Zn-catalyzed growth processes and ferromagnetism of Mn-doped ZnO nanorods on Si substrate

Well-aligned ZnO nanorods and Mn-doped ZnO nanorods are fabricated on Si (1 0 0) substrate according to the contribution of Zn metal catalysts. Scanning electron microscopy and high-resolution transmission electron microscopy images indicate that the influence of Zn catalyst on the properties of ZnO can be excluded and the growth of ZnO nanorods follows a vapor-liquid-solid and self-catalyzed model. Mn-doped ZnO nanorods show a typical room temperature ferromagnetic characteristic with a saturation magnetization (M_S) of 0.273μ_B/Mn. Cathodoluminescence suggests that the ferromagnetism of Mn-doped ZnO nanorods originates from the Mn²⁺-Mn²⁺ ferromagnetic coupling mediated by oxygen vacancies. This technique provides exciting prospect for the integration of next generation Si-technology-based ZnO spintronic devices.     

非线性随机延迟微分方程Heun方法的数值稳定性

本文讨论一般非线性随机延迟微分方程Heun方法的数值稳定性,证明了如果问题本身满足零解是均方指数稳定和均方渐近稳定的充分条件,则当方程的漂移项进一步满足一定的条件时,Heun方法是Ms.稳定的,带线性插值的Heun方法是均方指数稳定的和GMS-稳定的理论结果.文末的数值试验进一步验证了所得的相关结论.     

循环图C(12,2)与路P_n的笛卡尔积的交叉数

循环图C(m,2)表示由圈Cm(v_1v_2…v_mv_1)增加边v_iv_i+2(i=1,2,…,m,i+2(modm))所得到的图,本文证明了循环图C(12,2)与路P_n的笛卡尔积的交叉数是12n.     

Superconvergence of a combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem

A combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem which includes molecular diffusion and dispersion in porous media is investigated. That is to say, the mixed finite element method with Raviart-Thomas space is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin (SIPG) approximation. Based on projection interpolations and induction hypotheses, a superconvergence estimate is obtained. During the analysis, an extension of the Darcy velocity along the Gauss line is also used in the evaluation of the coefficients in the Galerkin procedure for the concentration.     

One-step Synthesis of ε-Caprolactam by the Liquid Phase Nitrosation of Cyciohexane over the Catalysts Containing CH3COO-or-COOH

ε-Caprolactam（CL or CPL） is one of the most important intermediates used in polymer industry for the production of several million tons of nylon-6 every year^[1]. All current commercial processes for the production of caprolactam are based on either benzene or tolueneI21. Caprolactam is synthesized by the Beckmann rearrangement of cyclohexanone oxime with fuming sulfuric acid or sulfuric acid as the reaction medium, and cyclohexanone oxime is produced by the reaction between cyclohexanone and hydro- xylamine（only one exception is the Toray PNC process）.     

Light transmission through metal films perforated with arrays of asymmetric cross-shaped hole

The transmission characteristics of metallic film perforated with an array of asymmetric cross-shaped hole are studied by using the three-dimensional finite difference time-domain method. We find that the wavelengths and intensities of transmission peaks depend strongly on the asymmetric parameters of the cross-shaped hole. The transmission peaks in the structure of asymmetric cross-shaped hole array originate from the splitting of the transmission peak in the corresponding one of symmetric cross-shaped hole array. Moreover, it is also found that the transmission spectra can be adjusted by changing other geometrical parameters of asymmetric cross-shaped hole due to the their effect on the distribution of the oscillating charges on metal surfaces.     

Error estimates of triangular mixed finite element methods for quasilinear optimal control problems

The goal of this paper is to study a mixed finite element approximation of the general convex optimal control problems governed by quasilinear elliptic partial differential equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a priori error estimates both for the state variables and the control variable. Finally, some numerical examples are given to demonstrate the theoretical results.     

A note on Bartholdi zeta function and graph invariants based on resistance distance

Let $G$ be a finite connected graph. In this note, we show that the complexity of $G$ can be obtained from the partial derivatives at $(1?\frac{1}{t},t)$ of a determinant in terms of the Bartholdi zeta function of $G$. Moreover, the second order partial derivatives at $(1?\frac{1}{t},t)$ of this determinant can all be expressed as the linear combination of the Kirchhoff index, the additive degree-Kirchhoff index, and the multiplicative degree-Kirchhoff index of the graph $G$.     

Generalizations of the Krasnoselskii fixed point theorem

We obtain new generalized forms of the Krasnoselskii theorem on fixed points for a sum of two operators and show that our new results encompass a number of previously known generalizations of the theorem.