Electron Transfer and Charge Transfer: Twin Themes in Unifying the Mechanisms of Organic and Organometallic Reactions

The broad varieties of organic and organometallic reactions merge into a common unifying mechanism by considering all nucleophiles and electrophiles as electron donors (D) and electron acceptors (A), respectively. Comparison of outer-sphere and inner-sphere electron transfers with the aid of Marcus theory provides the thermochemical basis for the generalized free energy relationship for electron transfer (FERET) in Equation (37) and its corollaries in Equations (43) and (44) that have wide predictive applicability to electrophilic aromatic substitutions, olefin additions, organometallic cleavages, etc. The FERET is based on the conversion of the weak nucleophile–electrophile interactions extant in the ubiquitous electron donor—acceptor (EDA) precursor complex [D, A] to the radical ion pair [D^⊕, A^?], for which the free energy change can be evaluated from the charge-transfer absorption spectra according to Mulliken theory. FERET analysis thus indicates that the charge-transfer ion pairs [D^⊕, A^?] are energetically equivalent to the transition states for nucleophile/electrophile transformations. The behavior of such ion pairs can be directly observed immediately following the irradiation of the charge-transfer bands of various EDA complexes with a 25-ps laser pulse. Such studies confirm the radical ion pair [Arene^⊕, NO₂] as a viable intermediate in electrophilic aromatic nitration, as presented in the electron-transfer mechanism between arenes and the nitryl cation (NO) electrophile.     

高能闪光照相中影响光程确定的几个因素

 利用闪光照相基本原理和成像原理，在直接记录法和转换屏记录法的情况下，研究了闪光照相中影响X射线在材料中光程确定的主要因素。结果表明，影响光程确定的几个因素是：散射效应、光源角分布效应、立体角效应和能谱效应。对于高能闪光照相，散射效应是影响光程确定的最主要因素，散射的存在使光程的测量值比实际值降低20%～40%。因此必须在做CT之前，对散射的影响进行修正。     

复数星图与单路的多染色拉姆齐数

对给定的简单图$H_1,H_2,\ldots,H_c$, 我们将使完全图$K_n$的任意边分解$\{G_i\}^c_{i=1}$都存在至少一个$G_i$有子图同构于$H_i$的最小正整数$n$称为多染色拉姆齐数 $R(H_1,H_2,\ldots,$ $H_c)$. 对正整数$m,n_1,n_2,\ldots,n_c$, 令$\Sigma=\sum_{i=1}^{c}(n_i-1)$. 在文献中,我们已经获得了$R(K_{1,n_1},\ldots,K_{1,n_c},P_m)$ 的一些界和精确值.Wang推测若$\Sigma\not\equiv 0\pmod{m-1}$且$\Sigma+1\ge (m-3)^2$, 则有$R(K_{1,n_1},\ldots, K_{1,n_c}, P_m)=\Sigma+m-1.$ 本文中, 我们给出了一个新的下界并给出$R(K_{1,n_1},\ldots,K_{1,n_c},P_m)$在$m\leq\Sigma$, $\Sigma\equiv k\pmod{m-1}$且$2\leq k \leq m-2$情况下的部分精确值. 这些结果部分证实了Wang的猜想.     

Conserved Control Path in Multilayer Networks

The determination of directed control paths in complex networks is important because control paths indicate the structure of the propagation of control signals through edges. A challenging problem is to identify them in complex networked systems characterized by different types of interactions that form multilayer networks. In this study, we describe a graph pattern called the conserved control path, which allows us to model a common control structure among different types of relations. We present a practical conserved control path detection method (CoPath), which is based on a maximum-weighted matching, to determine the paths that play the most consistent roles in controlling signal transmission in multilayer networks. As a pragmatic application, we demonstrate that the control paths detected in a multilayered pan-cancer network are statistically more consistent. Additionally, they lead to the effective identification of drug targets, thereby demonstrating their power in predicting key pathways that influence multiple cancers.     

谐振子的传播子

本文以谐振子为例，说明路径积分的一种计算方法。     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

Selection of response measurement locations to improve inverse force determination

The forces obtained by inverse methods are prone to errors. These arise due to a combination of errors in the measurements and high condition numbers in the matrix of transfer functions to be inverted. Ill-conditioning of the frequency response function matrix causes measurement errors to be magnified significantly. When the condition numbers are small, the measurement errors simply propagate without much amplification. Due to modal behaviour of the structure, the condition numbers can vary significantly over the frequency range and with the spatial location of the response measurements. The spatial variation can be quite considerable across the structure. The potential for using this characteristic to improve force determination is explored in this paper as an alternative to matrix regularization methods. The aim is to reduce error magnification in inverse methods by an ‘optimal’ spatial distribution of response locations. A method is proposed which is based on the minimization of the average condition number across the frequency range. If many possible locations are available, however, this can involve excessive calculation. An approximate method is therefore proposed which results in consistently good location selection for use in inverse force determination but involves much less computational effort. The error reduction in reconstructed forces is found to be significant in numerical simulations on a simply supported plate and in validation experiments.     

Analysis of the lateral displacement and optical path difference in wide-field-of-view polarization interference imaging spectrometer

The mechanism of beam splitting and principle of wide-field-of-view compensation of modified Savart polariscope in the wide-field-of-view polarization interference imaging spectrometer (WPIIS) are analyzed and discussed. Formulas for the lateral displacement and optical path difference (OPD) produced by the modified Savart polariscope are derived by ray-tracing method. The theoretical and practical guidance is thereby provided for the study, design, modulation, experiment and engineering of the polarization interference imaging spectrometers and other birefringent Fourier-transform spectrometers based on Savart polariscopes.     

无人机多阶段航迹预测协同任务规划

针对多无人机(Unmanned Aerial Vehicles, UAVs)协同控制问题,提出了一种UAVs多阶段航迹预测分布式任务规划方法。定义从一次任务分配开始到其中一项任务完成为一个任务周期。在每个规划周期,首先,各UAV使用A*算法快速预测到所有任务目标的路径,提供至任务分配;然后,采用聚类算法修改目标价值向量,协商分配结果,并实时计算探测范围内的最短路径;最后,采用三次B样条曲线平滑所分配的最短路径,在线规划出满足飞行约束的飞行航迹。通过仿真实验对算法的有效性进行了验证,结果表明,提出的算法能够实时获得近似最优的任务分配结果并规划出可飞行航迹,并有效处理突发任务。