完全非线性抛物型方程的整体解

本文所研究的是下列完全非线性抛物型方程的整体解:u_t=Δu+f(u,Du,D~2u),u(0)=u_0,其中,f∈C~(1+r),r>2/n,u_0属于介于 W_1~2(R~n)∩C~2(R~n)与 W_1~3(R~n)∩C~3(R~n) 间的中间空间,且充分小.从而推广了以往相应的工作.     

非线性Klein-Gordon方程柯西问题解的整体存在性与Blow-up

研究非线性Klein-Gordon方程的柯西问题u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0;u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n.通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果.     

退缩拟线性椭圆型方程某类边值问题的无穷多解

文[1]证明了如下D氏问题 -D_i(g|Du|~2)D_iu=f(x,u),x∈Ω, u=0,x∈Ω存在非平凡解,本文讨论上述方程的另一类边界问题 -D_i(g|Du|~2)D_iu=f(x,u),x∈Ω, g(|Du|~2)D_iu(0)(n,x_i)+h(x,u)=0,x∈Ω, (1)其中Ω∈R~n是具有光滑边界的有界区域,n(x)是Ω在x点的外法向,D_iu=u/x_i,Du=gradu=u,重复指标表示求和,与问题(1)相应的泛函为:     

NON-RADIAL SOLUTIONS OF A SEMILINEAR ELLIPTIC EQUATION

In this paper we consider the eigenvalue problem of semilinear elliptic equation in R~n(n≥~3)-△u+α(x)u=λf(x, u), u∈H~1(R~n).     

Global well-posedness and blow-up for the hartree equation

For 2 γ min{4, n}, we consider the focusing Hartree equation iu_t+ △u +(|x|~(-γ)* |u|~2)u = 0, x ∈ R~n.(0.1)Let M [u] and E [u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of-△ Q + Q =(|x|~(-γ)* |Q|~2)Q. Guo and Wang [Z. Angew. Math.Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of(0.1) if M [u]~(1-s_c)E [u]~(s_c) M [Q]~(1-s_c)E [Q]~(s_c)(s_c=(γ-2)/2). In this paper, we consider the complementary case M [u]~(1-s_c)E [u]~(s_c)≥ M [Q]~(1-s_c)E [Q]~(s_c) and obtain a criteria on blow-up and global existence for the Hartree equation(0.1).     

Global Existence and Scattering in L2 for the Mass-critical Hartree Equation With H0,1 Initial Data

In this paper we consider the Cauchy Problem for the mass-critical Hartree equation I(e)tu △u=μ(|x|2*|u|2)u,(t,x)∈R×Rn,n≥3,(1) u(0,x)=φ(x), x∈Rn,(2)     

Scattering Versus Blowup Beyond the Mass-Energy Threshold for the Davey–Stewartson Equation in R~3

We study the Cauchy problem for the Davey–Stewartson equation i?_tu + Δu + |u|~2 u + E_1(|u|~2)u = 0,(t, x) ∈ R × R~3.The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u_0)E(u_0) above the ground state threshold M(Q)E(Q).     

On Characterization of Poisson Integrals of Schrödinger Operators with Morrey Traces

Let L be a Schr?dinger operator of the form L =-Δ + V acting on L~2(R~n) where the nonnegative potential V belongs to the reverse H?lder class B_q for some q ≥ n. In this article we will show that a function f ∈ L~(2,λ)(R~n), 0 λ n, is the trace of the solution of L_u =-u_(tt) + L_u =0, u(x, 0) = f(x), where u satisfies a Carleson type condition sup x_B,r_Br_B~(-λ)∫_0~(rB)∫_(B(x_B,r_B))t|u(x,t)|~2dxdt≤C∞.Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces L_L~(2,λ)(R~n) associated to the operator L, i.e.L_L~(2,λ)(R~n)=L~(2,λ)(R~n).Conversely, this Carleson type condition characterizes all the L-harmonic functions whose traces belong to the space L~(2,λ)(R~n) for all 0 λ n.     

ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

§ 1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space W_t~2~(1,2)(O, +∞) into L_t~2~q(O, ∞), v>2. When v=N-1 we can get the radial solutions of problem where 2~*=2N/N-2 is the critical exponent of the Sobolev embedding H~1(R~n)→L~Q(R~N). Kurtz has discussed the existence of κ-node solution of (1.1), (1.2) for each κ∈N U{0} when the growth rate of |u|~(l-1)u+f(u) is lower then |u|~(v+3/v-1) i.e.     

