Search results for "Linear"
showing 10 items of 7165 documents
Serrin-Type Overdetermined Problems: an Alternative Proof
2008
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In the case of the Poisson equation, our proof is alternative to the proofs proposed by Serrin (moving planes) and by Weinberger. Moreover, our proof makes no direct use of the maximum principle while it sheds light on a relation between the Serrin problem and the isoperimetric inequality.
Are most of the stationary points in a molecular association minima? Application of Fraga's potential to benzene-benzene
1993
The importance of characterizing the stationary points of the intermolecular potential by means of Hessian eigenvalues is illustrated for the calculation of the benzene–benzene interaction using an atom-to-atom pair potential proposed by Fraga (FAAP). Two models, the standard one-center-per atom and another using three-centers-per atom due to Hunter and Sanders, are used to evaluate the electrostatic contributions and the results are compared. It is found in both cases that although using low-gradient thresholds allows optimization procedures to avoid many stationary points that are not true minima computing time considerations makes the usual procedure of using high-gradient thresholds [sa…
On the Symmetry of Solutions to a k-Hessian Type Equation
2013
Abstract In this note we prove that if u is a negative solution to a nonlinear elliptic equation involving a Hessian operator, and u is zero on the boundary of a ball, then u is radially symmetric and increasing along the radii.
Apertureless scanning near-field optical microscopy: a comparison between homodyne and heterodyne approaches
2006
International audience; In coherent homodyne apertureless scanning near-field optical microscopy (ASNOM) the background field cannot be fully suppressed because of the interference between the different collected fields, making the images difficult to interpret. We show that implementing the heterodyne version of ASNOM allows one to overcome this issue. We present a comparison between homodyne and heterodyne ASNOM through near-field analysis of gold nanowells, integrated waveguides, and a single evanescent wave generated by total internal reflection. The heterodyne approach allows for the control of the interferometric effect with the background light. In particular, the undesirable backgro…
ChemInform Abstract: Antimicrobial Activity Characterization in a Heterogeneous Group of Compounds.
2010
In this work we carry out a study of pattern recognition to detect the microbiological activity in a group of heterogeneous compounds. The structural descriptors utilized are the topological connectivity indexes. The methods followed are stepwise linear discriminant analysis (linear analysis) and artificial neural network (nonlinear analysis). Although both methods are appropriate to differentiate between active and inactive compounds, the artificial neural network is, in this case, more adequate, since it shows in a test set a prediction success of 98%, versus 92% obtained with linear discriminant analysis.
Antimicrobial Activity Characterization in a Heterogeneous Group of Compounds
1998
In this work we carry out a study of pattern recognition to detect the microbiological activity in a group of heterogeneous compounds. The structural descriptors utilized are the topological connectivity indexes. The methods followed are stepwise linear discriminant analysis (linear analysis) and artificial neural network (nonlinear analysis). Although both methods are appropriate to differentiate between active and inactive compounds, the artificial neural network is, in this case, more adequate, since it shows in a test set a prediction success of 98%, versus 92% obtained with linear discriminant analysis.
Experimental Sentinel-2 LAI estimation using parametric, non-parametric and physical retrieval methods – A comparison
2015
Abstract Given the forthcoming availability of Sentinel-2 (S2) images, this paper provides a systematic comparison of retrieval accuracy and processing speed of a multitude of parametric, non-parametric and physically-based retrieval methods using simulated S2 data. An experimental field dataset (SPARC), collected at the agricultural site of Barrax (Spain), was used to evaluate different retrieval methods on their ability to estimate leaf area index (LAI). With regard to parametric methods, all possible band combinations for several two-band and three-band index formulations and a linear regression fitting function have been evaluated. From a set of over ten thousand indices evaluated, the …
On the Intrinsic Complexity of Learning
1995
AbstractA new view of learning is presented. The basis of this view is a natural notion of reduction. We prove completeness and relative difficulty results. An infinite hierarchy of intrinsically more and more difficult to learn concepts is presented. Our results indicate that the complexity notion captured by our new notion of reduction differs dramatically from the traditional studies of the complexity of the algorithms performing learning tasks.
Beyond second-order convergence in simulations of binary neutron stars in full general relativity
2014
Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the Einstein-Euler system of equations. We report simulations of the inspiral of binary neutron stars in quasi-circular orbits computed with a new code employing high-order, high-resolution shock-capturing, finite-differencing schemes that, for the first time, go beyond the second-order barrier. In particular, without any tuning or alignment, we measure a convergence order above three both in the phase and in the amplitude of the gravitational waves. Because the new code is able to calculate waveforms with very small phase errors already at modest resolutions,…
Linear theory of the Rayleigh–Taylor instability at a discontinuous surface of a relativistic flow
2017
We address the linear stability of a discontinuous surface of a relativistic flow in the context of a jet that oscillates radially as it propagates. The restoring force of the oscillation is expected to drive a Rayleigh-Taylor instability (RTI) at the interface between the jet and its cocoon. We perform a linear analysis and numerical simulations of the growth of the RTI in the transverse plane to the jet flow with a uniform acceleration. In this system, an inertia force due to the uniform acceleration acts as the restoring force for the oscillation. We find that not only the difference in the inertia between the two fluids separated by the interface but also the pressure at the interface h…