Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.     

Tighter uncertainty principles for periodic signals in terms of frequency

In this study, we propose some new uncertainty principles for periodic signals with sharper lower bounds than those in the existing ones. The improved lower bounds, in particular, are related to the frequency of the signal. Three examples are employed to demonstrate sharpness of the new uncertainty principles. Copyright © 2014 John Wiley & Sons, Ltd.     

基于思维模型建构的高三化学复习教学*—— 以“平衡原理的应用”为例

以高三复习课“平衡原理的应用”为例,通过真实情境的剖析让学生感知模型,引导学生分析归纳提炼模型,并进行针对练习运用模型,变式训练体会模型,让学生在实践中以模型思维为突破,深入领悟建构模型的实质,有序解决复杂化学问题,提升科学思维能力,发展化学学科核心素养。     

Positive numerical splitting method for the Hull and White 2D Black–Scholes equation

We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015     

Large Hexagonal Bi‐ and Trilayer Graphene Single Crystals with Varied Interlayer Rotations

Bi‐ and trilayer graphene have attracted intensive interest due to their rich electronic and optical properties, which are dependent on interlayer rotations. However, the synthesis of high‐quality large‐size bi‐ and trilayer graphene single crystals still remains a challenge. Here, the synthesis of 100 μm pyramid‐like hexagonal bi‐ and trilayer graphene single‐crystal domains on Cu foils using chemical vapor deposition is reported. The as‐produced graphene domains show almost exclusively either 0° or 30° interlayer rotations. Raman spectroscopy, transmission electron microscopy, and Fourier‐transformed infrared spectroscopy were used to demonstrate that bilayer graphene domains with 0° interlayer stacking angles were Bernal stacked. Based on first‐principle calculations, it is proposed that rotations originate from the graphene nucleation at the Cu step, which explains the origin of the interlayer rotations and agrees well with the experimental observations.     

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

Viscoelastic materials with a double porosity structure

This paper in concerned with the linear theory of materials with memory that possess a double porosity structure. First, the formulation of the initial-boundary-value problem is presented. Then, a uniqueness result is established. The semigroup theory of linear operators is used to prove existence and continuous dependence of solutions. A minimum principle for the dynamical theory is also derived.     

U原子和CO反应机理的第一性原理的理论研究

在有关实验结果的基础上提出了U原子和CO分子的各种可能反应通道, 然后采用第一性原理对反应通道上的各物种的几何构型、谐振频率以及总能量进行了计算和研究, 计算结果表明, 初级和次级反应的稳定产物分别为CUO和(η²-C₂)UO₂. 提出了最可能反应通道为U原子以C端或侧位进攻CO分子引起反应, 并用分子轨道理论解释了该反应机理.     

Determination of the arc-root position in a DC plasma torch

The behavior of an arc operated in the nontransferred mode with a conical-shaped cathode and a nozzle-shaped anode is studied by applying general tyro-dimensional conservation equations and auxiliary relations for the simulation of arc channel flows. The position of the arc-root attachment at the anode surface is determined by using Steenbeck's minimum principle, which postulates a minimum arc voltage for a given current and certain given boundary conditions. The overall effects of the anode-arc root on the plasma flow are, studied by comparing the results with those of the transferred mode of operation. Specific arc-channel diameters are chosen in the simulation in order to verify flit, numerical model through comparisons with experimental results. The results show that Steenbeck's minimum principle is useful for determining the position of the arc-root attachment at the anode surface. Application of this method for control of the arc-anode attachment may be valuable in the design and operation of plasma spray torches to avoid jet instabilities.