New look at Gleason's theorem for signed measures

It is shown that the Gleason theorem holds not only for a finite but also for ann-finite signed measurem, wheren is a cardinal, defined on all closed subspaces of a Hilbert space whose dimension is a nonmeasurable cardinal 2, ifm is bounded from below on all one-dimensional subspaces.     

Some features of solar wind protons, α particles and heavy ions behaviour: The Prognoz 7 and Prognoz 8 experimental results

The paper describes the results of investigations of the solar wind ions, carried out on board the high apogee Prognoz 7 and Prognoz 8 Earth's satellites with the aid of an SKS instrument (USSR) and a Monitor instrument (USSR-SSR). Behaviour of proton and that of components on the front of Earth's bow and interplanetary shock waves were compared by means of the energoanalysis and energy-mass analysis techniques. In several long-term periods of observation the solar wind heavy ions — oxygen, silicon and iron were determined. It enabled us to estimate the solar corona chemical composition and electron temperature.Presented at the 5th General Assembly IAGA/IAMAP August 5–17, 1985, Prague, Czechoslovakia.     

Temperature dependence of development of slip bands and of strain hardening in AgCl crystals

The dependence of the flow stress and the slip band density on the plastic strain has been measured at 201 K, 293 K and 363 K. The growth of deformation concentrated in an average slip band has been stated. The types of obstacles acting against the rise and development of a slip band and the temperature dependence of the strain hardening in AgCl crystals are discussed. An equation stating the dependence of the flow stress on the slip band density is presented. The hardening in AgCl crystals is classified as the stage III — hardening.     

Hahn-Jordan decomposition for gleason measures

The possibility of the Hahn-Jordan decomposition forn-finite signed measures, wheren is a cardinal, defined on a quantum logic of all closed subspaces of a Hilbert space whose dimension is a nonmeasurable cardinal 2, is investigated.     

Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

Simple functional-differential equations for the bound-state wave-function components

We present a new method of a direct derivation of differential equations for the wave-function components of identical-pariticles systems. The method generates in a simple manner all the possible variants of these equations. In some cases they are the differential equations of Faddeev of Yakubovskii. It is shown that the case of the bound states allows to formulate very simple equations for the components which are equivalent to the Schrödinger equation for the complete wave function. The components with a minimal antisymmetry are defined and the corresponding equations are derived.     

Variable electronegativity SCF-MO calculations on the electronic structure and spectra of some substituted benzenes I. Monosubstitutions

π-electron SCF-MO theory in its variable electronegativity formalism has been applied to some monosubstituted benzenes. Calculated charge densities and bond orders for the ground and the first excited electronic states are correlated with chemical reactivity and the changes in molecular geometry on electronic excitation. The calculated results for spectra are compared with those obtained using the PPP method and also with the available experimental data.     

Stark broadening of halogen atom lines from (1 D)n p levels

We report results of a study of the Stark broadening of halogen atom lines from (¹ D)n p levels. Wall stabilized arc is used as a plasma source. Electron densities 2.2–3.2×10²² m^?3 are determined from the width ofH _α line and electron temperature 9300–10000 K from plasma composition data. The agreement with the results of simple semiclassical calculations is within the limits of the estimated errors of both experiment and theory. An explanation for the large discrepancy between theory and experiment detected for three BrI lines is offered.