Vibrational excitation differential cross sections of low-energy electron scattering from N2 molecule

The vibrational excitation differential cross sections (DCS) of low-energy electron-N₂ scattering are studied using vibrational close-coupling (VCC) scattering method and quantum scattering potentials which include static, exchange, and polarization contributions based onab initio calculations. By including the contributions of 11 partial waves (up tol = 21), 15 vibrational states, and 16 molecular symmetries (up to ∧ = 7), the converged vibrational excitation (0→2, 0→3, 0→4) DCSs, the scattering resonance, and the vibrational multi-peak structure agree well with experimental results. Project supported by the National Natural Science Foundation of China (Grant No. 19674038) and the Science Foundation of Chinese Education Ministry.     

Minimal Surfaces with an Elastic Boundary

LetD:= { C ³ (

Global existence for a class of strongly coupled parabolic systems

A class of strongly coupled parabolic systems is investigated. Sufficient conditions on the structure of the systems are found to assure that weak solutions are bounded and that they are Hölder continuous. Together, these results give the global existence of solutions. The theory is then applied to the general Shigesada–Kawasaki–Teramoto model in population dynamics.     

Korn's Inequality for an Arbitrary System of Distorted Thin Rods

We derive a weighted and anisotropic Korn inequality for a system of elastic thin rods and verify its asymptotic accuracy. The structure of the norms at the construction elements (rods and knots) is determined from classifying the elements and assigning them to the following categories: movable, hard-movable, and clamped. This classification was never involved while the constraints on the structure of systems of rods in the preceding reserach excluded the presence of movable elements.     

Deformability of expanded polystyrene under short-term compression

The results obtained in an experimental investigation of deformability of expanded polystyrene (EPS) under short-term compression are presented. The density of EPS varied from 13 to 28 kg/m³. The method of design of experiments was used to determine the elastic modulus and the ultimate strain (corresponding to the end of quasi-linear deformability) under compression stresses operating perpendicularly and parallel to the faces of EPS products. A graphical interpretation of the models is also presented. Based on the experimental data obtained, it was concluded that the expanded polystyrene was homogeneous in mutually perpendicular planes with respect to its deformability in compression. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 639–656, September–October, 2007.     

Boscovich's geometrical principle of continuity,and the “mysteries of the infinity”

In this paper we give a detailed account of Boscovich's geometrical principle of continuity. We also compare his ideas with those of his forerunners and successors, in order to cast some light on his possible sources of inspiration and to underline the elements of novelty in his approach to the subject.     

Existence for Semilinear Wave Equations with Low Regularity

In this paper, we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations utt-Δu=F(u, Du), u(0, x)=f(x)∈HS,(?)tu(0, x)=g(x)∈HS-1, where F is quadratic in Du with D = ((?)t,(?)x1,…,(?)xn). We proved that the range of s is s≥n 1/2 δ, respectively, withδ>1/4 if n = 2, andδ>0 if n = 3, andδ≥0 if n≥4. Which is consistent with Lindblad's counterexamples [3] for n = 3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.     

形变张量的特征值与Boussinesq方程组的正则性估计

讨论了二维及三维满足周期边界条件的Boussinesq方程初边值问题的局部正则解在有限时间内爆破的可能性.在二维情况下,用形变张量的特征值给出温度梯度的L²估计,从中看出若流体微团变形的速率大,则解爆破的可能性就大.在三维情况下,用形变张量的特征值和温度的偏导给出涡量的L²估计,从中发现若流体微团在大部分时间内一般是平面拉伸,且温度的偏导较小时,解爆破的可能性就大;若一般是线性拉伸,温度的偏导又不任意增大时,解爆破的可能性就小.