一个Grüs型积分不等式的单参数推广

利用Cauchy中值定理给出Pachpatte B G建立的一个Grüss型积分不等式的单参数推广.     

Assignation of Acidic Dissociation Constants of Dimethoxyphenylfluorone and Dibromodimethylaminophenylfluorone

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一种修正的拟Grünwald插值在Orlicz空间内的逼近度

修正了以第二类Chebyshev多项式的零点为插值结点组的拟Grünwald插值多项式,使之转化为积分形式,并利用不等式技巧和Hardy-Littlewood极大函数的方法,研究了此积分型拟Grünwald插值算子在带权Orlicz空间内的逼近问题,得出了意义相对广泛的逼近度估计的结果.     

On the eigenvalues of quaternion matrices

This article is a continuation of the article [F. Zhang, Ger?gorin type theorems for quaternionic matrices, Linear Algebra Appl. 424 (2007), pp. 139–153] on the study of the eigenvalues of quaternion matrices. Profound differences in the eigenvalue problems for complex and quaternion matrices are discussed. We show that Brauer's theorem for the inclusion of the eigenvalues of complex matrices cannot be extended to the right eigenvalues of quaternion matrices. We also provide necessary and sufficient conditions for a complex square matrix to have infinitely many left eigenvalues, and analyse the roots of the characteristic polynomials for 2?×?2 matrices. We establish a characterisation for the set of left eigenvalues to intersect or be part of the boundary of the quaternion balls of Ger?gorin.     

Nonlinear Optical Switching in Regioregular Porphyrin Covalent Organic Frameworks

Covalent organic frameworks (COFs) have garnered immense scientific interest among porous materials because of their structural tunability and diverse properties. However, the response of such materials toward laser‐induced nonlinear optical (NLO) applications is hardly understood and demands prompt attention. Three novel regioregular porphyrin (Por)‐based porous COFs—Por‐COF‐HH and its dual metalated congeners Por‐COF‐ZnCu and Por‐COF‐ZnNi—have been prepared and present excellent NLO properties. Notably, intensity‐dependent NLO switching behavior was observed for these Por‐COFs, which is highly desirable for optical switching and optical limiting devices. Moreover, the efficient π‐conjugation and charge‐transfer transition in ZnCu‐Por‐COF enabled a high nonlinear absorption coefficient (β=4470 cm/GW) and figure of merit (FOM=σ₁/σ_o, 3565) value compared to other state‐of‐the‐art materials, including molecular porphyrins (β≈100–400 cm/GW), metal–organic frameworks (MOFs; β≈0.3–0.5 cm/GW), and graphene (β=900 cm/GW).     

Designed Synthesis of a 2D Porphyrin‐Based sp2 Carbon‐Conjugated Covalent Organic Framework for Heterogeneous Photocatalysis

The construction of stable covalent organic frameworks (COFs) for various applications is highly desirable. Herein, we report the synthesis of a novel two‐dimensional (2D) porphyrin‐based sp² carbon‐conjugated COF (Por‐sp²c‐COF), which adopts an eclipsed AA stacking structure with a Brunauer—Emmett—Teller surface area of 689 m² g^?1. Owing to the C=C linkages, Por‐sp²c‐COF shows a high chemical stability under various conditions, even under harsh conditions such as 9 m HCl and 9 m NaOH solutions. Interestingly, Por‐sp²c‐COF can be used as a metal‐free heterogeneous photocatalyst for the visible‐light‐induced aerobic oxidation of amines to imines. More importantly, in comparison to imine‐linked Por‐COF, the inherent structure of Por‐sp²c‐COF equips it with several advantages as a photocatalyst, including reusability and high photocatalytic performance. This clearly demonstrates that sp² carbon‐linked 2D COFs can provide an interesting platform for heterogeneous photocatalysis.     

