A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions

In this paper we establish the complete multifractal formalism for equilibrium measures for Hölder continuous conformal expanding maps andexpanding Markov Moran-like geometric constructions. Examples include Markov maps of an interval, beta transformations of an interval, rational maps with hyperbolic Julia sets, and conformal toral endomorphisms. We also construct a Hölder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex, and hence the multifractal formalism fails.     

Deconstructing Wigner’s density matrix concerning the mind-body question

In honor of the centennial of Eugene Wigner’s birth, a possible interpretation is given of the density matrix appearing in his classic paper, “Remarks on the mind-body question.” It is argued that nearinstantaneous vanishing of the quantum coherences of the reduced density matrix of the measured object would occur either in the case of Wigner’s friend, or in the case of any complex measuring automaton (conscious or not) making the measurement.     

Structural investigation of model compounds for an acceptor component of a new type of charge-transfer complexes based on viologen analogues. Characteristic features of the molecular and supramolecular structures

The crystal and molecular structures of six perchlorates (viologen analogues) are studied. These compounds serve as models of the acceptor component of new charge-transfer complexes containing bis(18-crown-6)stilbene as the donor. The polycyclic aromatic system of divalent cations is demonstrated to be virtually planar. In all cations, the side chains at the nitrogen atoms are oriented in opposite directions almost perpendicular to the plane of the cyclic system. This orientation of the spacers of these carbocations is indicative of their preorganization for the formation of 1: 2 charge-transfer complexes. Analysis of the crystal packings provides evidence that two positive charges on the conjugated systems of the organic cations and the perchlorate anions play a destructive role in the formation of stacking motifs. An increase in the size of the conjugated system and the involvement of an aromatic solvent molecule as an additional building block in a supramolecular system are favorable for the formation of a stacking supramolecular architecture.     

The heat of fusion of copolymers of tetrafluoroethylene and hexafluoropropylene

The Clapeyron equation has been applied to determine the heat of fusion of two copolymers of tetrafluoroethylene and hexafluoropropylene. The values obtained are within experimental uncertainty of that for the homopolymer, PTFE. This study supports the conclusion of earlier workers that the CF₃ side groups are included in the crystal lattice. In both PTFE and polyethylene, C₁ side groups are included in the crystal but have little if any effect on its density. We believe that the same relationship between the crystallinity and the heat of fusion can be used for both PTFE and copolymers of TFE and HFP.     

“Virtual effects of excited quarks as probes of a possible new hardonic mass scale”

The effects of $\text{spin}\text{-}\text{3}\text{2}$ excited quarks are considered as probes of a possible new hadronic mass-scale Λ. A specific model is developed which describes virtual $\text{spin}\text{-}\text{3}\text{2}$ quarks of mass of O(Λ). Induced effects, which are corrections to the standard SU(2) × U(1) electroweak model, include right-handed charged currents and flavor changing neutral currents. A model-independent classification of all SU(3) × SU(2) × U(1) invariant quark operators of dimension six or less is also presented. Ambiguities in converting this analysis and existing experiments to a definitive lower-bound for Λ are discussed. It is found, depending on the strength of certain Higgs couplings and the underlying global flavor symmetries in the absence of Higgs couplings, that a lower bound as small as Λ > 500 GeV or as large as Λ > 100 TeV is possible.     

Head and body imaging by hydrogen nuclear magnetic resonance

A hydrogen (¹H) nuclear magnetic resonance (NMR) imaging study of the normal head, thorax, and limbs is reported. The images are 10 to 15 mm thick transverse slices obtained in 2 to 4 min using a two-dimensional Fourier transform technique. Spatial resolution in the imaging plane is about 2 mm, enabling the optic nerve and many small blood vessels to be observed. Thorax scans show details of the cardiac chambers, aorta wall, and lungs without artefacts arising from physiological motion.     

Fermionic chemical potential

This paper gives a critical review of the physical meaning of the chemical potential, perhaps the most abstract of all thermodynamic quantities. To show its basic behavior, thereby to illustrate its physical significance, we have derived the chemical potential of a system of free electrons as a function of the density and temperature in different spatial dimensions. We have shown how to obtain the isothermal compressibility given the chemical potential. To emphasize the usefulness of the knowledge of dimensional dependence, both the compressibility and average kinetic energy are expressed as simple dimensional relationships of the density and, hence, the chemical potential. Finally, there is a certain temperature at which the chemical potential should identically vanish. Physical implications of zero chemical potential are discussed.     

Adsorption of polymers at the solution-solid interface. VIII. Competitive effects in the adsorption of polystyrenes on silica

The adsorption behavior on silica of some polystrenes of moderate molecular weight distribution, both singly and in mixtures, has been examined. The adsorption isotherms indicate that, in both a good solvent (trichloroethylene) and under theta conditions, the species of higher molecular weight is preferentially adsorbed at or near full surface coverage, but that the smaller adsorbate has an improved opportunity for adsorption at low surface coverage. The use of tritiated adsorbates substantiate the isotherm data in cyclohexane solution.