Symmetry Function Induced by a Convex Body

This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.

AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS

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.

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

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.

Principles and prospects of Bose-Einstein correlation study at BESIII

One method for determining the characteristic parameters of a hadron production source is to measure the Bose-Einstein correlation functions.In this study,we present fundamental concepts and formulas related to the Bose-Einstein correlations,focusing on the measurement principles and the Lund model from an experimental perspective.We perform Monte Carlo simulations using the Lund model generator in the 2-3 GeV energy range.Through these feasibility studies,we identify key features of the Bose-Einstein correlations that offer valuable insights for experimental measurements.Utilizing data samples collected at BESIII,we perform measurements of the Bose-Einstein correlation functions,with an expected experimental precision of a few percent for the hadron source radius and incoherence parameter.

3-硝基-1,2,4-三唑-5-酮(NTO)热分解机理的对称破缺密度泛函理论研究

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.

A machine learning vibrational spectroscopy protocol for spectrum prediction and spectrum-based structure recognition

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.

Exact Solutions of Atmospheric(2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space.