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.     

Low temperature synthesis, structure and bioactivity of xCaO· (1−x)SiO2 glasses

Glasses of composition expressed by the following general formula xCaO·(1?x)SiO₂ (0.30≤x≤0.50) can be prepared by means of the sol-gel route starting from tetramethylorthosilicate and calcium nitrate tetrahydrate They are all difficult to prepare by means of the traditional technique of quenching the melt, because of the high liquidus temperature,T ₁ t that in the case ofx=0.3 glass isT ₁ =1650°C. The DTA apparatus appears a valuable tool for defining the procedure necessary to obtain the glass through the sol-gel route. The glassx=0.3 is bioactive. The experimental results suggest that the gel structures, such as obtained at room temperature, are very similar; only at high temperature do the reactions of hydrolysis and polycondensation go to completion and the structural units characteristic of each glass are obtained.     

Thermal evolution of ferromagnetic metallic glasses

A traditional TG apparatus was modified by placing two permanent magnets producing a controlled magnetic field (TG(M): Magneto Thermogravimetry). This technique proved to be useful to study both structural relaxation and crystallisation of ferromagnetic metallic glasses. Results obtained for the amorphous alloys Fe₄₀Ni₄₀P₁₄B₆ and Fe_62.5Co₆Ni_7.5Zr₆Nb₂Cu₁B₁₅, are reported in this paper. Structural relaxation can be evaluated by measuring changes in Curie temperature induced by thermal treatments. Crystallisation in TG(M) is detected through a change in the measured apparent mass (difference between the sample mass and magnetic force driving it upward). These results were confirmed by DSC analysis. Whether the obtained crystalline phase is ferromagnetic, it can be identified through its Curie temperature, measured by TG(M). In fact the value of 770°C measured as Curie temperature of crystallised Fe_62.5Co₆Ni_7.5Zr₆Nb₂Cu₁B₁₅led to conclude that the only ferromagnetic crystalline phase is a-Fe. These hypothesis was confirmed by XRD analysis, showing that the first crystallisation yields to a-Fe nanocrystals. This revised version was published online in July 2006 with corrections to the Cover Date.     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

Application of ZrC-coated tubes to the determination of aluminum in serum by graphite furnace atomic absorption spectroscopy

An improved method for the determination of aluminum in serum by atomic absorption spectrometry with a graphite furnace is presented. The method is suitable for the analysis of serum samples having normal and elevated aluminum content. The serum sample can be analyzed diluted or undiluted because the selected temperatures program minimizes the matrix interferences. High temperatures are made possible by the use of graphite Zr-coated tubes. The detection limit is 0.7 μg Al/liter. The coefficient of variation is 3.2% for serum concentration of 5 μg Al/liter and 1% for serum concentration of 50 μg Al/liter.     

FLUORESCENCE STUDIES WITH HUMAN EPIDERMAL GROWTH FACTOR

Steady-state and time-resolved fluorescence studies have been performed with human epidermal growth factor, a small globular protein having two adjacent tryptophan residues near its C-terminus. Based on the relatively red fluorescence and accessibility to solute quenchers, the two tryptophan residues are found to be exposed to solvent. Anisotropy decay measurements show the dominant depolarizing process to have a sub-nanosecond rotational correlation time indicating the existence of rapid segmental motion of the fluorescing tryptophan residues. From an analysis of the low-temperature excitation anisotropy spectrum of the protein (and in comparison with that of tryptophan, the peptide melittin, and the dipeptide trp-trp), it is concluded that homo-energy transfer and/or exciton interaction occurs between the adjacent tryptophan residues. A thermal transition in the structure of the protein, which is observed by circular dichroism measurements, is not sensed by the steady-state fluorescence of the protein. This result, in conjunction with the anisotropy decay results, indicates that the two tryptophan residues are in a highly flexible C-terminus segment, which is not an integral part of the three-dimensional structure of the protein. Fluorescence measurements with three site-directed mutants also show very little variation.     

