Search results for "symbols"
showing 10 items of 6763 documents
On Taylor coefficients of entire functions integrable against exponential weights
2001
A New Family of Deformations of Darboux-Pöschl-Teller Potentials
2004
The aim of this Letter is to present a new family of integrable functional-difference deformations of the Schrodinger equation with Darboux–Poschl–Teller potentials. The related potentials are labeled by two integers m and n, and also depend on a deformation parameter h. When h→ 0 the classical Darboux–Poschl–Teller model is recovered.
A Method of Conversion of some Coefficient Inverse Parabolic Problems to a Unified Type of Integral-Differential Equation
2011
Coefficient inverse problems are reformulated to a unified integral differential equation. The presented method of conversion of the considered inverse problems to a unified Volterra integral-differential equation gives an opportunity to distribute the acquired results also to analogous inverse problems for non-linear parabolic equations of different types.
Jacobi Fields, Conjugate Points
2001
Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space.
Sensitivity analysis of Gaussian processes for oceanic chlorophyll prediction
2015
Gaussian Process Regression (GPR) for machine learning has lately been successfully introduced for chlorophyll content mapping from remotely sensed data. The method provides a fast, stable and accurate prediction of biophysical parameters. However, since GPR is a non-linear kernel regression method, the relevance of the features are not accessible. In this paper, we introduce a probabilistic approach for feature sensitivity analysis (SA) of the GPR in order to reveal the relative importance of the features (bands) being used in the regression process. We evaluated the SA on GPR ocean chlorophyll content prediction. The method revealed the importance of the spectral bands, thus allowing the …
Einstein Versus Neutrinos
2013
This article focuses on the news coverage given to the CERN (European Organization for Nuclear Research) announcement that neutrinos might exceed the speed of light, flying in the face of Albert Einstein’s theory. By studying 140 cartoons about the news item published between the CERN’s announcement at the end of September 2011 up until its refutation in February 2012, we selected 33 devoted to Albert Einstein. We study the iconographic use of Einstein’s figure, and how the suggestion he might have been wrong stirred up greater interest among the cartoonists than when it was proven his ideas are still fully in force.
High Resolution Coherent Anti-Stokes Raman Spectroscopy (CARS) Of O 2 And CO 2
1988
With the help of high spectral quality (linewidth , 6 MHz) injection-locked flashlamp-pumped dye lasers, high resolution Coherent Anti-Stokes Raman Spectroscopy (CARS) has been applied to the study of the Q-branches of 0 2 and CO 2 . The Q-branch linewidths of 02 were obtained from the first nine transitions (J 2 = 1 to 17) recorded at pressures from 0.094 to 1 atm at room temperature. A least squares program was employed to fit calculated spectra to experimental spectra by adjusting different parameters. The collisional broadening coefficients we have obtained are consistent with available Raman data. We have also studied the Q-branch of the fundamental v1 band of CO 2 in the Fermi resonan…
Beyond the spin model: exchange coupling in molecular magnets with unquenched orbital angular momenta.
2011
In this critical review we review the problem of exchange interactions in polynuclear metal complexes involving orbitally degenerate metal ions. The key feature of these systems is that, in general, they carry an unquenched orbital angular momentum that manifests itself in all their magnetic properties. Thus, interest in degenerate systems involves fundamental problems related to basic models in magnetism. In particular, the conventional Heisenberg-Dirac-Van Vleck model becomes inapplicable even as an approximation. In the first part we attempt to answer two key questions, namely which theoretical tools are to be used in the case of degeneracy, and how these tools can be employed. We demons…
Predictive Model for Cut-Edge Corrosion of Galvanized Steels
2006
A numerical model for the electrochemical behavior of cut-edge of galvanized steels is proposed. Some experimental data of current densities above cut-edge immersed in a 0.03M NaCl solution have been measured, using a scanning vibrating electrode technique, and compared with some simulated ones. A good fit has been obtained. The model geometry has been modified by decreasing the electrolyte thickness in order to tend towards an atmospheric corrosion case; such situation that is not easily accessible by electrochemical studies. Three regions can be distinguished according to the efficiency of the galvanic coupling to protect steel.