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  • Global Well-posedness for 3D Generalized Navier-Stokes-Boussinesq Equations
  • In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion:{ut+(u·▽)u+v∧2αu=-▽p+θe(3),e3=(0,0,1)T,θt+(u·▽)θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/4.Moreover,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique.Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.
  • Near-Optimal Controls of Differential Systems with Switching and Random Jumps Subject to Fast Switching and Wideband Noise Perturbation
  • This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching.The random switching is modeled by a continuous-time,time-inhomogeneous Markov chain.Under broad conditions,it is shown that there is an associated limit problem,which is a switching jump diffusion.Using near-optimal controls of the limit system,we then build controls for the original systems.It is shown that such constructed controls are nearly optimal.
  • Existence and Multiplicity of Solutions for Nonlocal Systems with Kirchhoff Type
  • Firstly,we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type.Then a multiplicity result is established by cohomological index of Fadell and Rabinowitz.We also consider the critical case and prove existence of positive least energy solution when the parameter β is sufficiently large.
  • Convergence Rates to Asymptotic Profile for Solutions of Quasilinear Hyperbolic Equations with Nonlinear Damping
  • The quasilinear hyperbolic equation with nonlinear damping is considered in this paper,a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding parabolic equation,the convergence rates of the new profile are better than that obtained by Nishihara(1997,J.Differential Equations 137,384-395) and H.-J.Zhao(2000,J.Differential Equations 167,467-494).
  • Improved Bounds on the Generalized Acyclic Chromatic Number
  • An r-acyclic edge chromatic number of a graph G,denoted by α’_r(G),is the minimum number of colors used to produce an edge coloring of the graph such that adjacent edges receive different colors and every cycle C has at least min {|C|,r} colors.We prove that α’_r(G) ≤(4r + 1)△(G),when the girth of the graph G equals to max{50,△A(G)} and 4 ≤ r ≤ 7.If we relax the restriction of the girth to max {220,A(G)},the upper bound of a’_r(G) is not larger than(2r + 5)△(G) with 4 ≤r≤ 10.
  • Multiple Limit Cycles Bifurcation From the Degenerate Singularity for a Class of Three-dimensional Systems
  • In this paper,bifurcation of small amplitude limit cycles from the degenerate equilibrium of a three-dimensional system is investigated.Firstly,the method to calculate the focal values at nilpotent critical point on center manifold is discussed.Then an example is studied,by computing the quasi-Lyapunov constants,the existence of at least 4 limit cycles on the center manifold is proved.In terms of degenerate singularity in high-dimensional systems,our work is new.
  • Multiplicity and Uniqueness of Positive Solutions for Nonhomogeneous Semilinear Elliptic Equation with Critical Exponent
  • In this paper,we consider the following problem {-Δu(x)+u(x)=λ(u~p(x)+h(x)),x∈R~N,u(x)∈h~1(R~N),u(x)>0,x∈R~N,(*)where λ > 0 is a parameter,p =(N+2)/(N—2).We will prove that there exists a positive constant 0 < A* < +00such that(*) has a minimal positive solution for λ∈(0,λ*),no solution for λ > λ*,a unique solution for λ = λ*.Furthermore,(*) possesses at least two positive solutions when λ∈(0,λ*) and 3 ≤ N ≤ 5.For N ≥ 6,under some monotonicity conditions of h we show that there exists a constant 0 <λ** < λ* such that problem(*)possesses a unique solution for λ∈(0,λ**).
  • On Frankl and Fredi's Conjecture for 3-uniform Hypergraphs
  • Frankl and Füredi in [1] conjectured that the r-graph with m edges formed by taking the first m sets in the colex ordering of N(r) has the largest Lagrangian of all r-graphs with m edges.Denote this r-graph by Cr,m and the Lagrangian of a hypergraph by λ(G).In this paper,we first show that if(3t-1) ≤m<(3t),G is a left-compressed 3-graph with m edges and on vertex set[t],the triple with minimum colex ordering in Gc is(t — 2 — i)(t — 2)t,then λ(G) ≤λ(C3,m).As an implication,the conjecture of Frankl and Fiiredi is true for(3t)-6≤m≤(3t).
