On justification of Cu(II) environment in mononuclear complexes: Joint X-ray and AIM studies

Interaction of copper(II) acetate with benzoic acid (benzene-1,3,5-tricarboxylic acid = H₃-btc and 3,5-dinitro-benzoic acid = H-dnb) and pyridine (Py) resulted in two mononuclear square-planar complexes with the compositions [Cu(H₂-btc)₂(Py)₂] (1) and [Cu(dnb)₂(Py)₂] (2). The recrystallization of 2 from dimethylsulfoxide (DMSO) yielded the square-bipyramidal complex [Cu(dnb)₂(DMSO)₂(H₂O)₂] (3). Crystal structures of 1-3 were determined by single crystal X-ray diffraction at 100 K. The square-planar Cu(II) geometry with the Cu-O and Cu-N distances of 1.924(2), 1.925(2) and 2.024(3) and 2.025(3) Å in 1, and 1.930(4) and 2.033(5) Å in 2 was found. The extended H-bonding system in 1 built on the robust carboxylic synthons is giving rise to the high-ordered porous layered structure. Insight into metal center environment and stabilizing intramolecular short interactions is obtained through quantum theory of atoms in molecules (QTAIM). As revealed by QTAIM, in octahedral complex 3 Cu-dnb and Cu-DMSO bonds are stronger than Cu-N bonds in 1 and 2.     

离散的Burgers-Ginzburg-Landau方程组的吸引子

文章通过对空间变量的有限差分方法离散了具有周期边值的Ｂｕｒｇｅｒｓ Ｇｉｎｚｂｕｒｇ Ｌａｎｄａｕ方程组．研究了这个离散方程组初值问题解的适定性．证明了当差分网格足够大时离散方程组存在吸引子，并得到了吸引子的Ｈａｕｓｄｏｒｆｆ维数和分形维数的上界估计．这个上界不会随着网格的加细而无限增大，因此数值分析离散的有限维系统的吸引子可以近似探讨原无限维系统的吸引子．     

分数阶耦合Burgers方程组的同伦摄动解

本文利用同伦摄动法求关于时间Burgers方程组的二阶近似解,为了说明此方法的有效性我们利用Maple 14软件作出了整数阶耦合Burgers方程组的近似解和精确解的图像.结果表明此方法计算量小,避免了对系数的复杂讨论过程并且得出的近似解精确度较高.     

Transport behaviors and mechanisms in cuspidal blockade region for silicon single-hole transistor

The Si single-hole transistor displays the anomalously-extended cuspidal blockade region, which is elongated toward the 45°-tilted direction normal to gate vs. drain bias voltage regions in the Coulomb blockade diagram. This is attributed to the formation of an ultra small Si quantum dot (QD) into the gate-all-around (GAA) stack. Namely, the large one-electron-addition energy (= 447 meV) from the 2-nm-size Si QD enables the clear Coulomb-blockade events at room temperature, and the large voltage gain from the GAA stack allows the cuspidal extension of the blockade region through the renormalization of Coulomb-blockade energies at the adjacent bias points near the initial Coulomb-blockade state.     

Nonlinear differential identities for cnoidal waves

This article presents a family of nonlinear differential identities for the spatially periodic function , which is essentially the Jacobian elliptic function with one non‐trivial parameter . More precisely, we show that this function fulfills equations of the form for all . We give explicit expressions for the coefficients and for given s. Moreover, we show that for any s the set of functions constitutes a basis for . By virtue of our formulas the problem of finding a periodic solution to any nonlinear wave equation reduces to a problem in the coefficients. A finite ansatz exactly solves the KdV equation (giving the well‐known cnoidal wave solution) and the Kawahara equation. An infinite ansatz is expected to be especially efficient if the equation to be solved can be considered a perturbation of the KdV equation.     

Large-time behavior for the solution to the generalized Benjamin–Bona–Mahony–Burgers equation with large initial data in the whole-space

In this paper, we consider the global existence as well as the optimal decay estimates of the Cauchy problem for the multi-dimensional Benjamin–Bona–Mahony–Burgers equation with large initial data in the whole-space. And these results are obtained by Green?s function method, Fourier analysis method, energy estimates method combined with the time-frequency decomposition method.     

The Caputo–Fabrizio time-fractional Sharma–Tasso–Olver–Burgers equation and its valid approximations

Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention, in the last decades. The main aim of the current investigation is to consider the time-fractional Sharma–Tasso–Olver–Burgers (STOB) equation in the Caputo–Fabrizio (CF) context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method (HAM) and the Laplace transform. The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition for $\varphi \left(x,t;u\right)$ as the kernel and giving some theorems. To illustrate the CF operator effect on the dynamics of the obtained solitons, several two- and three-dimensional plots are formally considered. It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.     

Effect of transmitter positions on received power and bandwidth in diffuse indoor optical wireless systems

Diffuse Indoor Optical wireless systems (DIOWS) have potential applications in indoor WLAN. The major problems faced by these systems are their reduced bandwidth and restricted mobility caused by multi-path reflections from the indoor surfaces. These systems also suffer from non-uniform power distribution. Over the last decade several techniques have been suggested to circumvent these problems, most of them requiring complex trans-receiver design. One simple technique that can solve the non-uniformity problem is the use of multiple sources in place of a single source. In this paper we compare the received power levels on the floor computed using the extended ceiling bounce and the modified recursive models. The effect of multiple sources and their positions on the channel bandwidth is also analyzed. We show that the channel bandwidth for a given trans-receiver configuration depends on both the horizontal separation (between the transmitter and the receiver) and their actual positions.