On the realization of Riemannian symmetric spaces in Lie groups

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G.     

Roles of SiH4 and SiF4 in growth and structural changes of poly-Si films

The structural properties of polycrystalline silicon films, prepared by plasma enhanced chemical vapor deposition system, with different flow rates of SiH₄/SiF₄ mixtures at 300 °C were investigated. This study indicates that the low hydrogen coverage on the growing surface, under optimum fluorine radicals, will be leaded to an improvement of crystallized area as compared with case of high hydrogen coverage surface. Moreover, the studies of the role of SiH₄ and SiF₄ radicals show that the SiH₄ radicals are important in the nucleation and growth of grains. However, SiF₄ radicals are effective in the structural change of grain boundaries regions and by this way, in the present system, establish the growth of grains under the dominant 〈1 1 0〉 direction. The stress investigation indicates that addition of high flow rate of SiF₄ in amorphous film, results in the nearly stress free films. Finally, we found that the changes in g-value reflect the changes in the intrinsic compressive and tensile stress in the both polycrystalline and amorphous silicon films.     

HgCl2/I2复合催化剂协同催化合成异丙醇钇的研究

以金属钇和异丙醇为原料，以HgCl2/I2为复合催化剂，通过对金属钇的机械加工以增加其比表面，并将异丙醇脱水使其含水量降低至0．05％，体系在82℃回流5h，经过滤、减压蒸馏，得到了白色海绵状异丙醇钇，其产率高达83％，合成时间比文献报道的缩短了19h，产率提高了8％。文章确定了催化剂的最佳用量为20gY加入60mg HgCl2/I2，研究了合成产率与HgCl2/I2催化剂和HgCl2催化剂的依赖关系及异丙醇中含水量对合成产率的影响，并对HgCl2/I2的催化作用机理进行了初步探讨。     

Solving Problems with Min-Type Functions by Disjunctive Programming

We consider applications of disjunctive programming to global optimization and problems with equilibrium constraints. We propose a modification of the algorithm of F. Beaumont for disjunctive programming problems and show its numerical efficiency.     

Nonsensitiveness Regions for Threshold Ellipsoids

The problem is to determine nonsensitiveness regions for threshold ellipsoids within a regular mixed linear model.     

Sharp estimates in terms of moduli of smoothness for compound cubature rules

Summary In 1980 Dahmen-DeVore-Scherer introduced a modulus of continuity which turns out to reflect invariance properties of compound cubature rules effectively. Accordingly, sharp error bounds are derived, the existence of relevant counterexamples being a consequence of a quantitative resonance principle, established previously.     

Sensitivity analysis for discrete optimal control problems

We present local sensitivity analysis for discrete optimal control problems with varying endpoints in the case when the customary regularity of boundary conditions can be violated. We study the behavior of the optimal solutions subject to parametric perturbations of the problem.     

On the density of the space of continuous and uniformly continuous functions

For X a metrizable space and (Y,ρ) a metric space, with Y pathwise connected, we compute the density of (C(X,(Y,ρ)),σ)—the space of all continuous functions from X to (Y,ρ), endowed with the supremum metric σ. Also, for (X,d) a metric space and (Y,‖⋅‖) a normed space, we compute the density of (UC((X,d),(Y,ρ)),σ) (the space of all uniformly continuous functions from (X,d) to (Y,ρ), where ρ is the metric induced on Y by ‖⋅‖). We also prove that the latter result extends only partially to the case where (Y,ρ) is an arbitrary pathwise connected metric space.To carry such an investigation out, the notions of generalized compact and generalized totally bounded metric space, introduced by the author and A. Barbati in a former paper, turn out to play a crucial rôle. Moreover, we show that the first-mentioned concept provides a precise characterization of those metrizable spaces which attain their extent.     

Coxeter complexes and graph-associahedra

Given a graph Γ, we construct a simple, convex polytope, dubbed graph-associahedra, whose face poset is based on the connected subgraphs of Γ. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves.     

On extremally disconnected topological groups

We introduce the notion of a partially selective ultrafilter and prove that (a) if G is an extremally disconnected topological group and p is a converging nonprincipal ultrafilter on G containing a countable discrete subset, then p is partially selective, and (b) the existence of a nonprincipal partially selective ultrafilter on a countable set implies the existence of a P-point in ω^∗. Thus it is consistent with ZFC that there is no extremally disconnected topological group containing a countable discrete nonclosed subset.