Periodic Delone Tilings

Given a periodic point set in 3-dimensional Euclidean space, an algorithm is described for computing the corresponding Delone tiling (and its Delaney symbol). Examples of applications in tiling theory and crystallography are discussed.     

Structure and bonding issues at the interface between gold and self-assembled conjugated dithiol monolayers

Organic thiols have received extensive attention recently because of their relative stability and ease of examination compared to other potential molecular electronic materials. In this work, scanning probe microscopy (SPM) is used to study (i) the structural properties of self-assembled monolayers (SAMs) containing conjugated dithiols and (ii) the formation of the upper molecule-metal interface on dithiol SAMs. The top gold film is deposited either by thermal evaporation or by nano-transfer printing (nTP). Generally, the utility of thermal evaporation is limited because of Au diffusion through the SAMs. However, several dithiol SAMs are identified in this work that bond well to Au overlayers and act as satisfactory diffusion barriers. Coassembly of conjugated dithiols and alkanemonothiols is suggested as a route to obtain dithiols that are denser packed and more vertical (than is obtained from pure dithiol routes). High-yield nTP is demonstrated on coassembled SAMs. Advantages and limitations of different Au deposition and transfer techniques are compared on a variety of length scales.     

Stereochemical studies—XXV: Conformational equilibria of 2-substituted 1,1-dialkylcyclohexanes

The positions of the conformational equilibria in a series of 1,1,2-trisubstituted cyclohexanes have been determined by ¹H NMR. The gauche-interaction of substituents in the 1,1-dimethyl series are, in general, very close to those of monosubstituted cyclohexanes. However, in the spiro-compounds 5 and 6 the equatorial conformers are somewhat destabilized by gauche-interactions though still enthalpy preferred. In contrast, the enthalpy preferred conformer in the 1,1-diethyl series is the axial one.     

Novikov-type coordinates for HJ separable metrics

Synchronous frames are known to remove (at least partially) deficiencies inherent in Killing coordinates. Strangely enough, no constructive general method of finding these frames has been formulated, though it follows from the definition of synchronous coordinates; We propose here such a method and apply it to the Kerr metric to obtain a Novikov-type synchronous frame. The removal of nonphysical singularities is discussed in the context of 3-metric and 3-curvature on the spatial hypersurfaces in this frame.We are thankful to Dr. I. D. Novikov and Professor R. Gautreau for the interest shown in the work, and whose ideas helped to bring this work to completion.     

Primary quenching in a track of ionizing particle for organic scintillation crystalline materials

The primary quenching in a track of a recoil proton or an alpha particle was studied on the base of “one step” model for molecular crystals of stilbene and doped p-terphenyl as well as for composite scintillators based on the grains of these single crystals. This approach is the first, which takes into account the influence the effect of polarization on recombination of polarons those are generated by ionizing radiation. It was shown that the primary quenching has to be concentration controlled process, which is faster than the track formation along it full length. Results obtained are in good agreement with results of studies of organic crystals as organic semiconductor materials.     

Homogeneous solutions to fully nonlinear elliptic equations

We classify homogeneous degree solutions to fully nonlinear elliptic equations.

     

Deformation Quantization of a Certain Type of Open Systems

We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of the open time evolution. The usual example of linearly coupled harmonic oscillators is discussed.     

The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization

The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079–1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed.