New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

Preparation,structure elucidation,and antioxidant activity of new bis(thiosemicarbazone) derivatives

Schiff-base–bearing new bis(thiosemicarbazone) derivatives were prepared from terephthalaldehyde and various thiosemicarbazides. FT–IR, ¹H NMR, ¹³C NMR, and UV–Vis spectroscopic methods and elemental analysis were used to elucidate the identification of the synthesized molecules. The in vitro antioxidant activity of the synthesized compounds was analysed with the 1,1-diphenyl-2-picryl hydrazyl free-radical–trapping process. The synthesized compounds exhibited lower antioxidant activity than the standard ascorbic acid. IC₅₀ values of the synthesized molecules measured from 3.81 ± 0.01 to 29.05 ± 0.11 μM. Among the synthesized compounds, compound 3 had the best antioxidant activity. Moreover, this study explained the structure–activity relationship of the synthesized molecules with different substituents in radical trapping reactions.     

Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.     

小直径棒材超声横波检测仿真分析

采用超声水浸聚焦斜入射方式进行小棒材表面、近表缺陷检测时,声波在水/棒和棒/缺陷界面会发生反射、折射、散射、衍射及波形转换等一系列物理变换。此时缺陷可检性对声波入射条件十分敏感,常出现由于检测条件设置不当而导致缺陷漏检、误检的情况。为解决这一问题,本文针对小棒材超声斜入射检测中的主要参数——入射角和水距,开展声场及缺陷声响应仿真,研究检测参数对不同部位缺陷检测能力的影响,并对仿真结果进行试验验证。通过研究得到了检测水距、入射角度对缺陷检测能力的影响,并得到最优检测条件。试验验证结果表明研究制定的检测方案可有效检测出表面、近表面裂纹缺陷。     

Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.     

语音通信降噪研究

语音通信系统中，语音通过信道传输将不可避免地引入码间串扰和信号畸变，同时受到噪声污染。本文在分析自适应盲均衡算法CMA(constant modulus algorithm）和改进盲均衡算法的基础上，考虑到自适应盲均衡技术在语音噪声控制方面能力有限，将自适应盲均衡技术与小波包掩蔽阈值降噪算法联合使用，形成一种基带语音增强新方法。仿真试验结果显示自适应盲均衡技术可以使星座图变得清晰而紧凑，有效减小误码率。研究证实该方法在语音信号ISI和畸变严重情况下，在白噪及有色噪声不同的噪声环境中都具有稳定的降噪能力，消噪同时可获得汉语普通话良好的听觉效果。     

A Biosilification Fusion Protein for a ‘Self‐immobilising’ Sarcosine Oxidase Amperometric Enzyme Biosensor

Monomeric sarcosine oxidase (mSOx) fusion with the silaffin peptide, R5, designed previously for easy protein production in low resource areas, was used in a biosilification process to form an enzyme layer electrode biosensor. mSOx is a low activity enzyme (10–20 U/mg) requiring high amounts of enzyme to obtain an amperometric biosensor signal, in the clinically useful range <1 mM sarcosine, especially since the K_m is >10 mM. An amperometric biosensor model was fitted to experimental data to investigate dynamic range. mSOx constructs were designed with 6H (6×histidine) and R5 (silaffin) peptide tags and compared with native mSOx. Glutaraldehyde (GA) cross‐linked proteins retained ～5 % activity for mSOx and mSOx‐6H and only 0.5 % for mSOx‐R5. In contrast R5 catalysed biosilification on (3‐mercaptopropyl) trimethoxysilane (MPTMS) and tetramethyl orthosilicate (TMOS) particles created a ‘self‐immobilisation’ matrix retaining 40 % and 76 % activity respectively. The TMOS matrix produced a thick layer (>500 μm) on a glassy carbon electrode with a mediated current due to sarcosine in the clinical range for sarcosinemia (0–1 mM). The mSOx‐R5 fusion protein was also used to catalyse biosilification in the presence of creatinase and creatininase, entrapping all three enzymes. A mediated GC enzyme linked current was obtained with dynamic range available for creatinine determination of 0.1–2 mM for an enzyme layer ～800 nm.     

Comparative study on transport properties of N-, P-, and As-doped SiC nanowires: Calculated based on first principles

According to the one-dimensional quantum state distribution, carrier scattering, and fixed range hopping model, the structural stability and electron transport properties of N-, P-, and As-doped SiC nanowires(N-SiCNWs, P-SiCNWs, and As-SiCNWs) are simulated by using the first principles calculations. The results show that the lattice structure of NSiCNWs is the most stable in the lattice structures of the above three kinds of doped SiCNWs. At room temperature,for unpassivated SiCNWs, the doping effect of P and As are better than that of N. After passivation, the conductivities of all doped SiCNWs increase by approximately two orders of magnitude. The N-SiCNW has the lowest conductivity. In addition, the N-, P-, As-doped SiCNWs before and after passivation have the same conductivity–temperature characteristics,that is, above room temperature, the conductivity values of the doped SiCNWs all increase with temperature increasing.These results contribute to the electronic application of nanodevices.