Monadic dynamic algebras

The main purpose of this work is to introduce the class of the monadic dynamic algebras (dynamic algebras with one quantifier). Similarly to a theorem of Kozen we establish that every separable monadic dynamic algebra is isomorphic to a monadic (possibly non‐standard) Kripke structure. We also classify the simple (monadic) dynamic algebras. Moreover, in the dynamic duality theory, we analyze the conditions under which a hemimorphism of a dynamic algebra into itself defines a quantifier. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The polarographic and chronopotentiometric investigation of the copper(II)-ethylenedithioldiacetic acid system

The electrode process of the Cu(II)-ethylenedithioldiacetic acid chelatereduction occurs in two one-electron reduction steps. The reversibility of the first polarographic wave was confirmed by microcoulometry at constant potential. The second wave was found to be quasi-reversible unless the chelate forming agent is present in great excess. The kinetic parameters of these electrode processes were evaluated from the Koutecký and Matsuda-Ayabe theories. The value of activation energy at E=0 vs. NHE, was also found.The chronopotentiometric investigations of the same system gave resultswhich are in good agreement with those obtained polarographically.     

Pressure dependence of elastic behaviour and force constants of GaP

The six third order elastic constants of GaP have been obtained from measurements of the effect of hydrostatic and uniaxial pressures on ultrasonic wave velocities. The valence force field model has been used to obtain the bond-bending and stretching force constants. Confirmatory evidence is added to the hypotheses that zinc blende structure crystals undergo the densification transition under pressure when (1) a modified Born stability criterion that equals about 0.2 is reached at the phase transition pressure Pub>tub>, and (2) the ratio of the second order bond-bending βub>tub> to bond-stretching αub>tub>, force constants is about 0.1. These findings suggest that a macroscopic shear takes place at the transition     

Quantal master equation valid for any time scale

A new memoryless expression for the equation of motion for the reduced density matrix is derived. It is equivalent to that proposed by Tokuyama and Mori, but has a more convenient form for the application of the perturbational expansion method. The master equation derived from this form of equation in the first Born approximation is applied to two examples, the Brownian motion of a quantal oscillator and that of a spin. In both examples the master equation is rewritten into the coherent-state representation. A comparison is made with the stochastic theory of the spectral line shape given by Kubo, and it is shown that this theory of the line shape can be incorporated into the framework of the present theory.     

The thermochemical behaviour of zeolite inclusion complexes

The thermochemical behaviour of nitrate inclusion complexes of zeolites of type A was investigated and DTA curves recorded. An attempt was made to identify thermal effects. Supplementary information was obtained from the IR spectra of the solid phase before and after heating as well as from the process of denitration of inclusion complexes.     

Elastic constant pressure derivatives and stability of the bcc phase of InTl alloys

Hydrostatic-pressure derivatives of the elastic stiffness constants have been measured ultrasonically in a bcc InTl alloy of composition near the eutectoid. The shear modulus is small, but does not soften under pressure: the eutectoid reaction is not directly associated with a mode softening shear instability. Anharmonic contributions to the excess vibrational entropy from the q 〈110〉, e 〈1$\text{1}$0〉 modes which stabilize the bcc structure are small compared with the harmonic contributions.     

Low momentum transfer theorem for two photon exchange in lepton hadron scattering

The two photon exchange contribution to lepton-hadron scattering is considered. Under the assumptions of Lorentz covariance, gauge invariance, unitarity and analyticity, we prove a low momentum transfer theorem for the relevant amplitudes. Fixed energy dispersion relations tell us that their nonanalytic part, in the neighbourhood of t = 0, is given by the contribution of the two photon cut in the t-channel. The t-channel absorptive parts are obtained from unitarity. Their calculation has as input the two amplitudes corresponding to Compton scattering on the hadron with a pole contribution, and the continuum controlled at low t by the electromagnetic polarizabilities. By means of the dispersion integral, one proves the expansion for the continuum contribution, where kub>1ub>(s) is the only unknown. Explicit expressions are obtained for the pole contribution as M → ∞, where M is the hadron mass, and for the continuum when (?t) <Λ and (?t) < 4mup>2up>, where m is the muon mass and Λ is a characteristic parameter of the hadron structure.     

Long-range potentials and the electromagnetic polarizabilities

The long-range spin and velocity independent forces of electromagnetic origin which act between any two systems are studied for those cases in which no forces of this type exist to order eup>2up>. It is shown that they are uniquely determined by the charge, magnetic moment, and polarizabilities of both systems, not only to the dominant order rup>?nup>, but also to the next one rup>?(n+1)up>. These potentials provide the link between Compton scattering polarizabilities (response to real photons) and classically defined polarizabilities (response to static electromagnetic field). The two definitions are shown to be equivalent for neutral spinless systems; the problems arising for a neutral particle with magnetic moment are studied in detail. The rup>?(n+1)up> terms have no classical counterpart, since they are due to the relativistic quantum propagation of the system which carries charge or magnetic moment. The results are of general validity with analyticity, crossing, unitarity, and gauge invariance as only inputs. The most general conclusion is that the polarizabilities represent electromagnetic properties of a system at order eup>2up>, as the charge and magnetic moment do at order e. Thus they give the strength of the response to electric and magnetic fields, independently of the specific characteristics of the electromagnetic agent.