Feb 2017, Volume 12 Issue 2
    

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  • RESEARCH ARTICLE
    Claus BAUER

    We use the large sieve inequality with sparse sets of moduli to prove a new estimate for exponential sums over primes. Subsequently, we apply this estimate to establish new results on the binary Goldbach problem where the primes are restricted to given arithmetic progressions.

  • RESEARCH ARTICLE
    Jiecheng CHEN,Belay Mitiku DAMTEW,Xiangrong ZHU

    We consider the oscillatory hyper Hilbert transform Hγ,α,βf(x)=0f(xΓ(t))eitβt(1+α)dt, where Γ(t) = (t, γ(t)) in ?2 is a general curve. When γ is convex, we give a simple condition on γ such that Hγ,α,β is bounded on L2 when β3α,β>0. As a corollary, under this condition, we obtain the Lp-boundedness of Hγ,α,β when 2β/(2β3α)<p<2β(3α). When Γ is a general nonconvex curve, we give some more complicated conditions on γ such that Hγ,α,β is bounded on L2. As an application, we construct a class of strictly convex curves along which Hγ,α,β is bounded on L2 only if β>2α>0.

  • RESEARCH ARTICLE
    Shangdi CHEN,Huihui WEI

    Key distribution patterns (KDPs) are finite incidence structures satisfying a certain property which makes them widely used in minimizing the key storage and ensuring the security of communication between users in a large network. We construct a new KDP using t-design and combine two ω-KDPs to give new (ω−1)-KDPs, which provide secure communication in a large network and minimize the amount of key storage.

  • RESEARCH ARTICLE
    Kai DENG,Heping ZHANG

    The anti-forcing number of a perfect matching M of a graph G is the minimal number of edges not in M whose removal makes M a unique perfect matching of the resulting graph. The anti-forcing spectrum of G is the set of anti-forcing numbers over all perfect matchings of G: In this paper, we prove that the anti-forcing spectrum of any cata-condensed hexagonal system is continuous, that is, it is a finite set of consecutive integers.

  • RESEARCH ARTICLE
    Yanxia DONG,Erfang SHAN,Xiao MIN

    Let G = (V,A) be a digraph and k1 an integer. For u, vV, we say that the vertex u distance k-dominate v if the distance from u to v at most k. A set D of vertices in G is a distance k-dominating set if each vertex of V \ D is distance k-dominated by some vertex of D. The distance k-domination number of G, denoted by γk(G), is the minimum cardinality of a distance k-dominating set of G. Generalized de Bruijn digraphs GB(n, d) and generalized Kautz digraphs GK(n, d) are good candidates for interconnection networks. Denote Δk:=(j=0kdj)1. F. Tian and J. Xu showed that ?nΔk?γk(GB(n,d))?n/dk? and ?nΔk?γk(GK(n,d))?n/dk?. In this paper, we prove that every generalized de Bruijn digraph GB(n, d) has the distance kdomination number ?nΔk? or ?nΔk? +1, and the distance k-domination number of every generalized Kautz digraph GK(n, d) bounded above by ?n/dk1+dk?. Additionally, we present various sufficient conditions for γk(GB(n,d))=?nΔk? and γk(GK(n,d))=?nΔk?.

  • RESEARCH ARTICLE
    Jishan FAN,Fucai LI,Gen NAKAMURA

    We prove two new regularity criteria for the 3D incompressible Navier-Stokes equations in a bounded domain. Our results also hold for the 3D Boussinesq system with zero heat conductivity.

  • RESEARCH ARTICLE
    Bin FENG,Zhen CUI

    We study the Cesàro means related to the divisor function. We show that the DDT Theorem holds over square-free numbers in short interval, which generalizes some results established by Deshouillers-Dress-Tenenbaum and by Cui-Wu.

  • RESEARCH ARTICLE
    Wei JIN

    We classify the family of pentavalent vertex-transitive graphs Γ with diameter 2. Suppose that the automorphism group of Γ is transitive on the set of ordered distance 2 vertex pairs. Then we show that either Γ is distance-transitive or Γ is one of C8¯,K5K2,C5[K2],2C4¯, or K3K4 .

