Homotopical algebra in homotopical categories

We develop here a version of abstract homotopical algebra based onhomotopy kernels andcokernels, which are particular homotopy limits and colimits. These notions are introduced in anh-category, a sort of two-dimensional context more general than a 2-category, abstracting thenearly 2-categorical properties of topological spaces, continuous maps and homotopies. A setting which applies also, at different extents, to cubical or simplicial sets, chain complexes, chain algebras, ... and in which homotopical algebra can be established as a two-dimensional enrichment of homological algebra.Actually, a hierarchy of notions ofh-,h1-, ...h4-categories is introduced, through progressive enrichment of thevertical structure of homotopies, so that the strongest notion,h4-category, is a sort of relaxed 2-category. After investigating homotopy pullbacks and homotopical diagrammatical lemmas in these settings, we introduceright semihomotopical categories, ash-categories provided with terminal object and homotopy cokernels (mapping cones), andright homotopical categories, provided also with anh4-structure and verifying second-order regularity properties forh-cokernels.In these frames we study the Puppe sequence of a map, its comparison with the sequence of iterated homotopy cokernels and theh-cogroup structure of the suspension endofunctor. Left (semi-) homotopical categories, based on homotopy kernels, give the fibration sequence of a map and theh-group of loops. Finally, the self-dual notion of homotopical categories is considered, together with their stability properties.Lavoro esequito nell'ambito dei progetti di ricerca del MURST.     

Right distributive quasigroups on algebraic varieties

In this paper we develop a structure theory of algebraic right distributive quasigroups which correspond to closed and connected conjugacy classes generating algebraic Fischer groups (in the sense of [6]) such that the mappingx x ^–1 ax, fora , is an automorphism of (as variety). We also give examples of algebraic Fischer groups where this does not happen. It becomes clear that the class of algebraic right distributive quasigroups has nice properties concerning subquasigroups, normal subquasigroups and direct product.We give a complete classification of one- and two-dimensional as well as of minimal algebraic right distributive quasigroups.     

A generalized,one-way,stackless quicksort

This note generalizes the one-way, stackless quicksort of Huang and Knuth to work for any type of sort key. It thus proves that quicksort can run with minimal space inO(N logN) average time.On leave from FH Fulda, D-6400 Fulda (Germany).     

稀土焦绿石化合物R2Fe4/3W2/3O7的高温高压稳定性研究和X射线相分析

 本文利用X射线粉末衍射和位敏探测技术，研究了R₂Fe_4/3W_2/3O₇（R=Er、Yb、Dy）化合物经高温高压处理后的变化情况。在3.7 GPa，1 200 ℃条件下，六方相R₂Fe_4/3W_2/3O₇化合物按两种方式分解，而直接由R₂O₃，Fe₂O₃和WO₃原料出发，经上述同样的高温高压条件合成所得的产物与六方相高温高压分解产物相同，均为R₂WO₆、RFeO₃、WO₃和Fe₂O₃的多相聚合物。同时给出了R₂Fe_4/3W_2/3O₇六方相高温高压下的稳定区范围。     

荧光光谱法研究酸性大红3R与牛血清白蛋白的结合作用

在Tris缓冲溶液(pH 7.4)体系中,运用荧光光谱法和紫外光谱法首次研究了染料酸性大红3R(AS)与牛血清白蛋白(BSA)的相互作用,并考察了表面活性剂对体系荧光强度的影响。结果表明,酸性大红3R与牛血清白蛋白能形成基态复合物,从而导致BSA内源荧光猝灭,猝灭机理主要涉及静态猝灭和非     

Low Pass metallic mesh interference filters for operation in the 165 GHz to 880 GHz region

Low Pass metallic mesh interference filters have been designed and constructed for operation in the region 340 m (880 GHz) to 1.8 mm (165 GHz). These filters have been shown to have excellent edge characteristics and good rejection regions. The results show that the mesh filter can be effectively used in both millimetre and submillimetre regions.Part of this work was performed while this author was at Heriot-Watt University, Edinburgh, U.K.     

Tunable CW laser oscillation of NdP5O14 at 1.3 μm

Low-threshold tunable cw laser oscillation is achieved at the⁴ F _3/2⁴ I _13/2 transition of NdP₅O₁₄. Continuous tunign over 1.8% of the central wavelenght is possible with 55 mW of absorbed pump power. At gain line maximum near 1.32 , the output power exceeded 1 mW. Pump threshold as low as 8 mW was observed. Reliable cw operation of the 1.3 m NdP₅O₁₄ laser pumped by a 15 mW AlGaAs laser diode is demonstrated.     

Reducible quadrature methods for Volterra integral equations of the first kind

Quadrature rules, generated by linear multistep methods for ordinary differential equations, are employed to construct a wide class of direct quadrature methods for the numerical solution of first kind Volterra integral equations. Our class covers several methods previously considered in the literature. The methods are convergent provided that both the first and second characteristic polynomial of the linear multistep method satisfy the root condition. Furthermore, the stability behaviour for fixed positive values of the stepsizeh is analyzed, and it turns out that convergence implies (fixedh) stability. The subclass formed by the backward differentiation methods up to order six is discussed and illustrated with numerical examples.     

Backward differentiation type formulas for Volterra integral equations of the second kind

Summary Numerical integration formulas are discussed which are obtained by differentiation of the Volterra integral equation and by applying backward differentiation formulas to the resulting integro-differential equation. In particular, the stability of the method is investigated for a class of convolution kernels. The accuracy and stability behaviour of the method proposed in this paper is compared with that of (i) a block-implicit Runge-Kutta scheme, and (ii) the scheme obtained by applying directly a quadrature rule which is reducible to the backward differentiation formulas. The present method is particularly advantageous in the case of stiff Volterra integral equations.