The mixing time of the giant component of a random graph

We show that the total variation mixing time of the simple random walk on the giant component of supercritical and is . This statement was proved, independently, by Fountoulakis and Reed. Our proof follows from a structure result for these graphs which is interesting in its own right. We show that these graphs are “decorated expanders” — an expander glued to graphs whose size has constant expectation and exponential tail, and such that each vertex in the expander is glued to no more than a constant number of decorations. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 383–407, 2014     

33 W quasi-continuous-wave narrow-band sodium D_(2a) laser by sum-frequency generation in LBO

We demonstrate an all-solid quasi-continuous-wave （QCW） narrow-band source tunable to sodium D2a line at 589.159 nm. The source is based on sum-frequency mixing between lasers at 1064 nm and 1319 nm in a LBO crystal. The 1064 nm and 1319 nm lasers are produced from two diode side-pumped Nd：YAG master oscillator power amplifier （MOPA） laser systems, respectively. A 33 W output of 589 nm laser is obtained with beam quality factor M^2 = 1.25, frequency stability better than ±0.2 GHz and linewidth less than 0.44 GHz. A prototype 589 nm laser system is assembled, and a sodium laser guided star has been successfully observed in the field test.     

非接触四波混频技术测试InP单晶

利用四波混频(FWM)技术测试了非掺杂、掺Fe半绝缘InP单晶的光电特性,对载流子的产生、复合和输运等过程进行了研究,分析了深陷阱在载流子的产生与输运中的作用,并给予了解释。利用光栅衰减动力学得到在不同激发水平下非平衡自由载流子的扩散系数和复合时间。通过分析衍射效率和激发能量之间的相互关系,测定了缺陷的电学特性,即它们在光照下的传输和对载流子传输的贡献。这种技术可以通过测量时间和空间上的载流子分布,进而利用光学技术测试半导体材料的光电特性。     

改进的视频会议系统混音算法及实现

由嵌入式设备所构建的视频会议系统终端,在会话建立后,需要对来自各方的媒体信息诸如语音进行混音处理。在信令集中、媒体流分布的系统中,媒体的混合没有独立出来放在Focus中,而是将与会的各终端发来的语音媒体流在会议参与者主机上实现端混合。在众多混音方案的比对中,这里介绍一种改进的符合语音信号特征的混音架构及溢出处理算法,并用语音信号的短时能量及短时过零率对混音过程进行动态修正。在嵌入式系统的实现验证中表明,该算法提高了混音溢出处理的效率,降低了噪音,具有较低的算法复杂度,并有良好的听觉舒适感。     

A stable optical comb with double-Brillouin-frequency spacing assisted by multiple four-wave mixing processes

A stable optical comb with a double-Brillouin-frequency spacing, employing a 2.5-km common single mode fiber (SMF) is proposed and demonstrated experimentally. The simultaneous existence of the first-order and third-order Stokes within the ring cavity excites the higher-order Stokes and anti-Stokes via multiple four-wave mixing (FWM) processes. Ten odd-order Stokes, nine odd-order anti-Stokes and a second-order Stokes signal with a wavelength spacing of 0.172 nm (∼20 GHz) are simultaneously achieved at a Brillouin pump (BP) level of 160 mW. The maximum power fluctuation of the proposed optical comb is less than 1 dB at room temperature within 100 min. The optical comb can show a good stability and flexibility in the choice of operating wavelength.     

“Greener” chemical syntheses using mechanochemical mixing or microwave and ultrasound irradiation