  • RESEARCH ARTICLE
    Dongsheng LI,Zhenjie LI

    We investigate the nonnegative solutions of the system involving the fractional Laplacian:

    {(Δ)αui(x)=fi(u),x?n,i=1,2,...,m,u(x)=(u1(x),u2(x),...,um(x)),

    Where 0α1, n2, fi(u),1≤im , are real-valued nonnegative functions of homogeneous degree pi≥0 and nondecreasing with respect to the independent variables u1, u2, . . . , um. By the method of moving planes, we show that under the above conditions, all the positive solutions are radially symmetric and monotone decreasing about some point x0 if pi=(n+2α)/(n2α) for each 1≤im; and the only nonnegative solution of this system is u ≡ 0 if 1pi(n+2α)/(n2α) for all 1≤im.

  • RESEARCH ARTICLE
    Senyue LOU,Ying SHI,Da-jun ZHANG

    Many multi-dimensional consistent discrete systems have soliton solutions with nonzero backgrounds, which brings difficulty in the investigation of integrable characteristics. In this paper, we derive infinitely many conserved quantities for the lattice potential Korteweg-de Vries equation whose solutions have nonzero backgrounds. The derivation is based on the fact that the scattering data a(z) is independent of discrete space and time and the analytic property of Jost solutions of the discrete Schrödinger spectral problem. The obtained conserved densities are asymptotic to zero when |n| (or |m|) tends to infinity. To obtain these results, we reconstruct a discrete Riccati equation by using a conformal map which transforms the upper complex plane to the inside of unit circle. Series solution to the Riccati equation is constructed based on the analytic and asymptotic properties of Jost solutions.

  • RESEARCH ARTICLE
    Hongchuan XIA,Chunping ZHONG

    Let (M,F) be a Finsler manifold, and let TM0 be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of (TM0,G) and study their geometric properties. Next, we use this approach to obtain new characterizations of Finsler manifolds with positive constant flag curvature. We also investigate the relations between Levi-Civita connection, Cartan connection, Vaisman connection, vertical foliation, and Reinhart spaces.

  • RESEARCH ARTICLE
    Baogang XU,Yingli ZHANG

    Let Gand Hbe two graphs. We say that G induces H if G has an induced subgraph isomorphic to H. A. Gyárfás and D. Sumner, independently, conjectured that, for every tree T; there exists a function fT; called binding function, depending only on T with the property that every graph G with chromatic number fT(ω(G)) induces T. A. Gyárfás, E. Szemerédi and Z. Tuza conrmed the conjecture for all trees of radius two on triangle-free graphs, and H. Kierstead and S. Penrice generalized the approach and the conclusion of A. Gyárfás et al. onto general graphs. A. Scott proved an interesting topological version of this conjecture asserting that for every integer kand every tree T of radius r, every graph G with ω(G)≤k and sufficient large chromatic number induces a subdivision of T of which each edge is subdivided at most O(14r–1(r–1)!) times. We extend the approach of A. Gyárfás and present a binding function for trees obtained by identifying one end of a path and the center of a star. We also improve A. Scott's upper bound by modifying his subtree structure and partition technique, and show that for every integer k and every tree T of radius r; every graph with ω(G)≤k and sufficient large chromatic number induces a subdivision of T of which each edge is subdivided at most O(6r–2) times.

  • RESEARCH ARTICLE
    Dan YANG,Yu FU,Lan LI

    Generalized constant ratio surfaces are defined by the property that the tangential component of the position vector is a principal direction on the surfaces. In this work, we study these class of surfaces in the 3-dimensional Minkowski space L3. We achieve a complete classification of spacelike generalized constant ratio surfaces in L3.

  • RESEARCH ARTICLE
    Sufang ZHANG,Kaitai LI,Hongen JIA

    Two-grid mixed finite element method is proposed based on backward Euler schemes for the unsteady reaction-diffusion equations. The scheme combines with the stabilized mixed finite element scheme by using the lowest equal-order pairs for the velocity and pressure. The space two-grid method is also used to reduce the time consuming. The benefits of this approach are to avoid the higher derivative, but to have more favorable stability, and to get the numerical solution of the two unknown variables simultaneously. Stability analysis and error estimates are given in this work. Finally, the theoretical results are verified by the numerical examples.

  • RESEARCH ARTICLE
    Zhimin ZHANG,Chaolin LIU

    We consider a perturbed compound Poisson risk model with randomized dividend-decision times. Different from the classical barrier dividend strategy, the insurance company makes decision on whether or not paying off dividends at some discrete time points (called dividend-decision times). Assume that at each dividend-decision time, if the surplus is larger than a barrier b>0, the excess value will be paid off as dividends. Under such a dividend strategy, we study how to compute the moments of the total discounted dividend payments paid off before ruin.