Energy-preserving algorithm for gyrocenter dynamics of charged particles

Numerical Algorithms - Gyrocenter dynamics of charged particles plays a fundamental and important role in plasma physics, which requires accuracy and conservation in a long-time simulation....     

Side-on-End-on Coordination of Dinitrogen on a Polynuclear Vanadium Nitride Cluster Anion [V5N5]−

The side-on-end-on coordination of N₂ can be very important to activate and functionalize this very stable molecule. However, such coordination has rarely been reported. This study reports a gas-phase species (a polynuclear vanadium nitride cluster anion [V₅N₅]⁻) that can capture N₂ efficiently (12 %), and the quantum chemistry modelling suggests an unusual side-on-end-on coordination. The cluster anions were generated by laser ablation and the reaction with N₂ has been characterized by mass spectrometry, photoelectron imaging spectroscopy, and density functional theory calculations. The back-donation interactions between the localized d–d bonding orbitals on the low-coordinated dual metal (V) sites and the antibonding π* orbitals of N₂ are the driving forces to adsorb N₂ with a high binding energy (about 2.0 eV).     

Parameter Estimation Based on Set-valued Signals: Theory and Application

Acta Mathematicae Applicatae Sinica, English Series - This paper summarizes the parameter estimation of systems with set-valued signals, which can be classified to three catalogs: one-time...     

Properties of G-martingales with finite variation and the application to G-Sobolev spaces

As is known, if $B={\left(B_t\right)}_{t\in [0,T]}$ is a $G$-Brownian motion, a process of form ${\int }_0^t{\eta }_{s}d{〈B〉}_s?{\int }_0^{t}2G\left({\eta }_s\right)ds$, $\eta \in M_G^1(0,T)$, is a non-increasing $G$-martingale. In this paper, we shall show that a non-increasing $G$-martingale cannot be form of ${\int }_0^t{\eta }_{s}ds$ or ${\int }_0^t{\gamma }_{s}d{〈B〉}_s$, $\eta ,\gamma \in M_G^1(0,T)$, which implies that the decomposition for generalized $G$-Itô processes is unique: For arbitrary $\zeta \in H_G^1(0,T)$, $\eta \in M_G^1(0,T)$ and non-increasing $G$-martingales $K,L$, if ${\int }_0^t{\zeta }_{s}d{B}_s+{\int }_0^t{\eta }_{s}ds+K_t=L_t,t\in [0,T],$then we have $\eta \equiv 0$, $\zeta \equiv 0$ and$K_t=L_t$. As an application, we give a characterization to the $G$-Sobolev spaces introduced in Peng and Song (2015).     

Symplectic integrators with adaptive time step applied to runaway electron dynamics

Numerical Algorithms - Studying the dynamics of runaway electrons has theoretical and practical significance. As the system is highly relativistic, multi-scale and nonlinear, accurate and efficient...     

时间延迟扩散-波动分数阶微分方程有限差分方法

本文提出求解时间延迟扩散-波动分数阶微分方程有限差分方法，方程中对时间的一阶导函数用α阶（0 < α < 1） Caputo分数阶导数代替.文章中利用Lubich线性多步法对分数阶微分进行差分离散，且文章利用分段区间证明该方法是稳定的，且利用数值实验加以验证.     

Closed form of inverse Plücker correspondence in line geometry

Science China Mathematics - By mapping the homogeneous coordinates of two points in space to the Plücker coordinates of the line they determine, any transformation of type SL(4) upon points in...     

航空器供油问题中完全逆序类中的多项式时间可解类

航空器供油问题是一类非线性组合优化问题,其目标函数为分式形式,该问题目前不存在多项式时间算法,也未被证明是NP完全问题。一般可以用置换来刻画n架飞机的一个供油顺序。该问题中有一类实例被称为“完全逆序类”,“完全逆序类”用动态规划算法求解计算时间为O(n2ⁿ),具有指数时间复杂度。本文通过对该“完全逆序类”问题做进一步分析,发现在“完全逆序类”中也存在着多项式时间可解的情况。定理1研究一类一次可解的情况,若问题满足定理1的条件,则求解一次即可找到其最优解;定理2研究一类多项式时间可解的情况,当问题满足定理2的条件时,其最优解可在多项式时间内获得。     

Lone-Pair Enhanced Birefringence in an Alkaline-Earth Metal Tin(II) Phosphate BaSn2(PO4)2

The first alkaline-earth metal tin(II) phosphate, BaSn₂(PO₄)₂, has been discovered, which consists of layered structures constructed from strictly alternating [SnO₃]⁴⁻ and [PO₄]³⁻ moieties. This compound is expected to have a large birefringence with Δn≈0.071 at 1064 nm, owing to the presence of stereochemically active lone pair metal cations.