Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetr...Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity.When the involved two potential vectors are scalar,all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.展开更多
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of t...By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.展开更多
共价键均裂在含能分子的热分解过程中普遍存在,因此极为重要.然而,以往的理论研究通常用键能(ΔH,BDE)估算均裂能垒,因忽略了熵效应,必然造成较大误差.采用对称破缺密度泛函方法(BS-UB3LYP/6-311+G**),对含能分子3-硝基-1,2,4-三唑-5-酮...共价键均裂在含能分子的热分解过程中普遍存在,因此极为重要.然而,以往的理论研究通常用键能(ΔH,BDE)估算均裂能垒,因忽略了熵效应,必然造成较大误差.采用对称破缺密度泛函方法(BS-UB3LYP/6-311+G**),对含能分子3-硝基-1,2,4-三唑-5-酮(NTO)的热分解机理进行了系统研究和梳理,计算了共价键均裂的过渡态及能垒.结果表明,C—NO_(2)键均裂和随后的自由基复合是最优途径,能垒为216.9 k J·mol^(-1)(523 K).随后产生的NO自由基通过多次“复合-均裂”过程促进三唑中间体开环,分解为HNCO,N_(2)O和CO等小分子,它们相互反应又生成NO_(2),N_(2)和CO_(2).这些分解产物与诸多实验观测结果一致.展开更多
Vibrational spectroscopy is one of the most commonly applied techniques for determining molecular structures.Conventional applications often involve extensive expertise or expensive first-principles computational effo...Vibrational spectroscopy is one of the most commonly applied techniques for determining molecular structures.Conventional applications often involve extensive expertise or expensive first-principles computational effort in order to establish one-to-one spectrum-structure relationships.Here we developed a machine-learning protocol to correlate spectral fingerprints with local molecular structures.Our protocol enables not only quick and accurate prediction of infrared(IR)absorption and Raman vibrational spectra based on molecular structures,but more importantly,also enables structure recognition of chemical groups from vibrational spectral features.IR and Raman spectral features arising from different selection rules were recurrently fed to the model to achieve a nearly zero error rate in structure recognition.Both the spectrum prediction and structure recognition models have good transferability,implying a high possibility of being extended to various spectral or non-spectral characteristics.This machine learning protocol may provide impovements to real-time field applications in many areas of spectroscopy.展开更多
基金The work was supported in part by NSF(DMS-1664561)NSFC(11975145 and 11972291)+1 种基金the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17KJB110020)Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT(2017XKZD11).
文摘Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity.When the involved two potential vectors are scalar,all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.
基金Project supported by the National Natural Science Foundation of China(Grant No.10671156)the Natural Science Foundation of Shaanxi Province of China(Grant No.SJ08A05)
文摘By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.
文摘共价键均裂在含能分子的热分解过程中普遍存在,因此极为重要.然而,以往的理论研究通常用键能(ΔH,BDE)估算均裂能垒,因忽略了熵效应,必然造成较大误差.采用对称破缺密度泛函方法(BS-UB3LYP/6-311+G**),对含能分子3-硝基-1,2,4-三唑-5-酮(NTO)的热分解机理进行了系统研究和梳理,计算了共价键均裂的过渡态及能垒.结果表明,C—NO_(2)键均裂和随后的自由基复合是最优途径,能垒为216.9 k J·mol^(-1)(523 K).随后产生的NO自由基通过多次“复合-均裂”过程促进三唑中间体开环,分解为HNCO,N_(2)O和CO等小分子,它们相互反应又生成NO_(2),N_(2)和CO_(2).这些分解产物与诸多实验观测结果一致.
基金This work was financially supported by the National Natural Science Foundation of China(21773309,21776315,21633006 and 21633007)the National Key Research and Development Program of China(2018YFA0208603,2017YFA0303500)+2 种基金the Fundamental Research Funds for the Central Universities(19CX05001A)the Anhui Initiative in Quantum Information Technologies(AHY090200)Hefei National Laboratory for Physical Sciences at Microscale(KF2020004)。
文摘Vibrational spectroscopy is one of the most commonly applied techniques for determining molecular structures.Conventional applications often involve extensive expertise or expensive first-principles computational effort in order to establish one-to-one spectrum-structure relationships.Here we developed a machine-learning protocol to correlate spectral fingerprints with local molecular structures.Our protocol enables not only quick and accurate prediction of infrared(IR)absorption and Raman vibrational spectra based on molecular structures,but more importantly,also enables structure recognition of chemical groups from vibrational spectral features.IR and Raman spectral features arising from different selection rules were recurrently fed to the model to achieve a nearly zero error rate in structure recognition.Both the spectrum prediction and structure recognition models have good transferability,implying a high possibility of being extended to various spectral or non-spectral characteristics.This machine learning protocol may provide impovements to real-time field applications in many areas of spectroscopy.
