The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem

Summary The finite element method with non-uniform mesh sizes is employed to approximately solve Helmholtz type equations in unbounded domains. The given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary. This approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. This results in a great reduction in the number of equations to be solved. It is proved that optimal error estimates hold inL ²,H ¹ andL , provided that certain relationships hold between the frequency, mesh size and outer radius.     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

X-H (X = C, N, O, Si, P, S) 键离解能计算的密度泛函方法研究

使用了不同密度泛函方法计算X-H (X = C, N, O, Si, P, S) 键离解能，并分析不同密度泛函方法的计算精度。研究发现大多数密度泛函方法包括B3LYP, B3P86, B3PW91, G96LYP, PBE1PBE，和BH&HLYP都明显低估键离解能13-25 kJ/mol。该现象与是否使用无限基组无关，因为即使使用无限基组键离解能仍然被低估。因此密度泛函方法不适合用于键离解能的估算。其中B3P86方法的偏差最小。进一步分析表明，使用限制性开壳层计算并无任何优势，在大多数情况下非限制性开壳层计算实际上比限制性开壳层计算要好。最后，我们发现了密度泛函方法对键离解能的低估是系统的，因此建议利用校准后的UDFT/6-311++G(d, p)方法计算化学键离解能。     

CH_3自由基和O（~3P）反应机理的量子化学研究

用分子轨道从头计算MP2（full）方法和密度泛函理论（DFT）中的B3LYP方法 研究了CH_3自由基和三线态O原子反应的微观机理，优化得到了反应途径上的反应 物、过渡态、中间体和产物的几何构型，通过振动分析对过渡态和中间体构型进行 了确认，在G3不平上计算了能量，同时用经典过渡态理论对该反应的绝对速率常数 进行了理论计算。研究结果表明：CH_3自由基与O（~3P）反应有四条不同的放热反 应通道，主反应通道为IM1→TS1→CH_2O + H，同时反应可彻底裂解生成CO, H_2 及H。     

On an alternative functional equation related to the Cauchy equation

We consider the following problem: Let (G, +) be an abelian group,B a complex Banach space,a, bB,b0,M a positive integer; find all functionsf:G B such that for every (x, y) G ×G the Cauchy differencef(x+y)–f(x)–f(y) belongs to the set {a, a+b, a+2b, ...,a+Mb}. We prove that all solutions of the above problem can be obtained by means of the injective homomorphisms fromG/H intoR/Z, whereH is a suitable proper subgroup ofG.     

Miniaturization of a thalliumiodide photodissociation laser

We report on the operation of a thallium photodissociation laser with an active medium in the form of a thin layer on a quartz wall. Laser emission has been obtained with layer thicknesses below 100 m. This gas laser seems to be feasible with an active volume as small as 10^–1 to 10^–2 mm³.     

Photochemistry of β, γ-unsaturated ketones-V: The direct irradiation of some γ-phenyl β, γ-enones

The photochemistry of some members of the two series of γ-phenyl substituted acyclic β, γ-unsaturated ketones 1 and 2 upon direct irradiation with γ 310nm has been investigated, viz 1c–1h and 2b+2c.The alkyl substituted (E)-5-phenyl-4-penten-2-ones 1c–1h yield the corresponding 1,3-acyl shift products and (Z)-isomers, and 1g and 1h in addition two decarbonylated products. 2b only yields the (Z)-isomer and some benzaldehyde, but 2c yields the 1,3-acyl shift product, the ODPM product, three hydrocarbons formed by disproportionation of the allyl radical, and some benzaldehyde. The β-phenyl β, γ-UK 3a proved to be photostable. The 1,3-acyl shift products of 1c–1h result mainly from the singlet excited state in a cage radical process. The exclusive formation of the (E)-configuration of the 1,3-acyl shift product is explained in terms of conformational preference of the intermediate allyl radical. It is proposed that the formation of the (Z)-isomer proceeds from ¹T(π -π^*) which is populated according to

. Evidence is presented which supports the proposed mechanism.The β,γ-UK 2b containing a benzoyl moiety leads to a higher degree of (E)-(Z) isomerization than the corresponding 1d which has an acetyl moiety.The triplet energies of (E)- and (Z)-1h are 56 and ca 70 kcal/mol respectively.     

273.15 K下Li2B4O7-LiCl-H2O体系热力学性质的等压研究及离子作用模型

用等压法研究了273.15 K下Li₂B₄O₇-LiCl-H₂O体系不同质量摩尔浓度分数的等压平衡浓度和水活度; 计算了LiCl和Li₂B₄O₇混合盐溶液的渗透系数等热力学性质. 用273.15 K下的实验数据对Pitzer离子相互作用模型进行了参数化研究, 拟合求取了273.15 K下Pitzer离子相互作用参数, 用获得的参数计算了LiCl和Li₂B₄O₇在Li₂B₄O₇-LiCl-H₂O体系中的活度系数. 273.15 K下由相应的Pitzer模型计算的渗透系数值与实验结果一致. 这对完善含锂、硼盐湖卤水体系的热力学模型具有重要意义.     

Caracterisation par analyse calorimetrique differentielle des complexes entre LiAlH4 et les ethers-couronnes 12-C-4, 15-C-5, dicyclohexano-18-C-6

The thermal behaviour of complexes [Li⁺-EC](AlH₄)^– withEC=12-C-4, 15-C-5, DC 18-C-6 (cis-anti-cis andcis-syn-cis isomers) was investigated by Differential Scanning Calorimetry (DSC). These complexes were prepared as solids from benzene solutions. Pure EC and several solvated species [Li⁺-EC](AlH₄)^–·nC₆H₆ (EC=15-C-5, DC 18-C-6syn) were also studied. DSC has revealed various phenomena. Solid-solid transitions were observed before melting for [Li⁺-EC](AlH₄)^– withEC=12-C-4 and 15-C-5. They are probably explained by small molecular modifications strongly dependent on the thermal history of the sample. A glass-transition was found for the pure crown-ether DC 18-C-6anti, the complex [Li⁺-EC](A1H₄)^– withEC=DC-18-C-6anti and the two solvates mentioned above.