for instance, that the set of positive integers of the form p + [(2 + √3)n], where p is a prime number and n is a positive integer, has a positive lower density. This generalizes a recent result of Enoch Lee. In passing, we show that the periods of linear recurrence sequences of order m modulo a prime number p cannot be "too small" for most prime numbers p.
  • Geng Sheng ZHANG, Hong Rui WANG
    Acta Mathematica Sinica. 2013, 29(12): 2261-2272. https://doi.org/10.1007/s10114-013-2726-7
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    Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.
  • Ming LIU, Xia ZHANG
    Acta Mathematica Sinica. 2013, 29(12): 2273-2282. https://doi.org/10.1007/s10114-013-2293-y
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    For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the universal and reduced quantum double constructions in the correspondence C*-algebraic settings, which generalize Drinfeld's quantum double construction and yield new C*-algebraic compact quantum groups.
  • Yue Wu LI, Gen Sun FANG
    Acta Mathematica Sinica. 2013, 29(12): 2283-2294. https://doi.org/10.1007/s10114-013-2212-2
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    In this paper, using an equivalent characterization of the Besov space by its wavelet coefficients and the discretization technique due to Maiorov, we determine the asymptotic degree of the Bernstein n-widths of the compact embeddings
    Bq0s+t(Lp0(Ω))→Bq1s(Lp1(Ω)), t>max{d(1/p0-1/p1), 0}, 1 ≤ p0, p1, q0, q1 ≤∞,
    where Bq0s+t(Lp0(Ω)) is a Besov space defined on the bounded Lipschitz domain Ω ⊂ Rd. The results we obtained here are just dual to the known results of Kolmogorov widths on the related classes of functions.
  • Rui LIU
    Acta Mathematica Sinica. 2013, 29(12): 2295-2304. https://doi.org/10.1007/s10114-013-2167-3
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    This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if (xi, fi) is a framing of a Banach space X, and (eimin) and (eimax) are the minimal unconditional basis and the maximal unconditional basis with respect to (xi, fi), respectively, then for any unconditional basis (ei) associated with (xi, fi), there are A,B > 0 such that
    for all (ai) ∈ c00.
    It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.
  • Deng Ju Mal, Han REN
    Acta Mathematica Sinica. 2013, 29(12): 2305-2320. https://doi.org/10.1007/s10114-013-2135-y
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    In this paper, we show that the nonorientable genus of Cm + Cn, the join of two cycles Cm and Cn, is equal to [((m-2)(n-2))/2] if m = 3, n ≡ 1 (mod 2), or m ≥ 4, n ≥ 4, (m, n) (4, 4). We determine that the nonorientable genus of C4 +C4 is 3, and that the nonorientable genus of C3 +Cn is n/2 if n ≡ 0 (mod 2). Our results show that a minimum nonorientable genus embedding of the complete bipartite graph Km,n cannot be extended to an embedding of the join of two cycles without increasing the genus of the surface.
  • Lin Tao MA, Wei Yi SU
    Acta Mathematica Sinica. 2013, 29(12): 2321-2342. https://doi.org/10.1007/s10114-013-1764-5
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    This paper focuses on two cases of two-dimensional wave equations with fractal boundaries. The first case is the equation with classical derivative. The formal solution is obtained. And a definition of the solution is given. Then we prove that under certain conditions, the solution is a kind of fractal function, which is continuous, differentiable nowhere in its domain. Next, for specific given initial position and 3 different initial velocities, the graphs of solutions are sketched. By computing the box dimensions of boundaries of cross-sections for solution surfaces, we evaluate the range of box dimension of the vibrating membrane. The second case is the equation with p-type derivative. The corresponding solution is shown and numerical example is given.
  • Xian Liang SHI, Wei WANG
    Acta Mathematica Sinica. 2013, 29(12): 2343-2354. https://doi.org/10.1007/s10114-013-1762-7
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    In this paper, a new result on pointwise convergence of wavelets of generalized Shannon type is proved, which improves a theorem established by Zayed.
  • Xiao Feng, WANG Jin XIA, Guang Fu CAO
    Acta Mathematica Sinica. 2013, 29(12): 2355-2366. https://doi.org/10.1007/s10114-013-1581-x
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    In this paper, we construct the function u in L2(Bn, dA) which is unbounded on any neighborhood of each boundary point of Bn such that Tu is the Schatten p-class (0 < p < ∞) operator on pluriharmonic Bergman space h2(Bn, dA) for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L1 symbols.
  • Xian Geng ZHOU, Min ZHANG
    Acta Mathematica Sinica. 2013, 29(12): 2367-2372. https://doi.org/10.1007/s10114-012-1503-3
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    Let I ⊂ 2N be an ideal and let XI = span{χI : II}, and let pI be the quotient norm of l/XI. In this paper, we show first that for each proper ideal I ⊂ 2N, the ideal convergence deduced by I is equivalent to pI-kernel convergence. In addition, let K = {x*oχ(·) : x*∂p(e)}, where p(x) = lim supn→∞1/n(∑k=1n|x(k)|, and let Iμ = {A ⊂ N : μ(A) = 0} for all μ = x*oχ(·) ∈ K. Then Iμ is a proper ideal. We also show that the ideal convergence deduced by the proper ideal Iμ, the p-kernel convergence and the statistical convergence are also equivalent.
  • Min LIU, Bin ZHAO
    Acta Mathematica Sinica. 2013, 29(12): 2373-2390. https://doi.org/10.1007/s10114-013-1240-2
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    A subset system Z assigns to each partially ordered set P a certain collection Z(P) of subsets. In this paper, a new kind of subset systems called directable subset systems is introduced. For a directable subset system Z, the concepts of FZ-way-below relation and FZ-domain are introduced. The well-known Scott topology is naturally generalized to the Z-level and the resulting topology is called FZ-Scott topology, and the continuous functions with respect to this topology are characterized by preserving the suprema of directed Z-sets. Then, we mainly consider a generalization of the cartesian closedness of the categories DCPO of directed complete posets, BF of bifinite domains and FS of FS-domains to the Z-level. Corresponding to them, it is proved that, for a suitable subset system Z, the categories FZCPO of Z-complete posets, FSFZ of finitely separated FZ-domains and BFFZ of bifinite FZ-domains are all cartesian closed. Some examples of these categories are given.
  • Long Yun DING, Zhi YIN
    Acta Mathematica Sinica. 2013, 29(12): 2391-2396. https://doi.org/10.1007/s10114-013-2110-7
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    In this paper, we show that, for each p > 1, there are continuum many Borel equivalence relations between Rω/l1 and Rω/p ordered by ≤B which are pairwise Borel incomparable.
  • Bao Huai SHENG, Dao Hong XIANG
    Acta Mathematica Sinica. 2013, 29(12): 2397-2408. https://doi.org/10.1007/s10114-013-0175-y
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    In the present paper, we give an investigation on the learning rate of l2-coefficient regularized classification with strong loss and the data dependent kernel functional spaces. The results show that the learning rate is influenced by the strong convexity.