Free control of far-field scattering angle of transmission terahertz wave using multilayer split-ring resonators’ metasurfaces

To enhance transmission efficiency of Pancharatnam–Berry (PB) phase metasurfaces, multilayer splitring resonators were proposed to develop encoding sequences. As per the generalized Snell’s law, the deflection angle of the PB phase encoding metasurfaces depends on the metasurface period’s size. Therefore, it is impossible to design an infinitesimal metasurface unit; consequently, the continuous transmission scattering angle cannot be obtained. In digital signal processing, this study introduces the Fourier convolution principle on encoding metasurface sequences to freely control the transmitted scattering angles. Both addition and subtraction operations between two different encoding sequences were then performed to achieve the continuous variation of the scattering angle. Furthermore, we established that the Fourier convolution principle can be applied to the checkerboard coded metasurfaces.     

New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Generating Artificial Reverberation via Genetic Algorithms for Real-Time Applications

We introduce a Virtual Studio Technology (VST) 2 audio effect plugin that performs convolution reverb using synthetic Room Impulse Responses (RIRs) generated via a Genetic Algorithm (GA). The parameters of the plugin include some of those defined under the ISO 3382-1 standard (e.g., reverberation time, early decay time, and clarity), which are used to determine the fitness values of potential RIRs so that the user has some control over the shape of the resulting RIRs. In the GA, these RIRs are initially generated via a custom Gaussian noise method, and then evolve via truncation selection, random weighted average crossover, and mutation via Gaussian multiplication in order to produce RIRs that resemble real-world, recorded ones. Binaural Room Impulse Responses (BRIRs) can also be generated by assigning two different RIRs to the left and right stereo channels. With the proposed audio effect, new RIRs that represent virtual rooms, some of which may even be impossible to replicate in the physical world, can be generated and stored. Objective evaluation of the GA shows that contradictory combinations of parameter values will produce RIRs with low fitness. Additionally, through subjective evaluation, it was determined that RIRs generated by the GA were still perceptually distinguishable from similar real-world RIRs, but the perceptual differences were reduced when longer execution times were used for generating the RIRs or the unprocessed audio signals were comprised of only speech.     

Everything you wanted to know about phase and reference frequency in one- and two-dimensional NMR spectroscopy

The fundamental concept of phase discussed in this tutorial aimed at providing students with an explanation of the delays and processing parameters they may find in nuclear magnetic resonance (NMR) pulse programs. We consider the phase of radio-frequency pulses, receiver, and magnetization and how all these parameters are related to phases and offsets of signals in spectra. The impact of the off-resonance effect on the phase of the magnetization is discussed before presenting an overview of how adjustment of the time reference of the free induction decay avoids first-order correction of the phase of spectra. The main objective of this tutorial is to show how the relative phase of a pulse and the receiver can be used to change the reference frequency along direct and indirect dimensions of NMR experiments. Unusual of phase incrementation with non-90° angles will be illustrated on one- and two-dimensional NMR spectra.     

深度卷积网络的多品种多厂商药品近红外光谱分类

近红外光谱（NIR）分析具有分析高效、样品无损、环境无污染以及可现场检测等优点，特别适合药品的快速建模分析。但NIR存在吸收强度弱以及谱带重叠等缺点，需要建立稳健可靠的化学计量学模型对其进行分析。深度卷积神经网络是深度学习方法中一个重要分支，它通过逐层抽取数据特征并进行组合、转换，形成更高层的语义特征，具有极强的建模能力，广泛应用于计算机视觉、语音识别等领域，而在药品NIR分析方面尚未见报道。基于深度卷积网络模型，对药品NIR多分类建模进行研究。针对药品NIR数据的特点，设计若干个面向多品种、多厂商药品NIR分类的一维深度卷积网络模型。模型中卷积层和池化层交叠排列用于逐层抽取NIR数据特征，输出层连接softmax分类器，对药品NIR数据进行分类概率预测。在输出层之前采用全局最大池化层，将特征图进行整体池化，形成一个特征点，用于解决全连接层存在的限制输入维度大小，参数过多的问题。同时，在网络模型中引入批处理操作和dropout机制，以防止梯度消失和减小网络过拟合的风险。在网络模型的设计过程中，通过设计不同的卷积网络层数以及不同的卷积核尺寸大小，分析其对建模效果的影响，同时分析五种经典数据预处理方法对NIR分析的影响。以我国7个厂商生产的头孢克肟片和11个厂商生产的苯妥英钠片样本NIR为实验对象， 建立药品的多品种、多厂商分类模型，该模型在二分类、多分类实验中取得了良好的分类效果。在十八分类实验中，当训练集与测试集比例为7∶3时，分类准确率为99.37±0.45，比SVM, BP, AE和ELM算法取得更优的分类性能。同时，深度卷积神经网络模型推理速度较快，优于SVM和ELM算法，但训练速度慢于二者。大量实验结果表明，深度卷积神经网络可对多品种、多厂商药品NIR数据准确、可靠地判别分类，且模型具有良好的鲁棒性和可扩展性。该方法也可推广到烟草、石化等其他领域的NIR数据分类应用中。     

