融合图卷积神经网络和注意力机制的PM2.5小时浓度多步预测

PM_2.5小时浓度多为单步预测。为实现PM_2.5小时浓度的多步预测，基于“编码器-解码器”的序列-序列预测（Seq2Seq）模型，集合图卷积神经网络提取非欧式空间数据特征的能力以及注意力机制自适应关注特征的能力，提出了融合图卷积神经网络和注意力机制的PM_2.5小时浓度多步预测（GCN_Attention_Seq2Seq）模型。并与Seq2Seq模型和使用了图卷积神经网络、未使用注意力机制的GCN_Seq2Seq模型进行了对照，以2015—2016年北京市22个空气质量监测站点的空气质量数据为样本进行实例验证，结果表明，Seq2Seq模型和图卷积神经网络（GCN）可对PM_2.5小时浓度数据的时空依赖进行有效建模，注意力机制有助于减缓多步预测中的预测精度衰减，提升PM_2.5小时浓度多步预测的精度。GCN_Attention_Seq2Seq模型可有效应用于多种长度的PM_2.5浓度预测窗口。     

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.     

Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine-induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine-induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ${?}_0^C$ related to the basic reproduction number ${?}_0$ of the deterministic model. The key aim of this paper is to generalize the θ-stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ-stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ${?}_0^C>1$. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.     

石英晶体板非线性高频振动的拓展伽辽金法分析

针对考虑几何和材料非线性的石英晶体板厚度剪切振动和弯曲振动的方程组,利用扩展伽辽金法对该方程组进行转化和求解,分别获得了强烈耦合的厚度剪切振动模态和弯曲振动模态的频率响应关系,绘制了不同振幅比和不同驱动电压影响下的频率响应曲线图。数值计算结果表明可以选取石英晶片的最佳长厚比尺寸来避免两种模态的强烈耦合。驱动电压的变化将引起石英晶体谐振器厚度剪切振动频率的明显改变,必须将振动频率的漂移值控制在常用压电声波器件的允许值之内。扩展伽辽金法对石英晶体板非线性振动方程组的求解为非线性有限元分析和偏场效应分析奠定了基础。     

Prediction of 195Pt NMR chemical shifts of dissolution products of H2[Pt(OH)6] in nitric acid solutions by DFT methods: how important are the counter‐ion effects?

¹⁹⁵Pt NMR chemical shifts of octahedral Pt(IV) complexes with general formula [Pt(NO₃)_n(OH)_{6 ? n}]^2?, [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} (n = 1–6), and [Pt(NO₃)_{6 ? n ? m}(OH)_m(OH₂)_n]^{?2 + n ? m} formed by dissolution of platinic acid, H₂[Pt(OH)₆], in aqueous nitric acid solutions are calculated employing density functional theory methods. Particularly, the gauge‐including atomic orbitals (GIAO)‐PBE0/segmented all‐electron relativistically contracted–zeroth‐order regular approximation (SARC–ZORA)(Pt) ∪ 6–31G(d,p)(E)/Polarizable Continuum Model computational protocol performs the best. Excellent second‐order polynomial plots of δ_calcd(¹⁹⁵Pt) versus δ_exptl(¹⁹⁵Pt) chemical shifts and δ_calcd(¹⁹⁵Pt) versus the natural atomic charge Q_Pt are obtained. Despite of neglecting relativistic and spin orbit effects the good agreement of the calculated δ ¹⁹⁵Pt chemical shifts with experimental values is probably because of the fact that the contribution of relativistic and spin orbit effects to computed σ^{iso 195}Pt magnetic shielding of Pt(IV) coordination compounds is effectively cancelled in the computed δ ¹⁹⁵Pt chemical shifts, because the relativistic corrections are expected to be similar in the complexes and the proper reference standard used. To probe the counter‐ion effects on the ¹⁹⁵Pt NMR chemical shifts of the anionic [Pt(NO₃)_n(OH)_{6 ? n}]^2? and cationic [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} (n = 0–3) complexes we calculated the ¹⁹⁵Pt NMR chemical shifts of the neutral (PyH)₂[Pt(NO₃)_n(OH)_{6 ? n}] (n = 1–6; PyH = pyridinium cation, C₅H₅NH⁺) and [Pt(NO₃)_n(H₂O)_{6 ? n}](NO₃)_{4 ? n} (n = 0–3) complexes. Counter‐anion effects are very important for the accurate prediction of the ¹⁹⁵Pt NMR chemical shifts of the cationic [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} complexes, while counter‐cation effects are less important for the anionic [Pt(NO₃)_n(OH)_{6 ? n}]^2? complexes. The simple computational protocol is easily implemented even by synthetic chemists in platinum coordination chemistry that dispose limited software availability, or locally existing routines and knowhow. Copyright © 2016 John Wiley & Sons, Ltd.     

A filter method for nonlinear semidefinite programming with global convergence

In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the sufficient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is effective.     

Structure–Property Relationships in Click‐Derived Donor–Triazole–Acceptor Materials

To shed light on intramolecular charge‐transfer phenomena in 1,2,3‐triazole‐linked materials, a series of 1,2,3‐triazole‐linked push–pull chromophores were prepared and studied experimentally and computationally. Investigated modifications include variation of donor and/or acceptor strength and linker moiety as well as regioisomers. Photophysical characterization of intramolecular charge‐transfer features revealed ambipolar behavior of the triazole linker, depending on the substitution position. Furthermore, non‐centrosymmetric materials were subjected to second‐harmonic generation measurements, which revealed the high nonlinear optical activity of this class of materials.