中国科学院数学与系统科学研究院期刊网

15 February 2015, Volume 31 Issue 2
    

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  • Xiao Ping XU
    Acta Mathematica Sinica. 2015, 31(2): 177-200. https://doi.org/10.1007/s10114-015-3533-0
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    By solving certain partial differential equations, we find the explicit decomposition of the polynomial algebra over the 56-dimensional basic irreducible module of the simple Lie algebra E7 into a sum of irreducible submodules. This essentially gives a partial differential equation proof of a combinatorial identity on the dimensions of certain irreducible modules of E7. We also determine two three-parameter families of irreducible submodules in the solution space of Cartan's well-known fourth-order E7-invariant partial differential equation.
  • De Ke ZHAO
    Acta Mathematica Sinica. 2015, 31(2): 201-215. https://doi.org/10.1007/s10114-015-4030-1
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    We define the Hochschild and cyclic (co)homology groups for superadditive categories and show that these (co)homology groups are graded Morita invariants. We also show that the Hochschild and cyclic homology are compatible with the tensor product of superadditive categories.
  • Ji Hui WANG, Qiao Ling, MA Xue HAN
    Acta Mathematica Sinica. 2015, 31(2): 216-224. https://doi.org/10.1007/s10114-015-4114-y
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    A total k-coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2,..., k}. Let f(u) denote the sum of the color on a vertex u and colors on all the edges incident to u. A k-neighbor sum distinguishing total coloring of G is a total k-coloring of G such that for each edge uvE(G), f(u) ≠ f(v). By χnsd"(G), we denote the smallest value k in such a coloring of G. Pil?niak and Wo?niak conjectured that χnsd"(G) ≤ Δ(G)+3 for any simple graph with maximum degree Δ(G). In this paper, by using the famous Combinatorial Nullstellensatz, we prove that the conjecture holds for any triangle free planar graph with maximum degree at least 7.
  • Cheng Yong DU, Bo Hui CHEN
    Acta Mathematica Sinica. 2015, 31(2): 225-254. https://doi.org/10.1007/s10114-015-3731-9
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    In this paper, by using the de Rham model of Chen-Ruan cohomology, we define the relative Chen-Ruan cohomology ring for a pair of almost complex orbifold (G,H) with H being an almost sub-orbifold of G. Then we use the Gromov-Witten invariants of ?, the blow-up of G along H, to give a quantum modification of the relative Chen-Ruan cohomology ring HCR*(G,H) when H is a compact symplectic sub-orbifold of the compact symplectic orbifold G.
  • Fang LIU, Xiao Ping YANG
    Acta Mathematica Sinica. 2015, 31(2): 255-271. https://doi.org/10.1007/s10114-015-3244-6
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    We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form
    ut - ΔNu =f,
    where ΔN denotes the so-called normalized infinity Laplacian given by .
  • Ming Shuo ZHOU
    Acta Mathematica Sinica. 2015, 31(2): 272-280. https://doi.org/10.1007/s10114-015-3450-2
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    Let k be an algebraically closed field, and V be a vector space of dimension n over k. For a set ω = ((1),...,(m)) of sequences of positive integers, denote by Lω the ample line bundle corresponding to the polarization on the product X =∏i=1m Flag(V,(i)) of flag varieties of type (i) determined by ω. We study the SL(V)-linearization of the diagonal action of SL(V) on X with respect to Lω. We give a sufficient and necessary condition on ω such that Xss(Lω) ≠ Ø (resp., Xs(Lω) ≠ Ø). As a consequence, we characterize the SL(V)-ample cone (for the diagonal action of SL(V) on X), which turns out to be a polyhedral convex cone.
  • Fang JIN, Hui OU, Xiang Qun YANG
    Acta Mathematica Sinica. 2015, 31(2): 281-294. https://doi.org/10.1007/s10114-015-4228-2
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    Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.
  • Wen Feng ZHANG, Xiao Quan XU
    Acta Mathematica Sinica. 2015, 31(2): 295-304. https://doi.org/10.1007/s10114-015-3676-z
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    In this paper, we show that (1) for each QFS-domain L, L is an ωQFS-domain iff L has a countable base for the Scott topology; (2) the Scott-continuous retracts of QFS-domains are QFSdomains; (3) for a quasicontinuous domain L, L is Lawson compact iff L is a finitely generated upper set and for any x1, x2L and finite G1, G2L with G1 << x1, G2 << x2, there is a finite subset FL such that ↑x1∩↑x2 ⊆↑F⊆↑ G1∩↑G2; (4) L is a QFS-domain iff L is a quasicontinuous domain and given any finitely many pairs {(Fi, xi) : Fi is finite, xiL with Fi << xi, 1 ≤ i ≤ n}, there is a quasi-finitely separating function δ on L such that Fi << δ(xi) << xi.
  • Ze Chun HU, Ling ZHOU
    Acta Mathematica Sinica. 2015, 31(2): 305-318. https://doi.org/10.1007/s10114-015-3212-1
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    In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.
  • Deng Pin LIU
    Acta Mathematica Sinica. 2015, 31(2): 319-330. https://doi.org/10.1007/s10114-015-3104-4
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    In this paper, we generalize the conception of characteristic function in toric topology and construct many new smooth manifolds by using it. As an application, we classify the Moment-Angle manifolds and the partial quotients manifolds of them over a polygon. In the appendix we give a simple new proof for Orlik-Raymond's theorem in terms of characteristic function which gives the classification for quasitoric manifolds of dimension 4.
  • Muhammad I. MUSTAFA
    Acta Mathematica Sinica. 2015, 31(2): 331-344. https://doi.org/10.1007/s10114-015-2687-0
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    In this paper we consider an n-dimensional thermoelastic system with viscoelastic damping. We establish an explicit and general decay rate result without imposing restrictive assumptions on the behavior of the relaxation function at infinity. Our result allows a larger class of relaxation functions and generalizes previous results existing in the literature.
  • Ximo GUAL-ARNAU, Silena HEROLD-GARCíA
    Acta Mathematica Sinica. 2015, 31(2): 345-352. https://doi.org/10.1007/s10114-015-1699-0
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    Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in R3. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume.