Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

Lower bound of overall exponential sums for polynomialsϕ(x d )

LetS ⁽¹⁾ (n, Q) denote the maximum module of exponential sums for polynomials of degree n over the Galois fieldF _Q . In a previous paper the transition to the multiple exponential sums allowed us to obtain a good lower bound of the valueS ⁽¹⁾ (n, Q), which coincides with Weil's bound whenn = q ^(m-1)/2 + 1, whereq, m are odd andm 3. Here the same approach is used for the estimation of the valueS ^(d) (n, Q), which corresponds to polynomials(x ^d ) overF _Q , whered is any divisor ofq – 1.     

Differential form methods in the theory of variational systems and Lagrangian field theories

This paper will attempt to unify diverse material from physics and engineering in terms of differential forms on manifolds. A variational system will be defined by means of a scalar-valued differential form on a manifold and an ideal in the Grassmann algebra of differential forms on that manifold to serve as constraints. Two types of extremal submanifolds will be defined. The first-called the Euler-Lagrange extremals-will be defined by a method that is the generalization of the classical methods in the calculus of variations. The second—a generalization of a method used by Cartan in his treatise Leçons sur les invariants intégraux-will define extremals as integral submanifolds of an exterior differential system invariently attached to the variational system. As examples, the variational systems attached to string theories in Riemannian manifolds and Yang-Mills fields will be discussed from this differential form point of view. Finally, as application, the differential geometric properties and definition of energy will be presented from the differential form point of view.This work was supported by a grant from the Applied Mathematics program of the National Science Foundation.     

The influence of substrate material and annealing procedure on the properties of superconducting thin films

Thin layers YBa₂Cu₃O_7–x. are deposited by a laser ablation technique using a pulsed excimer laser operating at 308 nm. The influence of the substrate material and the annealing procedure on the superconducting behaviour of the 123 film and the reactions between the film and the substrate are studied by resistance, X-ray patterns and TEM measurements. The best results are obtained for deposition on (100) SrTiO₃ substrates. The resistance of the 1 m thick film shows a metallic behaviour, an onset in superconductivity at a temperature of 90 K, and has zero resistance at 86 K. The 123 material has a preferential oriented c-axis perpendicular to the surface plane.     

基于褐藻酸钠-纳米金复合物作非酶标记的新型电化学免疫传感器的研制

比较了用三碘甲状腺氨酸抗体(T3抗体)、褐藻酸钠(AS)标记T3抗体及褐藻酸钠-纳米金复合物(ASN)标记的T3抗体,在通过免疫反应结合到免疫电极表面后,引起的电极表面微环境发生改变的程度;用Fe(CN)3-/4-6为电化学探针,用循环伏安法获取金电极表面微环境改变的电流信息来检测 T3抗体,检测的线性范围为100～1 600ng·ml-1,检出限为45ng·ml-1.     

TiSiW12O40/TiO2催化合成苹果酯

以固载杂多酸盐TiSiW12O40/TiO2为多相催化剂，通过乙酰乙酸乙酯和乙二醇反应合成了苹果酯，探讨TiSiW12O40/TiO2对缩酮反应的催化活性，较系统地研究了原料量比，催化剂肜量，反应时间诸因素对产品收率的影响，实验表明：TiSiW12O40/TiO2是合成苹果酯的良好催化剂，在n(乙酰乙酸乙酯）：n(乙二醇）＝1：1．5，催化剂用量为反应物料总质量的1．0％，环己烷为带水剂，反应时间50min的优化条件下，苹果酯的收率可达84．1％。     

Synthesis and Insulin—sensitizing Activity of a Series of 2—Benzyl—1,3—dicarbonyl Derivatives

A series of 2-benzyl-1,3-dicabonyl derivatives was synthesized.Their insulin-sensitizing activity was evaluated in 3T3-L1 preadipocyte cells.Compounds3,26 and 27 were found to possess strong insulin-sensitizing activity in vitro and were selected for further hypoglycemic evaluation in vivo.