Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Lamb波频域逆散射全聚焦成像方法研究

Lamb波因其传播距离远、衰减小常被用于板状结构的无损检测中,在基于Lamb波损伤检测的诸多成像技术中,全聚焦方法(Total Focus Method,TFM)方法因其成像分辨率高、信噪比高而受青睐。然而Lamb波的频散效应导致时域延时量不能被准确计算,进而影响传统TFM方法对损伤定位及成像的精度;此外,既有的TFM方法仅以回波幅值作为成像指标,忽略了Lamb波与损伤的相互作用,故而不能通过损伤表面的物理参数增强成像质量。针对这两个问题,本文首先在时域TFM基础上发展了频域TFM,在计算中纳入频散关系以规避频散的影响;其次以包含明确的损伤特征参数--反射率为成像指标,结合频域TFM方法建立损伤逆散射模型,以实现对损伤的准确成像。仿真和实验结果表明:频域逆散射TFM成像方法能够实现对铝板结构中的损伤检测,在工程实践中具有应用价值。     

Diffraction mode selection in planar Bragg resonators of optical and microwave wavelength ranges

Using the coupled waves approach complemented by the time-domain quasi-optical approximation, we solve a 2D diffraction problem which allows to evaluate the eigenfrequencies, quality factors and spatial structures of eigenmodes in planar Bragg resonators with a finite length and width of the corrugated area. We find the values of the Fresnel parameter determined by the geometrical dimensions of the system which allows for efficient transverse mode discrimination due to the larger diffraction losses of the modes with higher transverse numbers.     

基于多通道盲识别的自适应光学图像事后处理

为实时恢复天文或空间目标的湍流退化成像,提出一种适应大气湍流动态变化的多通道自适应光学图像恢复方法.以自适应光学校正后不同时刻的目标成像作为多个通道,建立求解系统点扩散函数的线性方程,根据解出的点扩散函数利用超拉普拉斯算法,求解待观测目标的估计值.结果表明:不同时刻的点扩散函数之间存在互质关系,满足多通道盲识别的理论要求.利用建立的线性方程求解出的点扩散函数与原点扩散函数的均方误差在10^-30~10^-27量级,采用超拉普拉斯算法恢复出的目标成像与原始目标之间的均方误差在10^-5~10^-4量级.本文研究为湍流退化图像的实时恢复提供了理论基础.     

一种基于序贯估计的直达声区水面舰船 被动测距方法 *

该文利用基于射线的盲解卷积方法，从直达声区的水面舰船噪声中提取出船和锚系于海底的垂直接收阵之间的时域信道响应，并利用直达波在不同阵元相对于参考阵元的到达时间差，通过序贯方法，利用射线模型和声速剖面信息，对水面舰船距接收阵的距离进行了估计。通过处理海深约为580 m的2016年美国圣巴巴拉海峡的实验数据，对1.6~3.5 km直达声区范围内Anna Maersk商船与垂直阵之间的距离进行了估计，验证了测距方法的有效性，并将结果与系统测量值和几何方法的估计值进行了比较。由于该方法不需要对海底参数进行估计，所以在海底参数未知时要优于传统匹配场方法；在声速剖面存在跃层且海底为多层分布的复杂信道条件下，该方法仍能对距离进行有效估计，且与测量值的相对误差在6%以内，小于几何方法的估计误差，测距结果精度较高。     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Salt Metathesis: Tetrafluoroborate Anion Rapidly Fluoridates Organoboronic Acids to give Organotrifluoroborates

Tetrafluoroborate (BF₄⁻) has long been used as a spectator counter anion. Herein, we report an unprecedented salt metathesis between a variety of BF₄⁻ salts and a series of organoboronic acids yielding the corresponding organotrifluoroborates. We identified conditions for fast and efficient fluoridation (<1 h) with minimal workup. Fundamentally, this work discloses the proclivity of BF₄⁻ to exchange fluoride atoms with organoboronates, highlighting the lability of BF₄⁻.     

Dopant-free NiOx Nanocrystals: A Low-cost and Stable Hole Transport Material for Commercializing Perovskite Optoelectronics

Advancing inverted (p-i-n) perovskite solar cells (PSCs) is critical for commercial applications given their compatibility with different bottom cells for tandem photovoltaics, low-temperature processability (≤100 °C), and promising operational stability. Although inverted PSCs have achieved an efficiency of over 25 % using doped or expensive organic hole transport materials (HTMs), their synthesis cost and stability still cannot meet the requirements for their commercialization. Recently, dopant-free and low-cost non-stoichiometric nickel oxide nanocrystals (NiO_x NCs) have been extensively studied as a low-cost and effective HTM in perovskite optoelectronics. In this minireview, we summarize the synthesis and surface-functionalization methods of NiO_x NCs. Then, the applications of NiO_x NCs in other perovskite optoelectronics beyond photovoltaics are discussed. Finally, we provide a perspective for the future development of NiO_x NCs for the commercialization of perovskite optoelectronics.     

Self-Accelerating Diels–Alder Reaction for Preparing Polymers of Intrinsic Microporosity

It is a formidable challenge in polycondensation to simultaneously construct multiple covalent bonds to prepare double-stranded polymers of intrinsic microporosity (PIMs) with fused multicyclic linkages. To the best of our knowledge, this is the first study to develop a self-accelerating Diels–Alder reaction for successfully preparing double-stranded PIMs with fused multicyclic backbone structures. A self-accelerating Diels–Alder reaction was developed based on the [4+2] cycloaddition of sym-dibenzo-1,5-cyclooctadiene-3,7-diyne (DIBOD) and ortho-quinone compounds. In this reaction, the cycloaddition of ortho-quinone with the first alkyne of DIBOD activates the second alkyne, which reacts with ortho-quinone at a rate constant 192 times larger than that of the original alkyne. Using this self-accelerating reaction to polymerize DIBOD and spirocyclic/cyclic difunctional ortho-quinone monomers, a novel stoichiometric imbalance-promoted step-growth polymerization method was developed to prepare PIMs. The resultant PIMs possess intrinsic ultramicropores with pore sizes between 0.45 to 0.7 nm, high specific surface areas above 646 m² g⁻¹, and good H₂ separation performance.