A note on Keller-Osserman conditions on Carnot groups

This paper deals with the study of differential inequalities with gradient terms on Carnot groups. We are mainly focused on inequalities of the form Δ_φu≥f(u)l(|∇₀u|), where f, l and φ are continuous functions satisfying suitable monotonicity assumptions and Δ_φ is the φ-Laplace operator, a natural generalization of the p-Laplace operator which has recently been studied in the context of Carnot groups. We extend to general Carnot groups the results proved in Magliaro et al. (2011) [7] for the Heisenberg group, showing the validity of Liouville-type theorems under a suitable Keller-Osserman condition. In doing so, we also prove a maximum principle for inequality Δ_φu≥f(u)l(|∇₀u|). Finally, we show sharpness of our results for a general φ-Laplacian.     

Existence of traveling waves in compressible Euler equations with viscosity and capillarity

Given any Lax shock of the compressible Euler dynamics equations, we show that there exists the corresponding traveling wave of the system when viscosity and capillarity are suitably added. For a traveling wave corresponding to a given Lax shock, the governing viscous–capillary system is reduced to a system of two differential equations of first-order, which admits an asymptotically stable equilibrium point and a saddle point. We then develop the method of estimating attraction domain of the asymptotically stable equilibrium point for the compressible Euler equations and show that the saddle point in fact lies on the boundary of this set. Then, we establish a saddle-to-stable connection by pointing out that there is a stable trajectory leaving the saddle point and entering the attraction domain of the asymptotically stable equilibrium point. This gives us a traveling wave of the viscous–capillary compressible Euler equations.     

Electronic and Optical Properties of KNbO3,NaNbO3 and K0.5 Na0.5 NbO3 in Paraelectric Cubic Phase：a Comparative First-principles Study

The structural,electronic and optical properties of KNbO 3 (KN),NaNbO3(NN)and K05 Na0.5NbO3(KNN) in paraelectric cubic phase were calculated employing the plane-wave pseudopotential method based on density functional theory (DFT).The calculated electronic structures of the three crystals show similar features in the valence bands and the lower conduction bands.However,the structures in higher conduction bands differ markedly due to the effect of Na and K atoms.The calculated optical properties reveal that the features of optical spectrum at low energy are dominated by the transitions from O2p valence bands to Nb 4d conduction bands and those at high energy are related to the transitions to K 4s4p and/or Na 3s3p states.Moreover,the optical constants of KNN are approximately the average of KN and NN at high energy.Therefore,the optical properties of KNN in high energy region can probably be altered by changing the ratio of Na/K.     

一种冲击分离式颗粒浓度测量装置的设计

为测量大气中颗粒物的粒度浓度,本文在传统的冲击采样原理的基础上设计出冲击式分级装置,并对其进行严格定标;运用消光法原理对分级后的样品进行测量,利用反射镜增大光程提高装置测量灵敏度,实现了对大气中0～5μm、5～20μm、15～40μm三个粒径区间的数量密度和质量浓度的准确测量.     

利用广义不确定关系计算Reissner-Nordstrm-de Sitter黑洞的统计力学熵

利用广义不确定关系修正的态密度方程并采用Wentzel-Kramers-Brillouin(WKB)近似方法,计算了Reissner-Nordstrm-de Sitter(RNdS)黑洞时空中标量场的统计力学熵.结果表明,由这种方法得到的黑洞熵与它的内、外视界面积和宇宙视界面积之和成正比,这与采用其他方法所得的结果一致,从而揭示了黑洞熵与视界面积之间的内在联系,也进一步表明了黑洞熵是视界面上量子态的熵,是一种量子效应.     

BaTi2As2O电子结构的第一性原理研究

利用基于密度泛函理论的平面波赝势方法,研究BaTi2As2O的能带结构、费米面和态密度.发现:BaTi2As2O是一种非磁性金属,费米能级处的态密度主要来自Ti原子的3d电子,Ti 3d轨道和As 4p轨道有较强的杂化.没有发现其磁性基态,说明Ti原子上没有局域磁矩,与Pickett对Na2Ti2Sb2O的研究结论相吻合.     

无电刷法拉第模型电动机的动力学原理

法拉第电动机使用电刷改变流经转子线圈中电流的方向,若无电刷的情况下法拉第电动机似乎不能维持转动.事实上无电刷法拉第模型电动机在人为给转子线圈初始角动量的情况下却可以不停地转动.提出了转子线圈转轴跳动假设,给出无电刷法拉第模型电动机转动的动力学解释,并得到实验验证.     

Evolution of emergent C-points, L-lines, and C-lines in free space

Polarization singularities,which emerge from the incoherent superposition of two vector electric fields with the same frequency,and their evolution in free space are studied analytically and illustrated by numerical examples.It is shown that there exist C-points,L-lines,in particular,C-lines in incoherently superimposed two-dimensional wavefields.Usually,the C-lines are unstable and disappear during the free-space propagation.The motion,pair creation-annihilation process of the emergent C-points,as well as the distortion of the L-lines may take place,and the degree of polarization of the emergent C-points varies upon propagation and may be less than 1.     

Practical use of variational principles for modeling water waves

This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a ‘relaxed’ variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is particularly suitable for the construction of approximate water wave models, since it allows more freedom while preserving a variational structure. The advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters, as well as arbitrary depths. Using subordinate constraints (e.g., irrotationality or free surface impermeability) in various combinations, several model equations are derived, some being well-known, other being new. The models obtained are studied analytically and exact traveling wave solutions are constructed when possible.     

Combining approximate solutions for linear discrete ill-posed problems

Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the singular value decomposition is available. This paper proposes to compute several approximate solutions by standard methods and then extract a new candidate solution from the linear subspace spanned by the available approximate solutions. We also describe how the method may be used for large-scale problems.