SOME SUBGROUPS OF THE EXTENDED HECKE GROUPS (λ_q)

The authors consider the extended Hecke groups H(λq) generated by T(z) = -1 / z, S(z) = -1/(z + λq,) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(λq), the second commutator subgroup H (λq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups H(λq) are studied. Also, relations between them are given.     

COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY

1.IntroductionThispaperisdevotedtothecalculatiollofT,ranchesofHopfpointswhichemallatefromacertaillsingularPointofatwopar:lmeterII()nlinearsystemwhereXisarealHillersspac(},Aabifllrcationparallleter,oranadditionalcontrolparameter,alldgisasnlootllmapping.\Nreassllllle(HI)gisA--synlnletric:thereexistsalillearoperators:X-Xsatisfying(I:identicaloperatorillX)Itiswellknottrnthat(1.2)irldllcestilesplittillgl)Th.firstauthorhasbeedsupportedbyar(>searchgralltoftileV'Olkswagen-StiftungWesaythatxiss…     

Photoinduced electron transport process in electrochemical cell I. Phenomenological description

The process of electron transport plays an essential role in the fundamental phenomena of life like photosynthesis, respiration and vision as well as in photoelectronic devices. However, the molecular mechanisms of the electron way and factors governing the transport rate in such systems are still unclear. Several groups have reported theoretical approaches for searching the mechanisms by using statistical mechanics, coherent dynamics and quantum mechanics. The current density vector inside the semiconducting layer is determined. In this paper we consider the problem of transport of electron promoted in the electrochemical cell constructed of two electrodes with the dye molecules immersed in. We describe the process of electron promotion by refractive light wave on the vacuum–semiconductor boundary as well as on the semiconducting electrode and the dye molecule layer in terms of extended phenomenological electrodynamics formalism. The results of our theoretical model show that such a theoretical approach will give more information on the mechanism of electron transport and will give insight in the determination of some electric features of materials.     

How bridging ligands and neighbouring groups tune the gold-gold bond strength

Gold-gold interactions in small polynuclear complexes are analysed using extended Hückel calculations. They are influenced by the nature of the ligand donor atoms, by the bridging ligands, but most by the formal oxidation state of the metal. Au---Au bonds are much stronger in complexes of Au(II) and Au(III), but a weak interaction between two d¹⁰ centres exists for Au(I) complexes, owing to mixing of the s and p orbitals with the d orbitals. Phosphines induce stronger metal-metal bonds when coordinated trans to the Au---Au bond in [Au(II)[(CH₂)₂PPh₂]L]₂ (Ph = phenyl), but have the opposite effect when bonded orthogonally to the metal-metal axis in Au(I) binuclear species. When two gold atoms are bridged by a single carbon atom, belonging either to mesityl (Mes = 2,4,6-Me₃C₆H₂) or CR₂, the former produces stronger Au(I)---Au(I) interactions, reflected in shorter distances. Formal oxidation states are proposed for the gold atoms in two mixed-valence clusters, [Au4(C₆F₅)₂((PPh₃)_{2CH})2(PPh3)2](ClO4)2 and [{(2,4,6-C6F3H2)Au(CH2PPh2CH2)2Au{in2}-Au(CH₂PPh₂CH₂)₂Au](ClO₄)₂. The results suggest a higher oxidation state for the outer gold atoms, in both the T-shaped tetranuclear cluster and the Au₆ linear chain.     

Quantized Hamilton Dynamics

The paper describes the quantized Hamilton dynamics (QHD) approach that extends classical Hamiltonian dynamics and captures quantum effects, such as zero point energy, tunneling, decoherence, branching, and state-specific dynamics. The approximations are made by closures of the hierarchy of Heisenberg equations for quantum observables with the higher order observables decomposed into products of the lower order ones. The technique is applied to the vibrational energy exchange in a water molecule, the tunneling escape from a metastable state, the double-slit interference, the population transfer, dephasing and vibrational coherence transfer in a two-level system coupled to a phonon, and the scattering of a light particle off a surface phonon, where QHD is coupled to quantum mechanics in the Schrödinger representation. Generation of thermal ensembles in the extended space of QHD variables is discussed. QHD reduces to classical mechanics at the first order, closely resembles classical mechanics at the higher orders, and requires little computational effort, providing an efficient tool for treatment of the quantum effects in large systems.     

含聚醚间隔链的扩链脲改性环氧树脂/双氰双胺固化体系性能研究

合成了一系列含不同分子量聚环氧丙烷 (PPG)柔性间隔链的扩链脲 ,系统考察了扩链脲改性环氧树脂E 5 1/双氰双胺 (dicy)固化体系的固化反应活性、动态力学行为、冲击性能和断裂面形态结构 ,并对体系的冲击性能、形态结构与动态力学行为之间的关系进行了探讨 .结果表明 ,改性体系固化反应活性明显提高 ,固化反应表观活化能降低 ,固化反应峰顶温度从 190℃降低至 14 0℃ ,固化反应的表观活化能由 14 5 5kJ/mol降至 70～ 80kJ mol;改性体系冲击强度明显提高 ,其中所含PPG柔性链分子量为 10 0 0的扩链脲改性的E 5 1/dicy体系冲击强度较未改性的E 5 1/dicy体系提高了 8倍 ,其冲击试样断裂面的形态具有明显的韧性断裂特征 ,微观两相网络结构的存在导致了改性体系冲击强度显著提高     

The effects of polymer chain rigidification, zeolite pore size and pore blockage on polyethersulfone (PES)-zeolite A mixed matrix membranes

The polyethersulfone (PES)-zeolite 3A, 4A and 5A mixed matrix membranes (MMMs) were fabricated with a modified solution-casting procedure at high temperatures close to the glass transition temperatures (T_g) of polymer materials. The effects of membrane preparation methodology, zeolite loading and pore size of zeolite on the gas separation performance of these mixed matrix membranes were studied. SEM results show the interface between polymer and zeolite in MMMs experiencing natural cooling is better (i.e., less defective) than that in MMMs experiencing immediate quenching. The increment of glass transition temperature (T_g) of MMMs with zeolite loading confirms the polymer chain rigidification induced by zeolite. The experimental results indicate that a higher zeolite loading results in a decrease in gas permeability and an increase in gas pair selectivity. The unmodified Maxwell model fails to correctly predict the permeability decrease induced by polymer chain rigidification near the zeolite surface and the partial pore blockage of zeolites by the polymer chains. A new modified Maxwell model is therefore proposed. It takes the combined effects of chain rigidification and partial pore blockage of zeolites into calculation. The new model shows much consistent permeability and selectivity predication with experimental data. Surprisingly, an increase in zeolite pore size from 3 to 5 Å generally not only increase gas permeability, but also gas pair selectivity. The O₂/N₂ selectivity of PES-zeolite 3A and PES-zeolite 4A membranes is very similar, while the O₂/N₂ selectivity of PES-zeolite 5A membranes is much higher. This implies the blockage may narrow a part of zeolite 5A pores to approximately 4 Å, which can discriminate the gas pair of O₂ and N₂, and narrow a part of zeolites 3A and 4A pores to smaller sizes. It is concluded that the partial pore blockage of zeolites by the polymer chains has equivalent or more influence on the separation properties of mixed matrix membranes compared with that of the polymer chain rigidification.     

Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem

The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations, or even exact expressions, for the Fukui function for electron attachment.