Intersection representation of digraphs in trees with few leaves

The leafage of a digraph is the minimum number of leaves in a host tree in which it has a subtree intersection representation. We discuss bounds on the leafage in terms of other parameters (including Ferrers dimension), obtaining a string of sharp inequalities. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 340–353, 1999     

黏性边界层网格自动生成

高雷诺数黏性流动在壁面附近存在边界层,在计算模拟中自动生成可靠且有效的计算网格仍然是计算流体力学存在的瓶颈.三棱柱/四面体混合网格技术在一定程度上缓解了这个困难.然而,对于复杂外形的情况,在边界层内自动高效生成高质量的三棱柱单元仍然十分困难.常用的层推进法在凹凸区域及角点处生成的边界层网格单元质量较差,边界层网格最外层尺寸不均匀.针对这些问题,发展了一种黏性边界层网格自动生成方法,通过顶点周围边的二面角识别物面网格特征确定多生长方向,预估并调整生长高度处理相交情况.同时提出一种三维前沿尺寸调节方式,提高了边界层网格单元的正交性,保证了边界层网格与远场网格尺寸的光滑过渡.通过ONERA M6翼型以及带发动机短舱的DLR-F6翼身组合体等外形的网格生成实例及绕流数值模拟,将计算值与标准实验值进行对比,结果表明:该方法能够自动高效地生成满足数值计算需求的混合网格.     

Decay Dynamics of N,N-Dimethylthioacetamide in S3(ππ*) State (cited: 1)

The decay dynamics of N,N-dimethylthioacetamide after excitation to the S₃(ππ^*) state was studied by using the resonance Raman spectroscopy and complete active space selfconsistent field method calculations. The UV-absorption and vibrational spectra were assigned. The A-band resonance Raman spectra were obtained in acetonitrile, methanol and water with the laser excitation wavelengths in resonance with the first intense absorption band to probe the Franck-Condon region structural dynamics. The CASSCF calculations were carried out to determine the excitation energies and optimized structures of the lowerlying singlet states and conical intersection point. The A-band structural dynamics and the corresponding decay mechanism were obtained by the analysis of the resonance Raman intensity pattern and the CASSCF calculated structural parameters. The major decay channel of _3,FC(ππ^*)→S₃(ππ^*)/S₁(nπ^*)→_{1(nπ^*) is proposed.}     

State to State Photodissociation Dynamics of Vibrationally Excited D2O in B Band

The state-to-state photodissociassion dynamics for the B band of D₂O have been explored from quantum dynamical calculations including the electronic ~X and ~B states. The calculations were carried out using a Chebyshev real wave packet method. The calculated absorption spectra, product state distributions, and branching ratios from different initial vibrational states show di?erent dynamic features, due to the different shapes of the vibrational wavefunctions. The initial bending mode (0,1,0) generates two lobes with a shallow minimum on the absorption spectrum and a slight inverted vibrational population of OD(~X )product at high total energies. The rotational state distributions of OD(~X , v=0) product are highly inverted and depend weakly on the initial state and total energy. On the other hand, the ro-vibrational distributions of OD(A~) product strongly oscillate with the total energy, which are dominated by the long-living resonances and depend sensitively on the potential surfaces. The antisymmetric stretching mode (0,0,1) has large OD( ~ A)/OD(~X ) branching ratios at high total energies, which indicates that the B band dissociation proceeds mainly via the adiabatic pathway in some cases.     

Separating invariants and finite reflection groups

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras.     

Existence theorems for variational inclusion problems and the set-valued vector Ekeland variational principle in a complete metric space

In this paper, we apply an existence theorem for the variational inclusion problem to study the existence results for the variational intersection problems in Ekeland’s sense and the existence results for some variants of set-valued vector Ekeland variational principles in a complete metric space. Our results contain Ekeland’s variational principle as a special case and our approaches are different to those for any existence theorems for such problems.     

Local Łojasiewicz exponents,Milnor numbers and mixed multiplicities of ideals

Let be a finite analytic map. We give an expression for the local Łojasiewicz exponent and for the multiplicity of g when the component functions of g satisfy certain condition with respect to a set of n monomial ideals I ₁,..., I _n . We give an effective method to compute Łojasiewicz exponents based on the computation of mixed multiplicities. As a consequence of our study, we give a numerical characterization of a class of functions that includes semi-weighted homogenous functions and Newton non-degenerate functions. Work supported by DGICYT Grant MTM2006-06027.     

On intersection and mixed intersection bodies

Duals of the basic projection and mixed projection inequalities are established for intersection and mixed intersection bodies.      

The inside outside intersection problem for hexagon triple systems

We give a complete solution of the following two problems:

1. (1)
   For which (n, x) does there exist a pair of hexagon triple systems of order n having x inside triples in common?
    
2. (2)
   For which (n, x) does there exist a pair of hexagon triple systems having x outside triples in common?
    

     

3-二甲氨基-2-甲基丙烯醛S2激发态结构动力学

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（）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一带短时结构动力学和其后的衰变动力学表明,C1=06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=06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S2,FC（ππ^＊）经由各锥形交叉点和各系间窜跃点回到S0或T1,min的两个衰变通道。