Characterizing directed path graphs by forbidden asteroids

An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central role in a classical characterization of interval graphs by Lekkerkerker and Boland. Their result says that a chordal graph is an interval graph if and only if it does not contain an asteroidal triple. In this paper, we prove an analogous theorem for directed path graphs which are the intersection graphs of directed paths in a directed tree. For this purpose, we introduce the notion of a special connection. Two non‐adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex‐disjoint chordless paths satisfying certain conditions. A special asteroidal triple is an asteroidal triple such that each pair is linked by a special connection. We prove that a chordal graph is a directed path graph if and only if it does not contain a special asteroidal triple. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:103‐112, 2011     

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.     

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.     

Excited‐State Intramolecular Proton Transfer: Photoswitching in Salicylidene Methylamine Derivatives

The effect of chemical substitutions on the photophysical properties of the salicylidene methylamine molecule (SMA) (J. Jankowska, M. F. Rode, J. Sadlej, A. L. Sobolewski, ChemPhysChem, 2012 , 13, 4287–4294) is studied with the aid of ab initio electronic structure methods. It is shown that combining π‐electron‐donating and π‐electron‐withdrawing substituents results in an electron‐density push‐and‐pull effect on the energetic landscape of the ground and the lowest excited ππ* and nπ* singlet states of the system. The presented search for the most appropriate SMA derivatives with respect to their photoswitching functionality offers an efficient prescreening tool for finding chemical structures before real synthetic realization.     

Intersection of Mcmullen set with its rational translation

In this paper,we study the intersection of Mcmullen set with its rational translation.The main difficulty is that the generating structure of the intersection.By the radix expansion of translating vector,we give its fractal characterization.We find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from translating the vector(x,y)with its radix expansion.     

Assessing solvent effects on the singlet excited state lifetime of uracil derivatives: A femtosecond fluorescence upconversion study in alcohols and D2O

The excited state lifetimes of uracil, thymine and 5-fluorouracil have been measured using femtosecond UV fluorescence upconversion in various protic and aprotic polar solvents. The fastest decays are observed in acetonitrile and the slowest in aqueous solution while those observed in alcohols are intermediate. No direct correlation with macroscopic solvent parameters such as polarity or viscosity is found, but hydrogen bonding is one key factor affecting the fluorescence decay. It is proposed that the solvent modulates the relative energy of two close-lying electronically excited states, the bright ππ^* and the dark nπ^* states. This relative energy gap controls the non-radiative relaxation of the ππ^* state through a conical intersection close to the Franck–Condon region competing with the ultrafast internal conversion to the ground state. In addition, an inverse isotope effect is observed in D₂O where the decays are faster than in H₂O.     

Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs

We prove the nonexistence of a distance-regular graph with intersection array {74,54,15;1,9,60} and of distance-regular graphs with intersection arrays

{4r³+8r²+6r+1,2r(r+1)(2r+1),2r²+2r+1;1,2r(r+1),(2r+1)(2r²+2r+1)}