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.     

SEPARATING SCN~- FROM DESULPHURIZATION WASTE SOLUTION OF COCKING PLANT BY D241 RESIN

1. INTRODUCTION In the process of coking plant, about 30%~35% sulfur is transformed to H2S and some other sulfide, which form impurity in coal gas together with NH3 and HCN. Only 0.1% H2S containing in air can lead to die, so it is very important to carry on desulphurization and decyanation with coal gas [1~3]. Currently desulphurization and decyanation craft technique have Dry Oxidation Technology, Wet Oxidation Technology and Liquid Absorption Technology [2] three main kinds. The…     

Effective magnetic properties of a composite material with circular conductive elements

Effective magnetic properties of a composite meta-material consisting of periodically arranged circular conductive elements are studied theoretically. A general expression for the effective bulk permeability is obtained with mutual effects and lattice ordering being taken into account. The resonance frequency of the permeability is found to be strongly dependent on the size and shape of the unit cell. Frequency dispersion of the permeability is studied with special attention paid to the frequency range, where negative values of the permeability are possible. Corresponding recommendations for optimisation of the meta-materials with negative permeability are made. The results are confirmed by numerical simulations of the finite structure behaviour in an external magnetic field. Received 19 April 2002 Published online 31 July 2002     

Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Charge transport in a polypeptide chain

Charge transport is one important example of signal transduction in a protein which is responsible for action at a distance, and is a fundamental process in biochemical action. A model is presented in which electronic effects interact with motional processes to combine into a bifunctional model. This model is investigated with new detailed molecular dynamics calculations and successfully explains such action at a distance. Received 1st February 2002 / Received in final form 26 May 2002 Published online 13 September 2002     

Spray Freeze-drying – The Process of Choice for Low Water Soluble Drugs?

Most of the novel highly potent drugs, developed on the basis of modern molecular medicine, taking into account cell surface recognition techniques, show poor water solubility. A chemical modification of the drug substance enhancing the solubility often decreases the pharmacological activity. Thus, as an alternative an increase of the solubility can be obtained by the reduction of the size of the drug particles. Unfortunately, it is often difficult to obtain micro or nanosized drug particles by classical or more advanced crystallization using supercritical gases or by milling techniques. In addition, nanosized particles are often not physically stable and need to be stabilized in an appropriate matrix. Thus, it may be of interest to manufacture directly nanosized drug particles stabilized in an inert hydrophilic matrix, i.e. nanostructured and nanocomposite systems. Solid solutions and solid dispersions represent nanostructured and nanocomposite systems. In this context, the use of the vacuum-fluidized-bed technique for the spray-drying of a low water soluble drug cosolubilized with a hydrophilic excipient in a polar organic solvent is discussed. In order to avoid the use of organic solvents, a special spray-freeze-drying technique working at atmospheric pressure is presented. This process is very suitable for temperature and otherwise sensitive drugs such as pharmaproteins.