More on the τ-μ-e problem: The process e+e−→l+l− in the region of the z-resonance

Theoretical and experimental aspects of the study of the e-- problem in effects of neutral weak currents in colliding e⁺e^– beams in the region of the Z resonance are discussed. Quantities that describe the degree of violation of e-- universality are analyzed. In particular, it is shown that by measuring the spin asymmetry for angles 160° it is possible to determine the degree of violation ofl-e universality =g _A ^e g _V ^l –g _V ^e g _A ^l to an accuracy of up to 0.01.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 88-91, May, 1989.     

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.     

Gorenstein curves and symmetry of the semigroup of values

LetO be the local ring of a irreducible algebroid curve and S its semigroup of values, Kunz in [7] proves thatO is a Gorenstein ring if and only if S is symmetrical. In this paper we give a generalization of this fact for the case of reduced curves with an arbitrary number of branches, d. For it we introduce a concept of symmetry for the semigroup of values S₊ ^d which generalizes the well known symmetry for d=1 (i.e. the irreducible case). This concept of symmetry is also closely related to the symmetry introduced by García in [4] (for the d=2 case) and the author in [3] (for arbitrary d) with the main goal of the explicit determination of S (in the case of plane curves).     

Forces of a fluid in a rotating straight pipe

The fluid flow through a rotating straight pipe is considered, the axis of rotation being perpendicular to the pipe axis. The flow of the fluid is taken as fully developed, i.e. the velocity field is assumed to be the same in all transverse cross sections of the pipe. The derivation presented applies to viscous and nonviscous incompressible fluids. For constant angular pipe velocity a simple and exact (Coriolis type) relationF=2Q(t) is derived between the forceF by which the fluid acts on the (unit length of the) pipe in the direction perpendicular to the two axes, the fluid mass flow rateQ(t) through the pipe, and the angular velocity. Variable angular velocities, i.e. , introduce an additional term into the expression for the inertial forceF, which depends only on and on known (constant) parameters; this term is known for given angular velocity(t). The flow configuration investigated here is an idealization of those appearing (over short space and time intervals) in the devices measuring mass flow rateQ(t) through the (Coriolis) forceF. Therefore the exact results derived here cast some light on the degree of precision one expects in these devices, where more complicated flow configurations are present than those looked at in this paper.     

Radiative processes and non-equilibrium thermodynamics

With the assumption of an elementary physical concept meteorologically effective radiative processes (absorption-emission, scattering) can be included consistently in nonequilibrium thermodynamics of irreversible phenomena. Analogously to the usual Gibbs relations a fundamental equation was formulated for monochromatic light rays as the nucleus of the theory.Using the methods of classical irreversible theory, a complete entropy balance equation is derived in which the entropy variations of the mass as well as of the radiation field are explicitly represented. The resulting entropy source strength function through its analytical structure reveals the dynamical character of the irreversible variation terms. The-expression being positive according to the second law of thermodynamics is found to have a bilinear form as a function of the irreversible fluxes representing the entropy generating radiative processes and their conjugated thermodynamic forces. The mathematical structure and the positive sign of, following the usual line of reasoning, motivate the assumption of constitutive relations for the irreversible radiative processes. These equations developed from purely thermodynamical reasoning turn out to be equivalent to the usual radiative transfer equation which is founded on a very different theoretical concept. A very fundamental relationship can be deduced in this context from the entropy production function. It provides a direct thermodynamical proof that in nonscattering media the definition of a local temperature is necessarily accompanied by the validity of the Kirchhoff law.     

Superbranching processes and projections of random Cantor sets

We study sequences (X ₀, X ₁, ...) of random variables, taking values in the positive integers, which grow faster than branching processes in the sense that , for m, n0, where the X _n (m, i) are distributed as X _n and have certain properties of independence. We prove that, under appropriate conditions, X _n ^1/n almost surely and in L ¹, where =sup E(X _n )^1/n . Our principal application of this result is to study the Lebesgue measure and (Hausdorff) dimension of certain projections of sets in a class of random Cantor sets, being those obtained by repeated random subdivisions of the M-adic subcubes of [0, 1] ^d . We establish a necessary and sufficient condition for the Lebesgue measure of a projection of such a random set to be non-zero, and determine the box dimension of this projection.Work done partly whilst visiting Cornell University with the aid of a Fulbright travel grant     

Rational contractive and unitary interpolants in realized form

A solution of the rational Nehari problem is given in terms of a realization. Other aspects of this problem, like one step extension, maximum entropy interpolants and unitary interpolants, are also analyzed for the rational case. The results are based on earlier work of H. Dym and I. Gohberg.Dedicated to M.S. Livic on the occasion of his seventieth birthday, with admiration     

Excitation functions for some output channels following the p +55Mn interaction atE p=1·3–2·0 MeV

Excitation functions for the⁵⁵Mn(p, p )⁵⁵Mn,⁵⁵Mn(p, n )⁵⁵Fe and⁵⁵Mn(p, )⁵⁶Fe reactions are studied for proton beam energyE _p=1·3–2 MeV. The excitation functions are established from yield functions for -rays emitted from the first excited states of final nuclei. Many resonances are observed and competition of their decay into all three output channels is analysed. Spin-parity assignment for some resonant states in the⁵⁶Fe compound nucleus is deduced.Participated partly in the course of his work on a Thesis.The authors wish to thank the staff of the Van de Graaff accelerator at Charles University in Prague for the efficient operation of the machine and dr. I. Wilhelm for the valuable technical help in the early period of the experimental work. One of us (N. A. N.) acknowledges the staff of the Dept. of Nuclear Physics of Charles University in Prague for the excellent working conditions.     

Proton-proton correlations at small relative momentum in neon-nucleus collisions at E/A=400 and 800 MeV

Proton-proton small angle correlations have been measured in neon-nucleus collisions, using the 4 pi detector Diogene, at 400 and 800 MeV per nucleon incident energies. Values of the size of the emitting region are obtained by comparison with the Koonin formula, taking into account the biases of the apparatus. The dependence of the density on target mass and incident energy is also analysed.