Abstract

Various emerging “greener” strategic pathways, researched primarily in the author's own laboratory, are summarized. They include solvent-free mechanochemical methods that involve the use of hypervalent iodine reagents at room temperature for the synthesis of heterocyclic entities, and useful conversion of ketones into β-keto sulfones and their α-tosyloxy derivatives in high yields. A solvent-free approach that involves microwave (MW) exposure of neat reactants (undiluted) catalyzed by the surfaces of less-expensive and recyclable mineral supports, such as alumina, silica, clay, or “doped” surfaces, is described; it is applicable to a wide range of cleavage, condensation, cyclization, rearrangement, oxidation, and reduction reactions, including rapid one-pot assembly of heterocyclic compounds from in situ generated reactive intermediates. The strategy is adaptable to multi-component reactions, e.g. Ugi and Biginelli reactions, for rapid assembly of a library of compounds. Synthesis of a wide variety of significant precursors and intermediates, namely enones, imines, enamines, nitroalkenes, and oxidized sulfur species, is possible and their value in concise MW synthesis of 2-aroylbenzofurans and thiazole derivatives is illustrated. Ultrasound- and MW-assisted solventless preparation of ionic liquids and their application in alkylation and metal-catalyzed multi-component reactions are described. With a view to consume greenhouse gas, carbon dioxide (CO₂), efficient reaction of epoxides with CO₂ provides ready access to cyclic carbonates using only a catalytic amount of recyclable indium-based ionic liquid. MW heating in aqueous reaction media enables expeditious N-alkylation reactions of amines and hydrazines to afford a series of heterocyclic ring systems, such as N-azacycloalkanes, 4,5-dihydropyrazoles, and pyrazolidines. A general and expeditious MW-enhanced nucleophilic substitution approach uses easily accessible starting materials such as halides or tosylates in reaction with alkali azides, thiocyanates, or sulfinates in the absence of any phase transfer catalyst to produce azides, thiocyanates, and sulfones, respectively, wherein a variety of reactive functional groups are tolerated. A three-component condensation (MCC) approach for the synthesis of useful 2-amino-2-chromenes is described using a recyclable nanosized magnesium oxide catalyst in aqueous poly (ethylene glycol) (PEG) medium at room temperature. A general greener approach to shape-selective generation of nanomaterials is summarized including their potential application as nanocomposites.     

Fiber‐based light sources for biomedical applications of coherent anti‐Stokes Raman scattering microscopy

During the past decade coherent anti‐Stokes Raman scattering (CARS) microscopy has evolved to one of the most powerful imaging techniques in the biomedical sciences, enabling the label‐free visualization of the chemical composition of tissue in vivo in real time. While the acquisition of high‐contrast images of single cells up to large tissue sections enables a wide range of medical applications from routine diagnostics to surgical guidance, to date CARS imaging is employed in fundamental research only, essentially because the synchronized multiple wavelength pulsed laser sources required for CARS microscopy are large, expensive and require regular maintenance. Laser sources based on optical fibers can overcome these limitations combining highest efficiency and peak powers with an excellent spatial beam profile and thermal stability. In this review we summarize the different fiber‐based approaches for laser sources dedicated to coherent Raman imaging, in particular active fiber technology and passive fiber‐based frequency conversion processes, i.e. supercontinuum generation, soliton self‐frequency shift and four‐wave mixing. We re‐evaluate the ideal laser parameters for CARS imaging and discuss the suitability of different laser concepts for turn‐key operation required for routine application in clinics.

     

Variational learning for finite Beta-Liouville mixture models

In the article, an improved variational inference （VI） framework for learning finite Beta-Liouville mixture models （BLM） is proposed for proportional data classification and clustering. Within the VI framework, some non-linear approximation techniques are adopted to obtain the approximated variational object functions. Analytical solutions are obtained for the variational posterior distributions. Compared to the expectation maximization （EM） algorithm which is commonly used for learning mixture models, underfitting and overfitting events can be prevented. Furthermore, parameters and complexity of the mixture model （model order） can be estimated simultaneously. Experiment shows that both synthetic and real-world data sets are to demonstrate the feasibility and advantages of the proposed method.     

改善显示品质的直下式LED背光技术

通过理论分析,在窄色域液晶屏的背光中选择合适谱线的RGB三基色LED背光,可以将显示器的色域从40%提升至70%。试验结果与理论相符合,但是三基色直下式背光的混光比为1.3∶1,比全白灯背光的1∶1大。在三基色LED背光中加入LED白灯,能够降低混光比。白光灯的亮度逐步增加时,色域会降低。当色域从70.2%下降到63.7%时,白灯发出的亮度占总亮度的30%,混光比也降低为1.1∶1。     

Well-posedness and exponential mixing for stochastic magneto-hydrodynamic equations with fractional dissipations

Consider d-dimensional magneto-hydrodynamic (MHD) equations with fractional dissipations driven by multiplicative noise. First, we prove the existence of martingale solutions for stochastic fractional MHD equations in the case of d = 2, 3 and \alpha \wedge \beta \rangle \mathrm{0}, where \alpha ,\beta are the parameters of the fractional dissipations in the equation. Second, for d = 2, 3 and \alpha \wedge \beta \ge {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}+{\displaystyle \frac{d}{\mathrm{4}}}, we show the pathwise uniqueness of solutions and then obtain the existence and uniqueness of strong solutions using the Yamada-Watanabe theorem. Furthermore, we establish the exponential mixing property for stochastic MHD equations with degenerate multiplicative noise when d = 2, 3 and \alpha \wedge \beta \ge {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}+{\displaystyle \frac{d}{\mathrm{4}}}.