Contravariant forms and extremal projectors

Tensor product of irreducible modules of highest weight over a semi-simple quantum group is completely reducible if and only if a natural contravariant form is non-degenerate when restricted to the span of singular vectors. We express this restriction through the extremal projector of the quantum group providing a computationally feasible criterion for complete reducibility of tensor products.     

Homology and cohomology intersection numbers of GKZ systems

We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twisted period relation, we obtain a formula of cohomology intersection numbers in terms of a Laurent series. We show that the cohomology intersection number depends rationally on the parameters. We also prove a conjecture of F. Beukers and C. Verschoor on the signature of the monodromy invariant hermitian form.     

Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .

     

Boundary value estimates for harmonic forms

We prove a bound for the -norm of harmonic forms in terms of certain -norms of their normal and tangential components. In turn, this is used to show the -norm equivalence of the normal and tangential components of harmonic forms on manifolds.

     

Synthesis and Crystal Structure of a Novel 1D Coordination Polymer: [Pr(BYBA)3(H2O)2]·[Pr(BYBA)3(H2O)]

The novel coordination polymer [Pr(BYBA)3(H2O)2]·[Pr(BYBA)3(H2O)] (BYBAH = 2-benzoylbenzoic acid) was yielded by hydrothermal synthesis, determined by single-crystal X-ray diffraction, and characterized by FT-IR and UV-Vis spectra. The crystal crystallizes in the triclinic system, space group P with a = 9.112(3), b = 14.644(5), c = 27.076(11) (A), α = 84.223(3), β = 87.816(4), γ = 88.902(4)o, V = 3592(2) (A)3, C84H60O21Pr2, Mr = 1687.14, Z = 2, F(000) = 1700, Dc = 1.560 g/cm3, μ = 1.419 mm-1, the final R = 0.0485 and wR = 0.1258 for 13035 observed reflections with I＞2((I). The compound contains two different building units, [Pr2(BYBA)6(H2O)4] and [Pr2(BYBA)6(H2O)2]. It is noticeable that [Pr2(BYBA)6(H2O)4] is an isolated binuclear building block, in which the Pr3 ion centers are both located in an eight-coordinated environment. However, in [Pr2(BYBA)6(H2O)2] the Pr3 ion centers are located in a nine-coordinated environment and connected by BYBA ligands to form 1D chains.     

激光Raman光谱研究2,4己二炔-1,6二醇的双苯异氰酸酯的聚合——晶型对固相聚合活性的影响

用激光Raman光谱研究了三种不同晶型的2,4-已二炔-1,6二醇的双苯异氰酸酯(HDPU)的聚合,发现不同晶型的HDPU的聚合活性与其C=C伸缩振动频率的频移之间存在内在联系。这说明单体晶格与聚合物晶格的匹配是HDPU具有高的聚合活性的必要条件。     

酞菁氧钛的合成及晶型转化

酞菁氧钛以联环己烷为溶剂，以邻苯二脂及四氯化钛直接反应生成。其优点是便于分离及纯化。同时对各晶型的获得及晶型间的相互转化进行了研究，并以Ｘ－射线粉末衍射及ＦＴ－ＩＲ进行了表征，并记录了不同晶型的酞菁氧钛在室温硫化硅橡胶中的吸收光谱。     

An unusual twist conformation of 2-O-methyl-1,3,4,5-tetrakis-O-tert-butyldiphenylsilyl-myo-inositol

The ring conformation of 2-O-methyl-1,3,4,5-tetrakis-O-tert-butyldiphenylsilyl-myo-inositol was in a twist form both in solid state and in solution. This is the first observation of a stable twist conformer induced by the introduction of bulky silyl protecting groups.     

Studies on Cyclodextrin Inclusion Complex by Fluorescence Anisotropy

An equation for determining the equilibrium association constant (KA) of cyclodextrin inclusion complex with fluorescence anisotropy is derived and used to determine KA of pyrene-B-cyclodextrin inclusion complex. The existing forms of cyclodextrin inclusion complex in solution, the interaction type of host with guest, and the possibility of application of B-cyclodextrin in the analysis of metal ions using naphthalene derivative as a ligand are discussed based on the equation derived along with the curve of fluorescence anisotropy versus cyclodextrin concentration of guest/cyclodextrin system.