Bis-peri-dinaphtho-rylenes: Facile Synthesis via Radical-Mediated Coupling Reactions and their Distinctive Electronic Structures

Polycyclic aromatic hydrocarbons (PAHs) with a one-dimensional (1D), ribbon-like structure have the potential to serve as both model compounds for corresponding graphene nanoribbons (GNRs) and as materials for optoelectronics applications. However, synthesizing molecules of this type with extended π-conjugation presents a significant challenge. In this study, we present a straightforward synthetic method for a series of bis-peri-dinaphtho-rylene molecules, wherein the peri-positions of perylene, quaterrylene, and hexarylene are fused with naphtho-units. These molecules were efficiently synthesized primarily through intramolecular or intermolecular radical coupling of in situ generated organic radical species. Their structures were confirmed using X-ray crystallographic analysis, which also revealed a slightly bent geometry due to the incorporation of a cyclopentadiene ring at the bay regions of the rylene backbones. Bond lengh analysis and theoretical calculations indicate that their electronic structures resemble pyrenacenes more than quinoidal rylenes. That is, the aromatic sextets are predominantly localized along the long axis of the skeletones. As the chain length increases, these molecules exhibit enhanced electronic absorption with a bathochromic shift, and multiple amphoteric redox waves. This study introduces a novel synthetic approach for generating 1D extended PAHs and GNRs, along with their structure-dependent electronic properties.     

Synergetic Coupling of Redox-Active Sites on Organic Electrode Material for Robust and High-Performance Sodium-Ion Storage

Organic electrode materials (OEMs), valued for their sustainability and structural tunability, have been attracting increasing attention for wide application in sodium-ion batteries (SIBs) and other rechargeable batteries. However, most OEMs are plagued with insufficient specific capacity or poor cycling stability. Therefore, it′s imperative to enhance their specific capacity and cycling stability through molecular design. Herein, we designed and synthesized a heteroaromatic molecule 2,3,8,9,14,15-hexanol hexaazatrinaphthalene (HATN-6OH) by the synergetic coupling of catechol (the precursor of ortho-quinone)/ortho-quinone functional groups and HATN conjugated core structures. The abundance of catechol/ortho-quinone and imine redox-active moieties delivers a high specific capacity of nine-electron transfer for SIBs. Most notably, the π–π interactions and intermolecular hydrogen bond forces among HATN-6OH molecules secure the stable long-term cycling performance of SIBs. Consequently, the as-prepared HATN-6OH electrode exhibited a high specific capacity (554 mAh g⁻¹ at 0.1 A g⁻¹), excellent rate capability (202 mAh g⁻¹ at 10 A g⁻¹), and stable long-term cycling performance (73 % after 3000 cycles at 10 A g⁻¹) in SIBs. Additionally, the nine-electron transfer mechanism is confirmed by systematic density functional theory (DFT) calculation, attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), and Raman analysis. The achievement of the synergetic coupling of the redox-active sites on OEMs could be an important key to the enhancement of SIBs and other metal-ion batteries.     

非齐次隐马尔可夫模型随机变换的若干强极限定理

利用鞅方法讨论了非齐次隐马尔可夫模型变换的强极限定理,作为特殊情形,将随机选择的概念拓展到非齐次隐马尔可夫模型中,得到了关于有限非齐次隐马尔可夫模型随机选择与随机公平比的若干极限定理.     

On the ratios between packing and domination parameters of a graph

The relationship ρ_L(G)≤ρ(G)≤γ(G) between the lower packing number ρ_L(G), the packing number ρ(G) and the domination number γ(G) of a graph G is well known. In this paper we establish best possible bounds on the ratios of the packing numbers of any (connected) graph to its six domination-related parameters (the lower and upper irredundance numbers ir and IR, the lower and upper independence numbers i and β, and the lower and upper domination numbers γ and Γ). In particular, best possible constants a_θ, b_θ, c_θ and d_θ are found for which the inequalities and hold for any connected graph G and all θ∈{ir,γ,i,β,Γ,IR}. From our work it follows, for example, that and for any connected graph G, and that these inequalities are best possible.     

一类带反凸约束的非线性比式和问题的全局优化算法

本文针对一类带有反凸约束的非线性比式和分式规划问题,提出一种求其全局最优解的单纯形分支和对偶定界算法.该算法利用Lagrange对偶理论将其中关键的定界问题转化为一系列易于求解的线性规划问题.收敛性分析和数值算例均表明提出的算法是可行的.     

A multilevel decoupled method for a mixed Stokes/Darcy model

This paper studies decoupled numerical methods for a mixed Stokes/Darcy model for coupling fluid and porous media flows. A two-level algorithm is proposed and analyzed in Mu and Xu (2007) [10]. We generalize the two-level algorithm to a multilevel algorithm in this paper and present numerical analysis on the error estimates for the multilevel algorithm. The multilevel algorithm solves the mixed Stokes/Darcy system by applying efficient legacy code for single model solvers to solve two decoupled Stokes and Darcy subproblems on all the subsequently refined meshes, except for a much smaller global problem only on a very coarse initial mesh. Numerical experiments are conducted for both the two-level and multilevel algorithms to illustrate their effectiveness and efficiency, and validate the related theoretical analysis.     

求线性比试和问题的确定性全局优化算法

为求线性比试和问题的全局最优解,本文给出了一个分支定界算法.通过一个等价问题和一个新的线性化松弛技巧,初始的非凸规划问题归结为一系列线性规划问题的求解.借助于这一系列线性规划问题的解,算法可收敛于初始非凸规划问题的最优解.算法的计算量主要是一些线性规划问题的求解.数值算例表明算法是切实可行的.     

Stability for a random evolution equation with Gaussian perturbation

In this paper we consider a random evolution equation which is perturbed by Gaussian type noise, and show how to construct its coupled solutions. On the basis of the coupling results, we discuss the asymptotic flatness and the stability in total variation norm for the solutions of the equation. In addition, we also prove the Feller continuity, and the existence and uniqueness of invariant measures of the solutions.     

Global Lipschitz regularizing effects for linear and nonlinear parabolic equations

In this paper we prove global bounds on the spatial gradient of viscosity solutions to second order linear and nonlinear parabolic equations in (0,T)×R^N$(0,T)\times {\mathbb{R}}^N$. Our assumptions include the case that the coefficients be both unbounded and with very mild local regularity (possibly weaker than the Dini continuity), the estimates only depending on the parabolicity constant and on the modulus of continuity of coefficients (but not on their L^∞$L^{\infty }$-norm). Our proof provides the analytic counterpart to the probabilistic proof used in Priola and Wang (2006) [35] (J. Funct. Anal. 2006) to get this type of gradient estimates in the linear case. We actually extend such estimates to the case of possibly unbounded data and solutions as well as to the case of nonlinear operators including Bellman–Isaacs equations. We investigate both the classical regularizing effect (at time t>0$t>0$) and the possible conservation of Lipschitz regularity from t=0$t=0$, and similarly we prove global Hölder estimates under weaker assumptions on the coefficients. The estimates we prove for unbounded data and solutions seem to be new even in the classical case of linear equations with bounded and Hölder continuous coefficients. Applications to Liouville type theorems are also given in the paper. Finally, we compare in an appendix the analytic and the probabilistic approach discussing the analogy between the doubling variables method of viscosity solutions and the probabilistic coupling method.     

Profitability in the car industry: New measures for estimating targets and target directions

In this paper we study the profitability of car manufacturers in relation to industry-wide profitability targets such as industry averages. Specifically we are interested in whether firms adjust their profitability in the direction of these targets, whether it is possible to detect any such change, and, if so, what the precise nature is of these changes.