Sign or root of unity ambiguities of certain Gauss sums

Gauss sums play an important role in number theory and arithmetic geometry. The main objects of study in this paper are Gauss sums over the finite field with q elements. Recently, the problem of explicit evaluation of Gauss sums in the small index case has been studied in several papers. In the process of the evaluation, it is realized that a sign (or a root of unity) ambiguity unavoidably occurs. These papers determined the ambiguities by the congruences modulo L, where L is certain divisor of the order of Gauss sum. However, such method is unavailable in some situations. This paper presents a new method to determine the sign (root of unity) ambiguities of Gauss sums in the index 2 case and index 4 case, which is not only suitable for all the situations with q being odd, but also comparatively more efficient and uniform than the previous method.     

非饱和土-隧道系统动力响应计算的波函数法

针对非饱和地基土中埋置隧道的三维动力响应计算问题, 提出了波函数法.采用无限长的Flügge薄壁圆柱壳模拟圆形隧道衬砌,采用流、固、气组成的三相介质模拟非饱和地基土体.分别采用分离变量法以及Helmholtz矢量分解定理求解薄壁圆柱壳的振动控制方程与非饱和土的波动方程.根据隧-土交界面与地表面处的应力、位移以及孔隙流体压力等边界条件,利用平面波与柱面波的转换性质,实现了隧道内作用单位简谐载荷时隧道衬砌与土体系统动力响应的耦合求解.通过与既有单相弹性介质2.5维有限元-边界元法、两相饱和多孔介质2.5维有限元-边界元法以及三相非饱和介质Pip in Pip半解析法的计算结果进行对比, 验证了本文计算方法的可靠性. 最后,基于该方法, 通过算例分析了不同饱和度下非饱和土-隧道系统的动力响应特征.结果表明, 饱和度对土体动位移与超孔隙水压力的幅值响应有较大影响.该方法的非饱和地基土参数退化后,也可用来计算和分析饱和地基土或单相弹性地基土与隧道系统的动力响应.      

等离子体屏蔽对He2+与H原子碰撞电离微分截面的影响

应用经典径迹Monte Carlo（CTMC）方法研究了He²⁺与H原子在等离子体环境下的碰撞电离过程,计算了在5—400 keV/u的能区随等离子体屏蔽作用变化的碰撞电离总截面和一阶微分截面.等离子体中带电粒子之间的相互作用采用Debye-Hückel模型来描述.由于等离子体屏蔽效应的存在,靶中束缚态电子能级及其经典微正则分布以及入射离子与靶电子的相互作用都发生了变化,而这些变化会直接影响碰撞电离过程.研究发现,碰撞电离总截面随等离子屏蔽的增加而增大,特别是在10 keV/u以下的低能区电离截面有量级的增加.对随能量变化的一阶微分截面,在低能碰撞过程中,屏蔽作用增加,微分截面呈量级增加,高能碰撞微分截面呈倍数增加.同时,屏蔽作用导致电离电子向高能方向移动,随着碰撞能量的增加两体碰撞机制的贡献越来越大,并在较高的出射电子能量出现了一个新的峰.对无屏蔽的自由原子碰撞过程,CTMC方法计算出的电离总截面在碰撞能量大于70 keV/u的较高能区在实验误差内与实验测量结果符合很好,而在较低的能区比实验值小30%—50%. 关键词： 重粒子碰撞电离 等离子体屏蔽效应 经典径迹Monte Carlo方法 Debye-Hückel模型     

Synthesis and characterization of <Emphasis Type="Italic">S,N</Emphasis>-heteroacenes by Bischler-Napieralski reaction

Bischler-Napieralski cyclization has been successfully employed to prepare planar S,N-heteroacenes (SNHs) with the analogue structures to 1,10-phenanthroline. The opto-/electrical properties and the packing modes of these S,Nheteroacenes were examined, which were dependent on the structure of the fused groups. SNH-based copolymers with high molecular weight and good solubility in common organic solvents or water have been synthesized by Suzuki-Miyaura- Schlüter polycondensation. The photophysical property studies revealed that the copolymers may be a promising chemosensor material.