An Arithmetic Analogue of Bezout's Theorem

In this paper, we prove two versions of an arithmetic analogue of Bezout's theorem, subject to some technical restrictions. The basic formula proven is deg(V)h(XY)=h(X)deg(Y)+h(Y)deg(X)+O(1), where X and Y are algebraic cycles varying in properly intersecting families on a regular subvariety V _S P _S ^N . The theorem is inspired by the arithmetic Bezout inequality of Bost, Gillet, and Soulé, but improve upon it in two ways. First, we obtain an equality up to O(1) as the intersecting cycles vary in projective families. Second, we generalise this result to intersections of divisors on any regular projective arithmetic variety.     

Fibrés d'intersection

Let f:XSbe a projective morphism of Noetherian schemes. We assume fpurely of relative dimension dand finite Tor-dimensional. We associate to d+1 invertible sheaves on Xa line bundle I _X/S ( ) on Sdepending additively on the , commuting to good base changes and which represents the integral along the fibres of fof the product of the first Chern classes of the . If d=0, I _X/S ( ) is the norm N _X/S ( ).     

Planar AIEgens with Enhanced Solid‐State Luminescence and ROS Generation for Multidrug‐Resistant Bacteria Treatment

Planar luminogens have encountered difficulties in overcoming intrinsic aggregation‐caused emission quenching by intermolecular π‐π stacking interactions. Although excited‐state double‐bond reorganization (ESDBR) can guide us on designing planar aggregation‐induced emission (AIE) luminogens (AIEgens), its mechanism has yet been elucidated. Major challenges in the field include methods to efficiently restrict ESDBR and enhance AIE performance without using bulky substituents (e.g., tetraphenylethylene and triphenylamine). In this study, we rationally developed fluoro‐substituent AIEgens with stronger intermolecular H‐bonding interaction for restricted molecular motions and increased crystal density, leading to decreased nonradiative decay rate by one order of magnitude. The adjusted ESDBR properties also show a corresponding response to variation in viscosity. Furthermore, their aggregation‐induced reactive oxygen species (ROS) generations have been discovered. The application of such planar AIEgen in treating multidrug‐resistant bacteria has been demonstrated in a mouse model. The relationship between ROS generation and distinct E/Z‐configurational stacking behaviors have been further understood, providing a design principle for synthesizing planar AIEgen‐based photosensitizers.     

Principles of Aggregation-Induced Emission: Design of Deactivation Pathways for Advanced AIEgens and Applications

Twenty years ago, the concept of aggregation-induced emission (AIE) was proposed, and this unique luminescent property has attracted scientific interest ever since. However, AIE denominates only the phenomenon, while the details of its underlying guiding principles remain to be elucidated. This minireview discusses the basic principles of AIE based on our previous mechanistic study of the photophysical behavior of 9,10-bis(N,N-dialkylamino)anthracene ( BDAA ) and the corresponding mechanistic analysis by quantum chemical calculations. BDAA comprises an anthracene core and small electron donors, which allows the quantum chemical aspects of AIE to be discussed. The key factor for AIE is the control over the non-radiative decay (deactivation) pathway, which can be visualized by considering the conical intersection (CI) on a potential energy surface. Controlling the conical intersection (CI) on the potential energy surface enables the separate formation of fluorescent (CI:high) and non-fluorescent (CI:low) molecules [control of conical intersection accessibility ( CCIA )]. The novelty and originality of AIE in the field of photochemistry lies in the creation of functionality by design and in the active control over deactivation pathways. Moreover, we provide a new design strategy for AIE luminogens (AIEgens) and discuss selected examples.     

3-二甲氨基-2-甲基丙烯醛S2激发态结构动力学 (cited: 3)

采用共振拉曼光谱和完全活性自洽场理论计算研究了3-二甲氨基-2-甲基丙烯醛(DMAMP)光激发到S₂(ππ^*)态后的光物理性能．在B3LYP/6-311++G(d,p)水平计算确定了DMAMP与其三种异构体之间的基态异构化能垒,指认了振动光谱．采用涵盖紫外强吸收带的激光波长,获得了DMAMP在环己烷、乙腈和甲醇溶剂中的A-带共振拉曼光谱,含时密度泛函方法计算确定了该光谱中基频的相对强度,发现振动-电子耦合发生在S₂(ππ^*)态的Franck-Condon区域．CASSCF计算方法确定低单重和三重激发态、势能面锥形交叉点和系间窜跃点的激发能．共振拉曼光谱强度模式分析和CASSCF计算获得了DMAMP的A-带短时结构动力学和其后的衰变动力学表明,C1=O6和C2=C3之间的瞬时去共轭效应发生在S₂(ππ^*)态的Franck-Condon区域,激发态电荷重分布机制表明,C3和二甲氨基之间以及C1和C2之间的共轭增强效应发生在波包离开Franck-Condon区域后．C1=O6和C2=C3之间的去共轭效应使得-C3=N(CH₃)₂沿着C2-C3键旋转更加容易,C1-C2之间以及C3和N(CH₃)的共轭增强效应使得绕C1-C2和C3-N5旋转变得比较困难．这些表明DMAMP初始结构动力学沿着CI-1(S₂/S₀)交叉点展开,而沿CI-2(S₂/S₀)和CI-3(S₂/S₀)交叉点展开的几率可以忽略．提出了DMAMP分子受光激发从S_2,FC(ππ^*)经由各锥形交叉点和各系间窜跃点回到S₀或T_1,min的两个衰变通道.     