Jacobian-determinant equation in the critical Besov spaces

Let Ω be a bounded domain in R~n with smooth boundary. Here we consider the following Jacobian-determinant equation det u(x)=f(x),x∈Ω;u(x)=x,x∈?Ω where f is a function on Ω with min_Ω f = δ 0 and Ωf(x)dx = |Ω|. We prove that if f ∈B_(p1)~(np)(Ω) for some p∈(n,∞), then there exists a solution u ∈ B_(p1)~(np+1)(Ω)C~1(Ω) to this equation. On the other hand, we give a simple example such that u ∈ C_0~1(R~2, R~2) while detu does not lie in B_(p1)~(2p)(R~2) for any p∞.     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

On the hyperbolicity of the period-doubling fixed point

We give a new proof of the hyperbolicity of the fixed point for the period-doubling renormalization operator using the local dynamics near a semi-attractive fixed point (in a Banach space) and the theory of holomorphic motions. We also give a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the period-doubling fixed point: our proof uses the non-existence of invariant line fields in the period-doubling tower (C. McMullen), the topological convergence (D. Sullivan), and a new infinitesimal argument.

     

考虑服务和退货的双渠道供应链定价问题研究

在考虑零售服务和消费者退货情况下,运用两阶段优化方法分别探究了集中式和分散式两种双渠道供应链的最优定价策略。研究发现零售服务有助于提高零售商的渠道权力,并始终使制造商获益,但只有当服务水平小于某一临界值时,才使制造商和零售商同时得到帕累托改进。零售价格和直销价格与退货率正相关,而与服务水平的关系受渠道结构的影响。服务水平的提高加剧了供应链的“双重边际化”效应,制造商通过生产与消费者需求相匹配的产品来降低退货风险可以减弱这种效应,从而提高供应链效率。     

树脂基复合材料粘接的优化设计

本文在试验数据和理论分析的基础上,提出树脂基复合材料单搭接的优化设计的原则,胶粘剂的选择、被粘物的设计,粘接长度的选择、胶层厚度的选择等.认为通过优化设计可以提高粘接强度,减轻产品的重量,提高其质量.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Stress intensity factors for a finite plate with an inclined crack by boundary collocation

In this paper, we combine the Muskhelishvili＇s complex variable method and boundary collocation method, and choose a set of new stress function based on the stress boundary condition of crack surface, the higher precision and less computation are reached. This method is applied to calculating the stress intensity factor for a finite plate with an inclined crack. The influence of θ （the obliquity of crack） on the stress intensity factors, as well as the number of summation terms on the stress intensity factor are studied and graphically represented.     

拍卖机制设计在区块链中的应用与挑战

区块链是新一代信息技术的重要组成部分,是分布式网络、加密技术、智能合约等多种技术集成的新型数据库软件。过去的十多年,区块链技术在全球范围内产生广泛影响。如今的区块链技术,已从最初的关注于解决货币和支付的去中心化问题,转入到解决市场的去中心化问题。智能合约的出现使得基于区块链技术的去中心化金融进入高速发展状态,也涌现出区块链环境下的各类拍卖场景。本文首次从机制设计角度,以区块链交易费机制,非同质化代币(Non-Fungible Token,NFT)拍卖和矿工可提取价值(Miner-Extractable Value,MEV)交易位置拍卖为主要对象,总结和剖析近些年来区块链上特有的拍卖机制;并针对区块链特性,提出区块链上拍卖机制设计所面临的挑战和未来亟待解决的问题。     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Adiabatic divergence of the chaotic layer width and acceleration of chaotic and noise-induced transport

We show that, in spatially periodic Hamiltonian systems driven by a time-periodic coordinate-independent (AC) force, the upper energy of the chaotic layer grows unlimitedly as the frequency of the force goes to zero. This remarkable effect is absent in any other physically significant systems. It gives rise to the divergence of the rate of the spatial chaotic transport. We also generalize this phenomenon for the presence of a weak noise and weak dissipation. We demonstrate for the latter case that the adiabatic AC force may greatly accelerate the spatial diffusion and the reset rate at a given threshold.