  • Analysis of a Nutrient-phytoplankton Model in the Presence of Viral Infection
  • In this paper,a system of reaction-diffusion equations arising in a nutrient-phytoplankton populations is investigated.The equations model a situation in which phytoplankton population is divided into two groups,namely susceptible phytoplankton and infected phytoplankton.A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given.If the diffusion coefficient of the infected phytoplankton is treated as bifurcation parameter,non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.
  • Causality Analysis of Futures Sugar Prices in Zhengzhou Based on Graphical Models for Multivariate Time Series
  • This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For every undirected edge in the partial correlation graph,the measures of linear feedback between two time series can help us decide its direction,then we obtain the mixed graph.Using this method,we construct a mixed graph for futures sugar prices in Zhengzhou(ZF),spot sugar prices in Zhengzhou(ZS) and futures sugar prices in New York(NF).The result shows that there is a bi-directional causality between ZF and ZS,an unidirectional causality from NF to ZF,but no causality between NF and ZS.更多还原
  • Divergent Solutions to the L^2-Supercritical NLS Equations Qing GUO
  • We investigate the nonlinear Schrdinger equation iut+△u+|u|p-1u = 0 with 1+4/N < p < 1+4/(N-2)(when N = 1,2,1 +4/N < p < ∞) in energy space H1 and study the divergent property of infinite-variance and nonradial solutions.If M(u)(1-sc)/sc E(u) < M(Q)(1-sc)/scE(Q) and ||u0||0(1-sc)/sc ||▽u0||2 > ||Q||(1-sc)/sc |▽Q||2,then either u(t) blows up in finite forward time or u(t) exists globally for positive time and there exists a time sequence tn→ +∞ such that || ▽u(tn)||2 →+∞.Here Q is the ground state solution of —(1 — sc)Q + △Q + |Q|p-1Q = 0.A similar result holds for negative time.This extend the result of the 3D cubic Schr(o|¨)dinger equation obtained by Holmer to the general mass-supercritical and energy-subcritical case.
  • A Markov Copula Model with Regime Switching and Its Application
  • Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals(X,H~i),i = 1,2,3 of the Markov copula model(X,H) are still Markov processes and have martingale property.In this proposed model,a pricing formula of credit default swap(CDS) with bilateral counterparty risk is derived.更多还原
  • Stability of Rarefaction Wave for Compressible Navier-Stokes Equations on the Half Line
  • This paper is concerned with the large-time behavior of solutions to an initial-boundary-value problem for full compressible Navier-Stokes equations on the half line(0,∞),which is named impermeable wall problem.It is shown that the 3-rarefaction wave is stable under partially large initial perturbation if the adiabatic exponent γ is close to 1.Here partially large initial perturbation means that the perturbation of absolute temperature is small,while the perturbations of specific volume and velocity can be large.The proof is given by the elementary energy method.
  • Vertex-Fault-Tolerant Cycles Embedding on Enhanced Hypercube Networks
  • In this paper,we focus on the vertex-fault-tolerant cycles embedding on enhanced hypercube,which is an attractive variant of hypercube and is obtained by adding some complementary edges from hypercube.Let Fv be the set of faulty vertices in the n-dimensional enhanced hypercube Qn,k(1 ≤ k≤n- 1).When |Fv| = 2,we showed that Qn,k-Fv contains a fault-free cycle of every even length from 4 to 2n- 4 where n(n ≥ 3) and fc have the same parity;and contains a fault-free cycle of every even length from 4 to 2n- 4,simultaneously,contains a cycle of every odd length from n — fc + 2 to 2n-3 where n(≥ 3) and fc have the different parity.Furthermore,when |Fv|= fv ≤ n- 2,we proof that there exists the longest fault-free cycle,which is of even length 2n- 2fv whether n(n > 3) and fe have the same parity or not;and there exists the longest fault-free cycle,which is of odd length 2n-2fv- 1 in Qn,k — Fv where n(≥ 3) and fc have the different parity.
