三硼酸锂晶体的生长形态

用自由生长系统研究了三硼酸锂ＬｉＢ_３Ｏ_５（ＬＢＯ）晶体的实际生长形态。实验表明，它的各晶面簇的重要性的顺序为：｛１１０｝＞｛０１１｝＞｛２０１｝＞｛１１１｝。讨论了ＬＢＯ晶体的生长习性与内部结构之间的关系并应用负离子配位多面体理论模型解释了ＬＢＯ晶体的生长形态。     

Quantum chemistry investigation on the active site of Mn-SOD

In this paper, we carried out a theoretical study on the active site structures of the Mn-SOD with ab initio Hartree–Fock SCF method, and analyzed the molecular orbital energies, charges and atomic orbital contribution to the frontier molecular orbital.     

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 .

     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

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.

     

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.