非齐次动力学方程的一种精细积分单步方法

针对非齐次动力学方程■,结合精细积分法和微分求积法,利用同阶的显式龙格-库塔法对计算过程中待求的v_(k+i/s)(i=1,2,…,s)进行预估,提出了一种避免状态矩阵求逆的高效精细积分单步方法。该方法采用精细积分法计算e~(Ht),而Duhamel积分项采用s级s阶的时域微分求积法,计算格式统一且易于编程,可灵活实现变阶变步长。仿真结果表明,与其他单步法及预估校正-辛时间子域法进行数值比较,该方法具有高精度、高效率及良好的稳定性,在求解大规模动力系统时间响应问题中具有较大的优势。     

黏弹性接触界面端附近的奇异应力场

研究蠕变加载条件下线黏弹性材料接触界面端附近的奇异应力场问题.考虑接触界面的摩擦,假设界面端的滑移方向不改变,相对滑移量微小,且其与位移同量级,由此线性化局部边界条件,根据对应原理得到Laplace变换域中的界面端应力场,导出时域中奇异应力场的卷积积分表达式.对卷积积分核函数进行数值反演,考虑接触材料的两类组合,一是持久模量具有量级上的差异,另一是持久模量接近相同.算例结果证实核函数可以用准弹性法求得的解析式较准确地近似.在此基础上,利用积分中值定理,并引入各应力分量的修正系数,得到黏弹性奇异应力场的简化式.结合核函数的数值反演结果分析修正系数表达式的取值范围,得到如下结论,若两相接触材料的持久模量相差很大,可以采用准弹性解的解析式较准确地描述界面端的奇异应力场;一般情况下,应力场不存在统一的奇异值和应力强度系数,当采用类似于准弹性解的表达式近似给出黏弹性应力场时,可以估计此近似描述的误差限.文中最后采用有限元分析黏弹性板端部嵌入部位的应力场,算例包括了黏弹性板与弹性金属支承、黏弹性板与黏弹性垫层所形成的滑移接触界面端,利用黏弹性有限元的数值结果验证理论分析所得结论的有效性.      

Closed‐form approximations for spread options in Lévy markets

We provide new closed‐form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, ie, when log‐returns are modeled as Brownian motions (Black‐Scholes model), variance gamma processes (VG model), or normal inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well‐known Margrabe formula (1978) that is valid in a Black‐Scholes model to the VG model under a homogeneity assumption.     

Stable blow-up dynamics in the -critical and -supercritical generalized Hartree equation

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: First, we consider the -critical case in dimensions and obtain that a generic blow-up has a self-similar structure and exhibits not only the square root blowup rate , but also the log-log correction (via asymptotic analysis and functional fitting), thus, behaving similarly to the stable blow-up regime in the -critical nonlinear Schrödinger equation. In this setting, we also study blow-up profiles and show that generic blow-up solutions converge to the rescaled , a ground state solution of the elliptic equation . We also consider the -supercritical case in dimensions . We derive the profile equation for the self-similar blow-up and establish the existence and local uniqueness of its solutions. As in the NLS -supercritical regime, the profile equation exhibits branches of nonoscillating, polynomially decaying (multi-bump) solutions. A numerical scheme of putting constraints into solving the corresponding ordinary differential equation is applied during the process of finding the multi-bump solutions. Direct numerical simulation of solutions to the generalized Hartree equation by the dynamic rescaling method indicates that the is the profile for the stable blow-up. In this supercritical case, we obtain the blow-up rate without any correction. This blow-up happens at the focusing level , and thus, numerically observable (unlike the -critical case). In summary, we find that the results are similar to the behavior of stable self-similar blowup solutions in the corresponding settings for the nonlinear Schrödinger equation. Consequently, one may expect that the form of the nonlinearity in the Schrödinger-type equations is not essential in the stable formation of singularities.