  • Multiple Solutions for a Quasilinear Second Order Differential Equation Depending on a Parameter
  • The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b]?R{-u’’=(λf(x,u)+g(u))h(u’),in(a,b),u(a)=u(b)=0under ppropriate hypotheses.We exhibit the existence of at least three(weak)solutions and,and the results are illustrated by examples.
  • Further Results on Mutually Nearly Orthogonal Latin Squares
  • Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level.In this paper,some constructions of mutually nearly orthogonal Latin squares are provided.It is proved that there exist 3 MNOLS(2m) if and only if m ≥3 nd there exist 4 MNOLS(2m) if and only if m ≥4 with some possible exceptions.
  • The Proportional Hazards Model for Multiple Type Recurrent Gap Times
  • Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies,and often more than one type of recurrent events is of interest.In this paper,we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covaxiates on the censored event processes of interest.An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions.We examine asymptotic properties of the proposed estimators.Finite sample properties of these estimators are demonstrated by simulations.
  • Infinitely Many Periodic Solutions for a Class of Second-order Hamiltonian Systems
  • In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems{ü(t)+A(t)u(t)+▽F(t,u(t))=0,u(0)-u(T)=(0)-(T)=0,where F(t,u) is even in u,and ▽(t,u) is of sublinear growth at infinity and satisfies the Ahmad-Lazer-Paul condition.
  • Global Well-posedness for 3D Generalized Navier-Stokes-Boussinesq Equations(Quan-sen JIU Huan YU)
    Near-Optimal Controls of Differential Systems with Switching and Random Jumps Subject to Fast Switching and Wideband Noise Perturbation(G.YIN;Xian-ping GUO;Yousef TALAFHA;Nicholas A.BARAN)
    Existence and Multiplicity of Solutions for Nonlocal Systems with Kirchhoff Type(Zhi-tao ZHANG;Yi-min SUN)
    Convergence Rates to Asymptotic Profile for Solutions of Quasilinear Hyperbolic Equations with Nonlinear Damping(Shi-feng GENG[1,2];Zhen WANG)
    Improved Bounds on the Generalized Acyclic Chromatic Number(Yu-wen WU;Kan-ran TAN;Gui-ying YAN)
    Multiple Limit Cycles Bifurcation From the Degenerate Singularity for a Class of Three-dimensional Systems(Qin-long WANG;Wen-tao HUANG;Yi-rong LIU)
    Multiplicity and Uniqueness of Positive Solutions for Nonhomogeneous Semilinear Elliptic Equation with Critical Exponent(Na BA;Yan-yan WANG;Lie ZHENG)
    On Frankl and Fredi's Conjecture for 3-uniform Hypergraphs(Qing-song TANG[1,2];Hao PENG;Cai-ling WANG;Yue-jian PENG)
    Analysis of a Nutrient-phytoplankton Model in the Presence of Viral Infection(Jian-jun LI;Wen-jie GAO)
    Causality Analysis of Futures Sugar Prices in Zhengzhou Based on Graphical Models for Multivariate Time Series(Jing XU;Xing-wei TONG)
    Divergent Solutions to the L^2-Supercritical NLS Equations Qing GUO(Qing GUO)
    A Markov Copula Model with Regime Switching and Its Application(Xue LIANG[1,2,3])
    Stability of Rarefaction Wave for Compressible Navier-Stokes Equations on the Half Line(Li-hua MIN;Xiao-hong QIN)
    Vertex-Fault-Tolerant Cycles Embedding on Enhanced Hypercube Networks(Min LIU;Hong-mei LIU)
    Multiple Solutions for a Quasilinear Second Order Differential Equation Depending on a Parameter(SHAPOUR HEIDARKHANI[1,2])
    Further Results on Mutually Nearly Orthogonal Latin Squares(Ke-jun CHEN;Yong ZHANG;Guang-zhou CHEN;Wen LI)
    The Proportional Hazards Model for Multiple Type Recurrent Gap Times(Ji-cai LIU;Huan-bin LIU;Ri-quan ZHANG[1,3])
    Infinitely Many Periodic Solutions for a Class of Second-order Hamiltonian Systems(Ming-hai YANG Yue-fen CHEN Yan-fang XUE)
    《应用数学学报:英文版》封面

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