Orlicz Spaces associated with a Semi-Finite Von Neumann Algebra

In the present paper we introduce a certain class of non commutative Orlicz spaces, associated with arbitrary faithful normal locally-finite weights on a semi-finite von Neumann algebra $M.$ We describe the dual spaces for such Orlicz spaces and, in the case of regular weights, we show that they can be realized as linear subspaces of the algebra of $LS(M)$ of locally measurable operators affiliated with $M.$Comment: 12 page

Examination of nanosecond laser melting thresholds in refractory metals by shear wave acoustics

Nanosecond laser pulse-induced melting thresholds in refractory (Nb, Mo, Ta and W) metals are measured using detected laser-generated acoustic shear waves. Obtained melting threshold values were found to be scaled with corresponding melting point temperatures of investigated materials displaying dissimilar shearing behavior. The experiments were conducted with motorized control of the incident laser pulse energies with small and uniform energy increments to reach high measurement accuracy and real-time monitoring of the epicentral acoustic waveforms from the opposite side of irradiated sample plates. Measured results were found to be in good agreement with numerical finite element model solving coupled elastodynamic and thermal conduction governing equations on structured quadrilateral mesh. Solid-melt phase transition was handled by means of apparent heat capacity method. The onset of melting was attributed to vanished shear modulus and rapid radial molten pool propagation within laser-heated metal leading to preferential generation of transverse acoustic waves from sources surrounding the molten mass resulting in the delay of shear wave transit times. Developed laser-based technique aims for applications involving remote examination of rapid melting processes of materials present in harsh environment (e.g. spent nuclear fuels) with high spatio-temporal resolution. © 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4993591

Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\"odinger Equation

We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped in a deep optical lattice. We find that under periodic variations of the heights of the interwell barriers (or equivalently of the scattering length), additionally to the modulational instability, a window of parametric instability becomes available to the system. We explore this instability through multiple-scale analysis and identify it numerically. Its principal dynamical characteristic is that, typically, it develops over much larger times than the modulational instability, a feature that is qualitatively justified by comparison of the corresponding instability growth rates

Dual role of DNA methylation inside and outside of CTCF-binding regions in the transcriptional regulation of the telomerase hTERT gene

Expression of hTERT is the major limiting factor for telomerase activity. We previously showed that methylation of the hTERT promoter is necessary for its transcription and that CTCF can repress hTERT transcription by binding to the first exon. In this study, we used electrophoretic mobility shift assay (EMSA) and chromatin immunoprecipitation (ChIP) to show that CTCF does not bind the methylated first exon of hTERT. Treatment of telomerase-positive cells with 5-azadC led to a strong demethylation of hTERT 5′-regulatory region, reactivation of CTCF binding and downregulation of hTERT. Although complete hTERT promoter methylation was associated with full transcriptional repression, detailed mapping showed that, in telomerase-positive cells, not all the CpG sites were methylated, especially in the promoter region. Using a methylation cassette assay, selective demethylation of 110 bp within the core promoter significantly increased hTERT transcriptional activity. This study underlines the dual role of DNA methylation in hTERT transcriptional regulation. In our model, hTERT methylation prevents binding of the CTCF repressor, but partial hypomethylation of the core promoter is necessary for hTERT expression

On the unique solvability of a nonlocal boundary value problem with the poincaré condition

As is known, it is customary in the literature to divide degenerate equations of mixed type into equations of the first and second kind. In the case of an equation of the second kind, in contrast to the first, the degeneracy line is simultaneously the envelope of a family of characteristics, i.e. is itself a characteristic, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In this paper, in order to establish the unique solvability of one nonlocal problem with the Poincaré condition for an elliptic-hyperbolic equation of the second kind developed a new principle extremum, which helps to prove the uniqueness of resolutions as signed problem. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which known by the Carleman-Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem

Four electrons in a two-leg Hubbard ladder: exact ground states

In the case of a two-leg Hubbard ladder we present a procedure which allows the exact deduction of the ground state for the four particle problem in arbitrary large lattice system, in a tractable manner, which involves only a reduced Hilbert space region containing the ground state. In the presented case, the method leads to nine analytic, linear, and coupled equations providing the ground state. The procedure which is applicable to few particle problems and other systems as well is based on an r-space representation of the wave functions and construction of symmetry adapted orthogonal basis wave vectors describing the Hilbert space region containing the ground state. Once the ground state is deduced, a complete quantum mechanical characterization of the studied state can be given. Since the analytic structure of the ground state becomes visible during the use of the method, its importance is not reduced only to the understanding of theoretical aspects connected to exact descriptions or potential numerical approximation scheme developments, but is relevant as well for a large number of potential technological application possibilities placed between nano-devices and quantum calculations, where the few particle behavior and deep understanding are important key aspects to know.Comment: 19 pages, 5 figure