Primitive points on constant elliptic curves over function fields

Letf:CE be a non-constant rational map between curves over a finite field, whereE is elliptic. We estimate the number of rational points ofC whose image underf generate the group of rational points ofE.     

Antiferromagnetism of type II in nonstoichiometric YbP

A polycrystalline smaple of nonstoichiometric ytterbium phosphide, YbP_0.84, was investigated by neutron scattering, Mössbauer spectroscopy and bulk magnetic measurements. Neutron diffraction experiments prove the existence of antiferromagnetic type II ordering belowT _N =0.64 K, in contrast to the observed antiferromagnetic type III ordering in the stoichiometric Kondo-like compounds YbN and YbAs. The temperature dependence of the average ordered magnetic moment per Yb³⁺ ion with saturation value _Yb = 1.03(7) _B is similar to that of YbN. Mössbauer experiments prove the magnetic phase transition to be first order with different regions in the sample having slightly different transition temperatures. By means of inelastic neutron scattering the crystal-field level scheme was established to be ₆ – ₈(19meV) – ₇(43meV).     

Nonlinear properties of surface “screw” instability in symmetric semiconductor plates

For the first time we study the nonlinear properties of the surface screw instability (SSI) when waves are excited at both faces of a plate and the interaction between them must be taken into account. The nature of the SSI development and the stability of surface screw waves against modulation are examined. Diagrams of the regions where the SSI development is soft and explosive as well as the regions of modulated waves are given in the space of parameters characterizing the electro-hole plasma and external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April 1990.     

Disordered charge distributions and dielectric loss in extra dense flint glasses

The complex permittivities of some extra dense flint glasses (EDF glasses) have been studied. The dielectric features of the samples are dominated by their PbO content. Both refractive indices and dielectric losses exhibit a close relation to the concentration of Pb ions. The latter are located either at sites of the network atoms or filling the potential minima interstitially. They can be identified by their different relaxation mechanisms. The dispersion in the submillimeter wave and FIR area is characterized by a very broad distribution of comparably sharp resonant states. Thermal lens — or hysteresis effects can be excluded.     

Large deviation estimates for a conditional probability distribution. Applications to random interaction Gibbs measures

Summary Let (X _i ,Y _i ) ^d , be independent identically distributed random variables with arbitrary distribution. We show that, for almost every(Y _i ) _i , the conditional law of the empirical field given(Y _i ) _i satisfies to large deviation inequalities. This applies to the study of Gibbs measures with random interaction, in the case of some mean-field models as well as of short range summable interaction. We show that the pressure is nonrandom, and is given by a variational formula. These random Gibbs measures have the same large deviation rate, which does not depend on the particular realization of the interaction; their local behaviour is described in terms of conditional probabilities given the interaction of solutions to the variational formula.     

A Dynamic location problem for graphs

We introduce a class of optimization problems, calleddynamic location problems, involving the processing of requests that occur sequentially at the nodes of a graphG. This leads to the definition of a new parameter of graphs, called the window indexWX(G), that measures how large a window into the future is needed to solve every instance of the dynamic location problem onG optimally on-line. We completely characterize this parameter:WX(G)k if and only ifG is a weak retract of a product of complete graphs of size at mostk. As a byproduct, we obtain two (polynomially recognizable) structural characterizations of such graphs, extending a result of Bandelt.     

Markovian network processes: Congestion-dependent routing and processing

A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367.     

Crystal structure oftrans-[PtCl2(Me2PhP)(cis-2,5-dimethylpyrrolidine)]

The complextrans-[PtCl₂ (Me₂PhP)(cis-2,4-dimethylpyrrolidine)] has been characterized by X-ray crystallography. It crystallizes in the monoclinic space group P 2₂/c witha=8.762(3),b=16.034(5),c=12.600(4)Å,=93.43(3)° andZ=4. The structure was solved by heavy atom method and refined toR=0.052 for 3251 observed counter reflections. The coordination sphere of the Pt atom is square-planar with a geometry very similar to that of the studied complexes of the type trans-[PtCl₂(R₃P)L] whereL is either one of the possible isomers of theC,C-dimethylpyrrolidine or the unsubstituted pyrrolidine. In the present complex the puckered five-membered ring of the dimethylpyrrolidine ligand assumes an envelope conformation with the maximum puckering at the N atom.     

Velocity and concentration fields in settling tank of non-interacting solid particles

Summary In this paper there is a synthetic presentation of the theoretical principles of the phase difference method for the simultaneous measurements of size, velocity and concentration of particles dispersed in fluid, its application to spherical glass particles free falling in water at rest, and the measured velocity and concentration fields of the particles in a settling tank model. Particles with diameter between 75÷150 m were used. The method used seems reliable in obtaining the necessary information to analyze the performance of settling tanks in relation to the influencing factors the particles settling.

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Sommario In questo articolo sono presentati in forma sintetica i principi teorici del metodo della differenza di fase per la misura simultanea di velocità, dimensione e concentrazione di particelle disperse in un fluido, ed un'applicazione di tale metodo al caso di particelle di vetro, di dimensioni fra i 75–150 m, disperse in acqua. Le misure effettuate sono relative alla sedimentazione di particelle in acqua in quiete ed ai campi di velocità e concentrazione delle particelle che si realizzano in un modello fisico di vasca di sedimentazione rettangolare. I risultati ottenuti sembrano confermare l'adeguatezza del metodo impiegato per analizzare l'efficienza delle vasche di sedimentazione in relazione ai fattori che influenzano la sedimentazione di particelle.

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This work was supported by the Italian Ministry of Education.