Search results for "Linear"

On large orbits of supersoluble subgroups of linear groups

2019

The research of this paper has been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union, by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades and the Agencia Estatal de Investigacion, Spain, and FEDER, European Union, and by the grant PROMETEO/2017/057 from the Generalitat, Valencian Community, Spain. The first author is supported by the predoctoral grant 201606890006 from the China Scholarship Council. The second author is supported by the grant 11401597 from the National Science Foundation of Chin

ON THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION WITH A QUASI-PERIODIC POTENTIAL

1980

Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons

2010

In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.

Multiple linear regression analysis of RF values of chlorinated catechols and guaiacols

1981

The multiple linear regression analysis of the RF values of chlorinated catechols and guaiacols has been carried out. The resolved terms, in the regression equation have been used to explain the relative mobility of chlorinated compounds to the reference compound (catechol or guaiacol). The best correlations have been observed for solvent systems which give the greatest standard deviations and relative differences between the RF values. A good correlation between the standard deviation of the RF values and the term which represents the effect of the chlorine atom ortho to the hydroxyl group(s) have also been observed.

1990

The countercurrent extraction method recently developed for the continuous polymer fractionation (CPF) was applied to linear polyethylene (Mw = 55 kg/mol; Mn = 16,7 kg/mol). At temperatures higher than 130°C, moderately concentrated solution of polyethylene were extracted to remove the low-molecular-weight components. Discontinuous fractionation experiments served to detect the best suited solvents. Diphenyl ether was chosen to demonstrate that the present extraction can be performed even with the same single solvent used to prepare the feed. For very high-molecular-weight polymers, mixed solvents are, however, normally better than single ones, since they allow an easier tailoring of thermo…

Reduced graphene oxide-based magnetic composite for trace determination of polycyclic aromatic hydrocarbons in cosmetics by stir bar sorptive dispers…

2020

This work describes a sensitive and rapid analytical method for trace determination of polycyclic aromatic hydrocarbons (PAHs) in cosmetic samples. The proposed method is based on stir bar sorptive-dispersive microextraction (SBSDME). A magnetic composite made of CoFe2O4 magnetic nanoparticles embedded into reduced graphene oxide sheets is used as sorbent phase. After the extraction, the target analytes are desorbed in toluene and then analyzed by gas chromatography-mass spectrometry (GC-MS). The main parameters involved in the extraction procedure (i.e., composite amount, extraction time and desorption time) were evaluated and optimized to provide the best extraction efficiency. The method…

Implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 with optimally reduced auxiliary basis dependence.

2008

An implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 using a single Slater-type geminal has been obtained with the aid of automated term generation and evaluation techniques. In contrast to a previously reported computer code [T. Shiozaki et al., J. Chem. Phys. 129, 071101 (2008)], our implementation features a reduced dependence on the auxiliary basis set due to the use of a reformulated evaluation of the so-called Z-intermediate rather than straight forward insertion of an auxiliary basis expansion, which allows an unambiguous comparison to more approximate CCSD-F12 models. First benchmark results for total correlation energies and reactio…

Bill2d - a software package for classical two-dimensional Hamiltonian systems

2015

Abstract We present Bill2d , a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincare sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a use…

2018

Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution. In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations o…

Optical implementation of the weighted sliced orthogonal nonlinear generalized correlation for nonuniform illumination conditions.

2002

Optical pattern recognition under variations of illumination is an important issue. The sliced orthogonal nonlinear generalized (SONG) correlation has been proposed as an optical pattern recognition tool to discriminate with high efficiency between objects. But, at the same time, the SONG correlation is very sensitive to gray-scale image variations. In a previous work, we expanded the definition of the SONG correlation to the Weighted SONG (WSONG) correlation to modify the discrimination capability in a controlled way. Here, we propose to use the WSONG when pattern recognition is obtained by means of optical correlation under nonuniform illumination. The calculation of the WSONG correlation…