Sulle classi filtrali di algebre

Summary Generalizing results of [1], we show that if a classK of algebras is filtral (as defined byMagari [1]), then so is the class of all simple algebras in the varietyW _K generated byK, and these simple objects are precisely all subalgebras of all ultraproducts of copies of algebras inK. All algebras inW _K are semisimple and regular. We then obtain charac terizations of filtral and semifiltral classes of algebras in terms of the existence of certain types of operations in these algebras, and illustrate our results with examples, mainly from ring theory.

---

---

L'autore era parzialmente sostenuto dal contratto GP 9152 della National Science Foundation.     

Weakly nonlinear conductivity of random composites: A series expansion approach

We present a series expansion calculation of the bulk effective coefficient of weakly nonlinear behavior in some continuum composite conductors and in simple cubic random resistor networks. The expansion is in powers of the relative difference between the linear Ohmic conductivities of the components. It is carried up to third order for an independent random bond network and a diagrammatic scheme is used to aid in implementing the calculation. For continuum composites, only the first term of the expansion can be calculated explicitly without detailed information about the microgeometry. Such information is difficult to acquire and even more difficult to exploit.     

Analysis and measurement of GAWBS spectrum in a nonlinear fiber ring

The spectral density of the phase noise of an optical pulse in a fiber produced by guided acoustic wave Brillouin scattering (GAWBS) is derived from first principles. The predictions are in good agreement with the experimental results in a fiber interferometer. The experiments show that the lower limit on the quantum noise reduction is set by GAWBS. The GAWBS are of sufficiently low level to permit 5 dB squeezing.     

Molecular mechanics of the ferroelectric to paraelectric phase transition in LiNbO3 via optical second harmonic generation

Temperature dependent optical second harmonic generation (SHG) results are used to monitor the 7° trigonal deformation of the NbO₆ octahedron in ferroelectric LiNbO₃. The SHG structural results compare favorably with those obtained from conventional (X-ray) techniques. The temperature dependence of the spontaneous polarization P_s, calculated via the same trigonal deformation model is consistent with the experimental observations.     

Infrared spectra of the matrix-isolated chlorides of iron,cobalt, and nickel

Iron, cobalt, and nickel metal cathodes were sputtered with various mixtures of ³⁷Cl₂/³⁵Cl₂/Ar to produce Ar matrices at 14 K that contained the mono-, di-, and trichlorides of the corresponding metal. The measured infrared absorption spectra of these matrices allowed the identification and characterization of FeCl₂, FeCl₃, CoCl, CoCl₂, CoCl₃, and NiCl₂. The derived vibrational constants of the electronic ground state of ⁵⁹Co³⁵Cl are ω_e = 457.8 ± 3.0 cm^?1 and ω_eχ_e = 2.0 ± 1.5 cm^?1. The antisymmetric stretching mode frequencies of six isotopomers of FeCl₂ and three isotopomers of CoCl₂ were identified and measured. The dichlorides of iron, cobalt, and nickel were all determined, in contrast with previous work, to be nonlinear with bond angles of 161, 157, and 161°, respectively. The estimated uncertainty is 5°. For both iron and cobalt trichlorides, the measured stretching mode frequencies were used to derive a ClMCl angle in excess of 120°, as would be expected for planar molecules with somewhat anharmonic vibrations. Observed adsorption peaks could be assigned to the ν₃(E) modes of planar (D_3h) Fe and Co trichlorides and the corresponding modes of the isotopomers. These observations strongly suggest that recent data supporting a pyramidal geometry for FeCl₃ should be reexamined. The geometry of CoCl₃ has not previously been determined.     

On the evolution of recombination in haploids and diploids: II. Stochastic models

In this article, we continue an investigation into the evolution of modifiers of recombination, comparing haploid and diploid models begun in Vol. 1, Issue 1, of Complexity. Here, we examine selection schemes that have been used recently in numerical studies of finite diploid populations and ask how recombination evolves in haploid versions of these models. Although the analysis keeps track of the recombination controlling locus rather than the time until a desired bit-string appears, our result may be of use to the practitioners of genetic algorithms (GA's). We find that as a rule high recombination evolves more easily when selection is on haploids than it does in the diploid case. This is especially true of Gaussian selection schemes with high recombination recessive to low recombination. When the fitness regime is more jagged, however, the results depend on the level of jaggedness, with high recombination favored under smoother regimes. We also find that the direction of mutation and dominance relationships among the modifying alleles affect the results. Although there remains much to be done in reconciling population genetic theory with the properties of genetic algorithms, many new and interesting questions have emerged from, and will continue to be stimulated by, interactions between practitioners of each approach.     

On a modification of Marquardt's compromise: Rationale and applications

The method of Marquardt's compromise for handling the problem of near-singularity in nonlinear regression is modified by (a) utilizing methods from ridge regression for computing the Marquardt parameter k, and (b) utilizing a search method of interpolation-extrapolation for determining the step size. The performance of these modifications is evaluated on a number of standard test problems from the literature. It is shown that the Lawless-Wang estimate of k without the benefit of interpolation- extrapolation competes favorably with standard algorithms implemented in packaged programs. An application to a model of plasma insulin dynamics is also given. Comparison of the modified procedure with the Nelder-Mead simplex method is given.