Metal benzoylpivaloylmethanates. Part II. 1,4-dioxane adducts of copper(II) chelates

Summary 1 : 1 Dioxane adducts of Copper(II) chelates withpara-subtituted benzoylpivaloylmethanes have been synthesized and their u.v., vis., i.r., mass, e.p.r. spectra as well as their magnetic moments and thermal stabilities investigated. Powdered samples of undiluted magnetically adducts were found to give well resolved e.p.r. spectra; the (S = 1) g_| signal being split into nine lines. Magnetic susceptibilities measured down to 4 K did not reveal exchange interactions. The uncommon structure of the e.p.r. spectra is believed to be due to the dimeric structure of the adduct in which an interion dipolar zero-field splitting of the triplet state occurs. The Cu-Cu distance estimated from the e.p.r. D_dd parameter is found to be 7.4 Å.     

Indirect determination of mercury(ii) with an air-gap cyanide sensor

The method is based on the stability of the dicyanomercurate(II) complex at pH 0.5–1, where most other cyanide complexes decompose. The selectivity is much better than that in the direct application of mercury-selective electrodes. The method is useful in the range 5 × 10^-5–5 × 10^-3 M mercury(II).     

On the balance laws of extended thermodynamics (ET) for non-ideal gases

The conservation laws of mass and momentum and the equations of balance of momentum flux and energy flux as well as the higher order balance laws are derived by means of the modified Klimontovich kinetic equation for non-ideal gases. The effect of the body forces and inertial forces during the persistence of a collision is taken into account in order to have the balance laws valid for general frames of reference. The sequence of macroscopic quantities appearing in the balance equations is decomposed into convective and non-convective parts and this decomposition is explained on the basis of statistical mechanics. A problem of symmetry or non-symmetry of tensors associated with the presence of interactions between microscopic particles is discussed from a molecular point of view. Explicit expressions for the energy density, the pressure, the pressure tensor, the heat flux and the other expressions characteristic for ET are given in terms of microscopic variables.     

Criticality and phase transition in stock-price fluctuations

We analyze the behavior of the U.S. S&P 500 index from 1984 to 1995, and characterize the non-Gaussian probability density functions (PDF) of the log returns. The temporal dependence of fat tails in the PDF of a ten-minute log return shows a gradual, systematic increase in the probability of the appearance of large increments on approaching black Monday in October 1987, reminiscent of parameter tuning towards criticality. On the occurrence of the black Monday crash, this culminates in an abrupt transition of the scale dependence of the non-Gaussian PDF towards scale-invariance characteristic of critical behavior. These facts suggest the need for revisiting the turbulent cascade paradigm recently proposed for modeling the underlying dynamics of the financial index, to account for time varying-phase transitionlike and scale invariant-critical-like behavior.     

Double excitations of helium in weak static electric fields

A dramatic electric field dependence has been observed in the fluorescence yield spectrum of the doubly excited states in helium, where a rich phenomenology is encountered below the threshold. Fluorescence yields of certain states can be tuned to zero, while other dipole-forbidden states are significantly enhanced, for fields much weaker than 1 kV/cm. Using an R-matrix multichannel quantum defect theory, spherical-to-parabolic frame transformation method, we are able to reproduce the main features of the observed spectrum, and we discuss the qualitative behavior in terms of weak electric field mixing.     

Pseudopotential method for higher partial wave scattering

We present a zero-range pseudopotential applicable for all partial wave interactions between neutral atoms. For p and d waves, we derive effective pseudopotentials, which are useful for problems involving anisotropic external potentials. Finally, we consider two nontrivial applications of the p-wave pseudopotential: we solve analytically the problem of two interacting spin-polarized fermions confined in a harmonic trap, and we analyze the scattering of p-wave interacting particles in a quasi-two-dimensional system.     

Affine representations of Fibonacci groups and flat manifolds

We construct examples of affine representations for a family of Fibonacci groups. As an application, we prove that all Hantzsche–Wendt groups of the same dimension are epimorphic images of the same Fibonacci group.