Algebras of Measurements: The Logical Structure of Quantum Mechanics

In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute. PACS: 02.10.-V.     

Macroscopic and microscopic examination of the relationship between crack velocity and path and Rayleigh surface wave speed in single crystal silicon

The speed of Rayleigh surface waves, denoted C_R, is the accepted upper limit for Mode I crack velocity in monolithic solids. In the current contribution, we discuss several critical issues associated with the velocity of Rayleigh surface waves and crack velocity in single crystal (SC) brittle solids, and the global and local influence of C_R on crack path selection in particular.Recent cleavage experiments in SC silicon showed that crack velocity at certain cleavage planes and crystallographic orientations cannot exceed a small fraction of C_R, and thereafter the crack deflects to other cleavage planes. Indeed, C_R defined by the continuum mechanics ignores atomistic phenomena occurring during rapid crack propagation, and therefore is limited in predicting the crack velocity. Examination of these anomalies shows that this limitation lies in microstructural lattice arrangement and in anisotropic phonon radiation during rapid crack propagation. Globally, C_R has no influence on the crack deflection phenomenon. However, the misfit in C_R between the original plane of propagation and the deflected plane generates local instabilities along the deflection zone.     

On decidable,finitely axiomatizable,modal and tense logics without the finite model property Part II

This paper is a continuation of Part I. A decidable extension of model K4 that lacks the finite model property is described. It is not known whether there are extensions of B that are decidable and lack the finite model property.     

Proof of the bieberbach conjecture for a certain class of univalent functions

In the following we prove that for a given univalent function such that |a ₂| <0.867, |a _n |≦n for eachn. The method of proof is closely related to Milin’s method.     

Enhanced electrical and mechanical properties of multiwall carbon nanotube rubber composites

Multiwall carbon nanotube‐filled elastomers are prepared by solution blending using a sonication process. It is shown that the processing conditions have a strong effect on the composite properties especially on electrical properties, which are very sensitive to nanotube dispersion within the elastomeric matrix. The percolation threshold is seen to be shifted to a lower nanotube content than that previously reported. With regard to the unfilled elastomer, large increases in the elastic and tensile moduli are obtained with the nanotube loading, thus highlighting the potential of this type of particles as reinforcing fillers for elastomeric matrices. Raman spectroscopy under strain has been used to evaluate the strength of the polymer–filler interface. Weak interfacial interactions are deduced, but the debundling of the nanotubes and the orientational effects of the polymeric chains are observed when the composite is submitted to a uniaxial deformation. Copyright © 2012 John Wiley & Sons, Ltd.     

Facile Debromination by Potassium-Graphite Intercalate

The dehalogenation of vic-dihalides can be performed with the easily accessible potassium-graphite intercalate C₈K. The reaction is a convenient one, the yields are good, and the workup us simple.     

A charged particle in bimetric general relativity

The gravitational field of a charged particle is investigated on the basis of the bimetric general relativity theory. It is found that the field differs from the Reissner-Nordström field only very close to the sphereR=m+(m ² –Q ²)^1/2. This sphere is impenetrable, and its interior is unphysical.