Stress and heat flux stabilization for viscous compressible medium equations with a nonmonotone state function

We study a system of quasilinear equations describing one-dimensional flow of a viscous compressible heat-conducting medium with a nonmonotone state function and mass force. The large-time behavior of solutions is considered for arbitrarily large initial data. In spite of possible nonuniqueness and discontinuity of the stationary solution, we prove L²-stabilization for the stress and heat flux as t → ∞ along with corresponding global energy estimates for them. The new method of proof utilizes a combination of energy type equalities for the stress and heat flux. Consequently, H¹-stabilization of the velocity and temperature along with global estimates for their derivatives are valid as well.     

Estimation over Curves of the Functions Given by Dirichlet Series on a Half-Plane

We study the maximal term of the Hadamard composition of Dirichlet series with real exponents. We obtain a lower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line.     

Fourier Transformation of the Renormalization-Invariant Coupling

We discuss integral transformations of the QCD renormalization-invariant coupling (running coupling constant). Special attention is paid to the Fourier transformation, i.e., to the transition from the space–time to the energy–momentum representation. Our first conclusion is that the condition for the possibility of such a transition provides one more argument against the real existence of unphysical singularities observed in the perturbative QCD. The second conclusion relates to a way to translate some singular long-wave asymptotic behaviors to the infrared region of transferred momenta. Such a transition must be performed with the Tauberian theorem taken into account. This comment relates to the recent ALPHA collaboration results on the asymptotic behavior of the QCD effective coupling obtained by numerical lattice simulation.     

高阶非线性时滞差分方程解的渐近性

研究如下的具强迫项的高阶非线性时滞差分方程△^my(n) u(n)l↑∑i=1 gi(y(n-τ))=v(n)其中，m≥1，u,v：N→R，gi：R→R且τ∈{0，1，2，3，…)，i=1，2，…，l，得到了使该方程的解具有某种渐近性态的充分条件。     

Bounded holomorphic functions and maps with some boundary behavior

Let Ω be a domain of . As a study of boundary behavior of functions and maps in Ω, we consider “the linear cluster set,” which is the cluster set along segment terminating at a boundary point of Ω. We prove that there exist bounded holomorphic functions and maps defined in Ω which have the linear cluster sets of positive measure at every point of a discrete subset of the boundary of Ω under some conditions.     

A fourth-order parabolic equation modeling epitaxial thin film growth

We study the continuum model for epitaxial thin film growth from Phys. D 132 (1999) 520-542, which is known to simulate experimentally observed dynamics very well. We show existence, uniqueness and regularity of solutions in an appropriate function space, and we characterize the existence of nontrivial equilibria in terms of the size of the underlying domain. In an investigation of asymptotical behavior, we give a weak assumption under which the ω-limit set of the dynamical system consists only of steady states. In the one-dimensional setting we can characterize the set of steady states and determine its unique asymptotically stable element. The article closes with some illustrative numerical examples.     

The critical behavior of Kac-type models for semi-infinite systems

The critical behavior of the layer magnetizations and local susceptibilities of theD-vector lattice models with Kac-type ferromagnetic interactions for a semi-infinite system is studied. These local quantities behave less singularly than the bulk ones, showing that this is not peculiar to the two-dimensional Ising model. Moreover, the limiting form (at the critical point) of the magnetization profile can be obtained, which, when properly scaled, satisfies the minimum condition in the Landau theory for a semi-infinite continuous system. Landau-type critical behavior is thus recovered.     

一类反应扩散方程解的渐近性质及其应用

本文讨论问题 ｕｔ＝Ａｕｘｘ＋ｆ（ｘ，ｔ，ｕ）， ｕｘ｜ｘ＝０＝０，ｕｘ｜ｘ＝１＝０， ｕ｜ｔ＝０＝ｕ０（ｘ）。 的解的渐近性质，将参考文献［１］的Ｌ＾２范数估计     

一个反应扩散方程的门槛结果

本文讨论反应扩散方程Ｃａｕｃｈｙ问题解的整体存在性，渐近性质和Ｂｌｏｗｕｐ问题．其中或者１＜ｑ＜ｐ＜＋∞，ｎ＝２．得到门槛结果．     

炭纤维织物/环氧树脂基复合材料的摩擦磨损性能研究

研究了炭纤维织物/环氧(CF/EP)复合材料与45#钢在环-环端面干摩擦状态下的摩擦磨损特性,考查了制备工艺和MoS2与石墨不同配比等对CF/EP复合材料干摩擦性能的影响,采用扫描电子显微镜观察复合材料及其偶件磨损表面形貌.结果表明:半干法制备的环氧树脂体积分数为40%的CF/EP复合材料的摩擦系数稳定;纯CF/EP复合材料主要表现为粘着磨损特性;MoS2与石墨改性后复合材料摩擦磨损性能明显改善,质量比为1.5∶1的MoS2与石墨改性CF/EP复合材料具有最佳的摩擦磨损性能,其稳态摩擦系数为0.14～0.15,磨损量3.15×10-5 mg/r.