Decay Dynamics of 3‐methyl‐3‐pentene‐2‐one from the light absorbing S2(ππ*) state ‐ Resonance Raman Spectroscopy and CASSCF Study

The photophysics of 3‐methyl‐3‐pentene‐2‐one (3M3P2O) after excitation to the S₂(ππ*) electronic state were studied using the resonance Raman spectroscopy and complete active space self‐consistent field (CASSCF) method calculations. The A‐band resonance Raman spectra were obtained in cyclohexane, acetonitrile, and methanol with excitation wavelengths in resonance with the first intense absorption band to probe the structural dynamics of 3M3P2O. The B3LYP‐TD/6‐31++G(d, p) computation was carried out to determine the relative A‐band resonance Raman intensities of the fundamental modes, and the result was used to reproduce the corresponding fundamental band intensities of the 223.1 nm resonance Raman spectrum and thus to examine whether the vibronic‐coupling existed in Franck‐Condon region or not. CASSCF calculations were carried out to determine the minimal singlet excitation energies of S_{1, FC}, S_1,min (nπ*), S_{2, FC}, S_2,min (ππ*), the transition energies of the conical intersection points S_n/S_π, S_n/S₀, and the optimized excited state geometries as well as the geometry structures of the conical intersection points. The A‐band short‐time structural dynamics and the corresponding decay dynamics of 3M3P2O were obtained by the analysis of the resonance Raman intensity pattern and CASSCF computations. It was revealed that the initial structural dynamics of 3M3P2O was towards the simultaneous C₃=C₄ and C₂=O₇ bond elongation, with the C₃=C₄ bond length lengthening greater at the very beginning, whereas the C₂=O₇ bond length changing greater at the later evolution time before reaching the CI(S₂/S₁) conical intersection point. The decay dynamics from S₂(ππ*) to S₁(nπ*) via S₂(ππ*)/S₁(nπ*) in singlet realm and from S₁(nπ*) to T₁(nπ*) via ISC[S₁(nπ*)/T₂(ππ*)/T₁(nπ*)] in triplet realm are proposed. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of spot size on cone formation in a XeCl laser ablation of polyethersulfone films

Radiation from the UV excimer lasers, with the fluence above the ablation threshold, can etch the polymer surfaces by photoablation. In some cases different microstructures may appear on the surface during the laser ablation. In this paper the effect of the laser spot size on the cone formation on polyethersulfone films has been investigated. The experiments have been performed with a XeCl laser at the wavelength of 308 nm and at the fluences of 70 and 100 mJ/cm² at air. For the investigation of the effect of the laser spot size on cone formation, the samples were irradiated at two different laser spot sizes of w₁ and w₂ = 0.1 w₁. The morphology of the processed surface was studied by scanning electron microscopy (SEM). It has shown that the shape, size and density of cones change with the change of the laser spot size. Also, the number of pulses and the pulse repetition rate which are needed for threshold of cone formation are affected by the laser beam spot size on the surface.     

序为(3,3)的正则拟多边形

利用距离正则图的特征值方法,得到如下结论:设Γ是一个有序对为(3,3)正则拟多边形,如果d=r+1,则cd≠1,2,3.     

基于元胞自动机的交叉口混合交通模型研究

在我国很多中小城市普遍存在着摩托车与小汽车混行的现象,摩托车既有类似自行车横向移动灵活、启动速度快的特点,又有类似小汽车纵向移动速度快的特点,特别是在城市交叉口附近范围内,摩托车与小汽车几乎速度相当.根据交叉口红灯起亮时,摩托车会灵活穿插,充分利用车道空间,绿灯起亮时,由于摩托车的启动速度比小汽车快,产生侧向膨胀效应,挤压小汽车行驶空间,从而使其速度减慢等现象,结合我国中小城市交叉口小汽车及摩托车的行驶特性,利用元胞自动机模型,建立信号交叉口小汽车与摩托车的混合交通模型.