Simple and flexible generation of vestigial side band modified duobinary return-to-zero signals at 10, 20 and 40 Gb/s

We propose and demonstrate a simple and flexible approach to generate vestigial side band modified duobinary return-to-zero (VSB MD-RZ) signals at 10-40 Gb/s, using a dual-drive Mach-Zehnder modulator and a detuned optical band-pass filter. The performance of the proposed VSB MD-RZ signal is investigated by comparing with double side band MD-RZ (DSB MD-RZ) and conventional VSB MD-RZ. Bit error ratio (BER) measurement at 10 Gb/s shows an error free operation for the generated signal. Good performance is further observed after 100 km of single-mode-fiber transmission at 40 Gb/s.     

High-pressure differential thermal analysis measurements of the melting curve of lithium

The pressure effect on the melting behavior of lithium has been measured by observing the latent heat signatures of melting and freezing using differential thermal analysis (DTA). Samples were repeatedly melted and recrystallized at selected pressures up to 15 GPa in a multianvil press. Despite the weak DTA signals due to small sample sizes at high pressure, the melting and freezing temperatures were clearly determined from the derivatives of the DTA traces. We measured a drop in the melting temperature between 9 and 12 GPa, yielding a maximum at 10(2) GPa and 245(2) ^°C. This work highlights both the successes and failures of recent theoretical models for the melting behavior of this and related systems.     

Optimal design of a multilayer diffractive optical element for dual wavebands

A method for optimal design of a multilayer diffractive optical element (MLDOE) for dual-wide-waveband optical systems is presented with consideration of polychromatic integral diffraction efficiency (PIDE) and the weight factors of PIDE for each waveband. The design process and simulation of a MLDOE in mid-wave and long-wave IR are described, and the comparison of diffraction efficiency of the MLDOEs for different design wavelength pairs determined by different methods is given. This method can make the design process more rational and more reasonable and can give a better design result than that with the conventional design method.     

On the Laplacian spectral characterization of Π-shape trees

A Π-shape tree is a tree with exactly two vertices having the maximum degree three. In this paper, we classify the Π-shape trees into two types, and complete the spectral characterization for one type. Exactly, we prove that all graphs of this type are determined by their Laplacian spectra with some exceptions. Moreover, we give some L-cospectral mates of some graphs for another type.     

The extended Riccati equation method for travelling wave solutions of ZK equation

In this article, the extended Riccati equation method is applied to seeking more general exact travelling wave solutions of the ZK equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. When the parameters are taken as special values, the solitary wave solutions are obtained from the hyperbolic function solutions. Similarly, the periodic wave solutions are also obtained from the trigonometric function solutions. The approach developed in this paper is effective and it may also be used for solving many other nonlinear evolution equations in mathematical physics.     

交货期差异下的双渠道订货与协调优化策略

由于顾客往往具有不同交货期的期望,从而导致线上与线下渠道冲突加剧,同时也为其进行合作提供了基础。因此针对该问题,以一个开辟线上渠道的制造商和一个线下零售商组成的双渠道供应链系统为研究对象,分别建立了考虑交货期差异下二者合作时的利润优化模型。在此基础上,首先采用不动点定理证明了制造商开辟的线上渠道与线下零售商订货纳什均衡的存在性与唯一性,并探讨了二者均衡订货量与交货期差异率的关系;其次,证明了仅仅采用批发价格与服务费用契约无法协调制造商与线下零售商组成的供应链系统,进一步优化设计了两部定价协调机制,并实现二者的双赢。最后通过算例证明了纳什均衡的存在性以及订货均衡与交货期差异率的关系。     

不同权力结构对制造商双渠道供应链的影响研究

在一个制造商和一个零售商组成的供应链中, 制造商拥有线下传统渠道及线上直销双渠道。首先根据消费者剩余理论, 构建了制造商双渠道需求函数;接着分别构建了两类Stackelberg博弈及Nash博弈三种权力结构下制造商和零售商的利润模型并对模型进行了求解;最后分析了三种不同权力结构对制造商双渠道供应链的影响。研究发现:制造商线上直销渠道价格不受三种博弈权力结构的影响;线下传统渠道零售价格、需求, 线上直销渠道需求及制造商双渠道供应链总利润不受两类Stackelberg博弈权力结构的影响;线下传统渠道零售价格及线上直销渠道需求在Nash博弈权力结构下最小, 而线下传统渠道需求及供应链总利润在Nash博弈权力结构下最大;制造商批发价格、利润及零售商利润对三种博弈权力结构较敏感, 随供应链成员自身博弈权力地位的下降而逐渐降低。     

阻尼Navier-Stokes系统的渐近吸引子

本文通过构造一个有限维解序列,研究了二维阻尼驱动Navier-Stokes方程的渐近吸引子,并证明了该解序列在长时间内无限逼近全局吸引子,最后给出了渐近吸引子的维数估计.     

The Sobolev Stability Threshold for 2D Shear Flows Near Couette

We consider the 2D Navier–Stokes equation on \(\mathbb T \times \mathbb R\), with initial datum that is \(\varepsilon \)-close in \(H^N\) to a shear flow (U(y), 0), where \(\Vert U(y) - y\Vert _{H^{N+4}} \ll 1\) and \(N>1\). We prove that if \(\varepsilon \ll \nu ^{1/2}\), where \(\nu \) denotes the inverse Reynolds number, then the solution of the Navier–Stokes equation remains \(\varepsilon \)-close in \(H^1\) to \((e^{t \nu \partial _{yy}}U(y),0)\) for all \(t>0\). Moreover, the solution converges to a decaying shear flow for times \(t \gg \nu ^{-1/3}\) by a mixing-enhanced dissipation effect, and experiences a transient growth of gradients. In particular, this shows that the stability threshold in finite regularity scales no worse than \(\nu ^{1/2}\) for 2D shear flows close to the Couette flow.