Rational cuspidal plane curves of type (d,d-4) with

In the present paper we classify rational cuspidal plane curves with maximal multiplicity deg C - 4 and at least three cusps and where (V,D) is the minimal (SNC) resolution of (ℙ²,C). Received: 28 August 1998     

Extension dans un cadre algébrique d'une formule de Weil

Let R be a commutative A-algebra, and f=(f ₁,…,f _n ) a quasi-regular sequence such that P=R/(f) is finitely generated and projective over A. In the algebraic residue formalism due to J. Lipman, we propose the analog of an analytic Weil's formula. As applications, we first give some criterions for homomorphism from A[z] to A[z] to be finite when A is a n\oe therian ring, and then an algebraic proof of the usual analytic Weil's formula. Received: 27 April 1998     

Schubert polynomials of types A--D

Schubert polynomials of type B, C, and D have been described first by S. Billey and M. Haiman [BH] using a combinatorial method. In this paper we give a unified algebraic treatment of Schubert polynomials of types A–D in the style of the Lascoux–Schützenberger theory in type A, i.e. Schubert polynomials are generated by the application of sequences of divided difference operators to “top polynomials”. The use of the creation operators for Q-Schur and P-Schur functions allows us to give: (1) simple and natural forms of the “top polynomials”, (2) formulas for the easy computation with all divided differences, (3) recursive structures, and (4) simplified derivations of basic properties. Received: 23 July 1998     

Linear systems on singular curves

We start this work by studying free linear systems on singular curves and related base point free linear systems on the non-singular model. We apply these results to the study of pencils of small degree on non-singular curves. We also prove a “base point free pencil trick” which holds for any (possibly) singular curve. Received: 15 June 1998     

Sur la fibre d'un polynôme à points critiques isolés

In this paper, we express the Euler characteristic of the fibers of a polynomial whose critical points are isolated in terms of signatures of appropriate bilinear symmetric forms. Received: 15 February 1999 / Revised version: 28 June 1999     

Generalized Shioda–Inose structures on K3 surfaces

In this note, we study the action of finite groups of symplectic automorphisms on K3 surfaces which yield quotients birational to generalized Kummer surfaces. For each possible group, we determine the Picard number of the K3 surface admitting such an action and for singular K3 surfaces we show the uniqueness of the associated abelian surface. Received: 9 April 1998 / Revised version: 17 July 1998     

Isolated rational curves on K3-fibered Calabi–Yau threefolds

In this paper we study 16 complete intersection K3-fibered Calabi--Yau variety types in biprojective space ℙ ^{n 1}}×ℙ¹. These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d,0) for every positive integer d on a general Calabi–Yau variety of these types. The proof depends heavily on existence theorems for curves on K3-surfaces proved by S. Mori and K. Oguiso. Some of these varieties are related to Calabi–Yau varieties in projective space by a determinantal contraction, and we use this to prove existence of rational curves of every degree for a general Calabi–Yau variety in projective space. Received: 14 October 1997 / Revised version: 18 January 1998     

含X-型二维液晶基元和冠醚环的液晶共聚酯的研究

合成了一系列新的含X-型二维液晶基元和反式-4,4'-双(4-羟基苯基偶氮)二苯并-14-冠-4冠醚环的主链型液晶共聚酯. 通过GPC, [η], DSC, TG, WAXD和POM对其液晶性研究发现, 所有的共聚酯都呈现出向列相的丝状织构或纹影织构. 共聚酯的熔融温度(T_m)和各向同性温度(T_i)随共聚酯分子中反式-4,4'-双(4-羟基苯基偶氮)二苯并-14-冠-4用量的改变呈规律性变化.     

Sol-gel synthesis of K3InF6 and structural characterization of K2InC10O10H6F9, K3InC12O14H4F18 and K3InC12O12F18

K₃InF₆ is synthesized by a sol-gel route starting from indium and potassium acetates dissolved in isopropanol in the stoichiometry 1:3, with trifluoroacetic acid as fluorinating agent. The crystal structures of the organic precursors were solved by X-ray diffraction methods on single crystals. Three organic compounds were isolated and identified: K₂InC₁₀O₁₀H₆F₉, K₃InC₁₂O₁₄H₄F₁₈ and K₃InC₁₂O₁₂F₁₈. The first one, deficient in potassium in comparison with the initial stoichiometry, is unstable. In its crystal structure, acetate as well as trifluoroacetate anions are coordinated to the indium atom. The two other precursors are obtained, respectively, by quick and slow evaporation of the solution. They correspond to the final organic compounds, which give K₃InF₆ by decomposition at high temperature. The crystal structure of K₃InC₁₂O₁₄H₄F₁₈ is characterized by complex anions [In(CF₃COO)₄(OH_x)₂]^(5−2x)− and isolated [CF₃COOH_2−x]^(x−1)− molecules with x=2 or 1, surrounded by K⁺ cations. The crystal structure of K₃InC₁₂O₁₂F₁₈ is only constituted by complex anions [In(CF₃COO)₆]³⁻ and K⁺ cations. For all these compounds, potassium cations ensure only the electroneutrality of the structure. IR spectra of K₂InC₁₀O₁₀H₆F₉ and K₃InC₁₂O₁₂F₁₈ were also performed at room temperature on pulverized crystals.     

质子导体固体氧化物燃料电池的Ba2Co9O14阴极材料

Ba₂Co₉O₁₄（BCO）是一种新型的电子-氧离子混合导体,在氧离子导体的固体氧化物燃料电池（SOFC）中,其作为阴极材料的应用可能性已经得到证实,本工作探索BCO在质子导体SOFC中的应用可能性。采用固相反应法制备BCO粉体,研究BCO与质子导体电解质BZCY （BaZr_0.1Ce_0.7Y_0.2O_3-δ）之间的化学相容性,分析BCO-BZCY复合阴极在BZCY电解质上的电化学性能。当复合阴极中BCO的质量含量为70%时,阴极性能最佳,界面阻抗活化能为1.26 eV。以BCO-BZCY为阴极,Ni-BZCY为阳极,BZCY为电解质的阳极支撑型单电池,700℃时,单电池的极化阻抗为0.15 Ω·cm²,最大功率密度为400 mW·cm^-2。