Spinodal decomposition during continuous cooling of a PbOB2O3Al2O3 glass

Spinodal decomposition during continuous cooling of the PbOB₂O₃Al₂O₃ quasi-binary glass system was analysed by numerical integration of Cook's differential equation (which includes the contribution of random density fluctuations) for small angle X-ray scattering (SAXS) intensity. The SAXS curves derived from the calculations have a wide range of k-Fourier components (0 < k < k_c) for which a positive amplification factor occurs and they show a “crossover” point at $\text{k}{}_{\mathrm{c}}\text{= 0.155}\text{A}\text{?}{}^{\mathrm{?1}}$. The wavenumber which receives maximal amplification, k_m, increases with the cooling rate, Q, as $\text{Q}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}$, with n = 10.9. This Q dependence of k_m is similar to that predicted by Huston et al., however our results show a higher value of n. The dependence on Q and k_m of the SAXS intensity I(k_m) was also deduced. The measurements of SAXS curves were performed on glass samples prepared by the splat-cooling technique. Because of the difficulties which arise in the determination of the cooling rate of the samples, the only experimental results that could be compared with the theory are the k_m dependence of I and the value of k_c. These results are satisfactorily understood in terms of the present analysis.     

On the rate of points in projective spaces

The rate of a standard gradedK-algebraR is a measure of the growth of the shifts in a minimal free resolution ofK as anR-module. It is known that rate(R)=1 if and only ifR is Koszul and that rate(R) ≥m(I)−1 wherem(I) denotes the highest degree of a generator of the defining idealI ofR. We show that the rate of the coordinate ring of certain sets of pointsX of the projective space P ⁿ is equal tom(I)−1. This extends a theorem of Kempf. We study also the rate of algebras defined by a space of forms of some fixed degreed and of small codimension.     

Intercalation of heterocyclic compounds in α-zirconium phosphate: Imidazole,benzimidazole, histamine and histidine

The intercalation of imidazole and some organic species containing the imidazole ring, between the layers of crystalline zirconium phosphate has been investigated. Fourteen new, well-ordered intercalation compounds are obtained with the batch procedure at r.t. and/or 60°C. A mechanism of formation of the various compounds is proposed on the basis of the interaction between the guest molecules (with their dimensions and geometries) and the free PO₃OH groups available between the layers of the host. The new phases have been characterized by TG and X-ray methods.     

Synthesis of new imidazole derivatives as potential inhibitors of thromboxane synthetase

The preparation of new imidazole derivatives containing a carboxylic moiety such as succinic, adipic or benzoic into the side chain, is reported starting from the suitable imidazole intermediates.     

Stability in kinetic theory of vehicular traffic

Summary We prove existence and uniqueness of the solution of a linearized version of the kinetic equation of vehicular traffic on a highway by using the theory of semigroups of linear bounded operators.We assume that a perturbation is introduced at the entrance of the highway, i. e., at x=0 and that it continues for a given time interval [0, ].We then study the behaviour of such a perturvation at values of x close to zero by using perturbation theory for linear operators.Finally, we prove that the perturbation attenuates and approaches zero as x+, i. e. at a large distance from the entrance of the highway.

---

Sommario Si prova l'esistenza e l'unicità della soluzione dell'equazione linearizzata del traffico automobilistico su un'autostrada con un'entrata in corrispondenza di x=0.Si studia poi il comportamento di una perturbazione, dovuta per esempio all'uscita da una partita di calcio, e si mostra come tale perturbazione si attenui al crescere della distanza dall'ingresso dell'autostrada.

---

---

Work performed under the auspices of the National Research Council (C.N.R., Gruppo Nazionale per la Fisica Matematica).     

On the dynamics of the perturbations in an ionized gas dominated by charge exchange

Summary An ionized gas whose dynamics is dominated by charge exchange is considered. The following two problems are studied: the time behaviour of sinusoidal waves in a uniform equilibrium; the propagation in a bounded equilibrium of sinusoidal oscillations forced to the wall. It is shown, in particular, that the equilibria considered, not necessarily thermal equilibria, are stable for any form of the distribution function.

---

Sommario Si considera un gas ionizzato, non necessariamente in equilibrio termico, la cui dinamica sia dominata dal processo di scambio di carica, e si studiano i seguenti due problemi: evoluzione temporale di onde sinusoidali su un equilibrio uniforme; propagazione di oscillazioni sinusoidali forzate alla parete in un equilibrio spazialmente limitato. Si mostra in particolare la stabilitá degli equilibri per qualunque forma della funzione di distribuzione.

---

---

Research supported in part by C.N.R., G.N.F.M.     

Comparison of the molecular structures of five benzene derivatives as determined independently by gas-phase electron diffraction in two different laboratories: a perspective

The merits and limitations of gas-phase electron diffraction as a technique for determining accurately the structures of small organic molecules are demonstrated by comparing the molecular structures of five benzene derivatives studied in two different laboratories. The existence of many possible representations of the structure of a molecule (r _a, r _g, r _α, r _α⁰, r _e, …), implying differences in the physical meaning of geometrical parameters, is discussed in some detail as it may cause difficulties in a comparison. Also illustrated are different ways of estimating and expressing uncertainties in the geometrical parameters from a gas-phase electron diffraction study.