The Symmetry Axioms in Laguerre Planes

We introduce two axioms in Laguerre geometry and prove that they provide a characterization of miquelian planes over fields of the characteristic different from 2. They allow to describe an involutory automorphism that sheds some new light on a Laguerre inversion as well as on a symmetry with respect to a pair of generators.     

Self-organizing neural networks for modeling robust 3D and 4D QSAR: application to dihydrofolate reductase inhibitors

We have used SOM and grid 3D and 4D QSAR schemes for modeling the activity of a series of dihydrofolate reductase inhibitors. Careful analysis of the performance and external predictivities proves that this method can provide an efficient inhibition model.     

A Generalization of the Bargmann’s Theory of Ray Representations

The paper contains a complete theory of factors for ray representations acting in a Hilbert bundle, which is a generalization of the known Bargmanns theory. With its help, we have reformulated the standard quantum theory so that the gauge freedom emerges naturally from the very nature of quantum laws. The theory is of primary importance in the investigations of covariance (in contradistinction to symmetry) of a quantum theory which possesses a nontrivial gauge freedom. In that case the group in question is not any symmetry group but a covariance group only – the case not yet investigated in depth. It is shown that the factor of a covariance group representation depends on space and time when the system in question possesses gauge freedom. In nonrelativistic theories, the factor depends on time only. In relativistic theory, the Hilbert bundle is built over spacetime while in the nonrelativistic case-over time. We explain two applications of this generalization: in the theory of a quantum particle in gravitational field in the nonrelativistic limit, and in quantum electrodynamics.     

A novel circuit for independent control of electron energy and emission current of a hot cathode electron source

The implementation of a non-linear combination of two reference voltages to control the anode voltage in the previously described biasing system of an electron source with a hot cathode allows elimination of the correlation between the emission current and the accelerating voltage. The presented system is highly suitable for applications in electron-impact mass spectrometers, ionization gauges and other instruments (for example, electron microscopes).     

Structure and thermodynamics of lipid bilayers on polyethylene glycol cushions: fact and fiction of PEG cushioned membranes

In developing well hydrated polymer cushioned membranes, structural studies are often neglected. In this work, neutron and X-ray reflectivity studies reveal that hybrid bilayer/polyethylene glycol (PEG) systems created from mixtures of phospholipids and PEG conjugated lipopolymers do not yield a hydrated cushion beneath the bilayer unless the terminal ends of the lipopolymers are functionalized with reactive end groups and can covalently bind (tether) to the underlying support surface. While reactive PEG tethered systems yielded bilayers with near complete surface coverage, a bimodal distribution of heights with sub-micrometer lateral dimensions was observed consisting of cushioned membrane domains and uncushioned regions in close proximity to the support. The membrane fraction cushioned by the hydrated polymer could be controlled by adjusting the molar ratio of lipopolymer in the bilayer. A general phase diagram based on the free energy of the various configurations is derived that qualitatively predicts the observed behavior and the resulting structure of such systems a priori. As further evidenced by ellipsometry, atomic force and fluorescence microscopy, the tethered system provides a simple means for fabricating small cushioned domains within a membrane.     

Scalar soliton generation in all-polarization-maintaining, graphene mode-locked fiber laser

All-polarization-maintaining, self-starting Erbium-doped fiber laser based on graphene-saturable absorber is presented. Scalar soliton pulses with 570 fs duration and 114.1 MHz repetition rate were achieved at a 1557 nm center wavelength and with 6 nm bandwidth. The graphene-saturable absorber was formed by mechanical exfoliation of pure graphite. The laser was environmentally stable and could operate for long periods of time with linearly polarized output and degree of polarization at the level of 98%.     

Lp-Lq time decay estimate to the solution of the Cauchy problem of the system of equations for nonlocal model of hyperbolic thermoelasticity theory

The aim of this paper is to present a new system of equations describing nonlocal model of hyperbolic thermoelasticity theory. We used the Papkin and Gurtin approach based on the constitutive relations for internal energy e(x), and heat flux q(x), with integral terms. Such system of equations describes the propagation of thermal perturbation with finite velocity. Using the modified Cagniard–de Hoop's method we constructed the matrix of fundamental solutions for this system of equations in three–dimensional space. Basing on the constructed matrix of fundamental solutions in the explicit formula we represent the solution of the Cauchy problem to this system of equations in the form of some kind of convolutions. Next, applying the method of Sobolev spaces, we obtain the L^p−L^q time decay estimate to the solution of the Cauchy problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)