Interactions between octyl-β-D-glucoside and α-amino acids or small peptides

The interactions between octyl--D-glucoside and glycine in water have been investigated by surface tension, viscosity, and density measurements. The results show that the -amino acid causes an unexpected lowering of the critical micellar concentration of octyl--D-glucoside. Such a finding has been interpreted in temss of dipole-dipole interactions between the hydrophilic site of the surfactant and the peptidic cosluttes. From three to seven amino acid molecules have been estimated to be coordinated with each glucoside unity in the micellar state. The research has been extended to glycine oligopeptides and L-lysine. The latter compound has effects similar to those observed with glycine whereas diglycine and triglycine show weaker effects on the micellization process.     

Preparation and characterization of bolaform surfactant vesicles

Vesicular formulations (liposomes and niosomes) play an increasingly important role since they can be used as drug delivery and targeting systems. We described the formation of two niosomal systems based on synthetic bolaform surfactants (4,7,10,13-pentaoxa-16-aza-cyclooctadecane)-hexadecanedioc acid diamide (BD-16) and alpha,omega-(4,7,10,13-pentaoxa-16-aza-cyclooctadecane)-hexadecane (BC-16). Systems containing BD-16 or BC-16 and different amount of cholesterol (CH) were prepared by aqueous dispersion of films, followed by examination of methylene blue (MB) entrapment, particle size and morphology. Indeed, we also studied the hydration in the distilled water and physiological solution, in order to investigate the complexing ability on vesicle formation. The results obtained in this study show a high encapsulation capacity and this ability and the size depends on cholesterol content.     

Spektrographische Bestimmung von Eisen,Nickel und Chrom in Platin-Netzen

Zusammenfassung Eine Methode zur spektrographischen Bestimmung von Eisen, Nickel und Chrom in Platin-Rhodium-Netzen, die als Katalysatoren bei der Cyanwasserstoffsynthese gebraucht werden, wurde beschrieben. Sie beruht auf der Verdünnung der in Königswasser gelösten Probe mit Aluminiumnitratlösung, die dann getrocknet und in Oxid verwandelt wird. Als Bezugselement dient Aluminium.

---

Summary A method is described for the spectrographic determination of iron, nickel and chromium in platinum-rhodium nettings that are employed as catalysts in the hydrocyanic synthesis. The method is based on the dilution, with aluminium nitrate solution, of the samples dissolved in aqua regia; the diluted solution is then taken to dryness and converted to oxide. Aluminium serves as reference element.

---

Résumé On a décrit une méthode de dosage spectrographique du fer, du nickel et du chrome dans les grilles platine-rhodium utilisées comme catalyseurs dans la synthèse de l'acide cyanhydrique. Elle repose sur la dilution par une solution de nitrate d'aluminium des échantillons dissous dans l'eau régale. Ils sont ensuite séchés et utilisés sous forme d'oxydes. On prend l'aluminium comme élément de référence.

---

---

Für die wertvolle Mitwirkung im experimentellen Teil dieser Arbeit bin ich HerrnR. Tacca zu groem Dank verpflichtet.     

The Skorohod oblique reflection problem in domains with corners and application to stochastic differential equations

Summary The Skorohod oblique reflection problem for (D, , w) (D a general domain in ^d , (x),xD, a convex cone of directions of reflection,w a function inD(⁺, ^d )) is considered. It is first proved, under a condition on (D, ), corresponding to (x) not being simultaneously too large and too much skewed with respect to D, that given a sequence {w ⁿ} of functions converging in the Skorohod topology tow, any sequence {(x ⁿ, ⁿ)} of solutions to the Skorohod problem for (D, , w ⁿ) is relatively compact and any of its limit points is a solution to the Skorohod problem for (D, , w). Next it is shown that if (D, ) satisfies the uniform exterior sphere condition and another requirement, then solutions to the Skorohod problem for (D, , w) exist for everywD(⁺, ^d ) with small enough jump size. The requirement is met in the case when D is piecewiseC _b ¹ , is generated by continuous vector fields on the faces ofD and (x) makes and angle (in a suitable sense) of less than /2 with the cone of inward normals atD, for everyxD. Existence of obliquely reflecting Brownian motion and of weak solutions to stochastic differential equations with oblique reflection boundary conditions is derived.