Search results for "Spectral"
showing 10 items of 3116 documents
Use of the red-edge excitation effect for investigation of dielectric interactions in biomembranes
1999
Dipole moments of the fluorescent probes 1-phenylnaphthylamine (1-AN) and 1-anilinonaphthalene-8-sulfonate (1,8-ANS) are measured using electro-optical absorption and emission methods. Dipole moments in the ground and excited states were measured in cyclohexane and dioxane. It is shown that the charge distributions in the 1-AN and 1,8-ANS molecules differ substantially. The spectral dependence of the electro-optical coefficients suggests that the absorption spectrum of 1,8-ANS is due to a superposition of (at least two) electronic transitions. It is found that spectra of 1-AN in erythocyte ghosts are inhomogeneously broadened. The above effect makes it possible to selectively excite probe m…
A Theoretical Study of the Electronic Spectra of N9 and N7 Purine Tautomers
1999
The complete active space (CAS) SCF method and multiconfigurational second-order perturbation theory (CASPT2) have been used to study electronic spectra of the N(9)H and N(7)H tautomers of purine. The calculations include vertical excitation energies, oscillator strengths, dipole moments, and transition moment directions in gas phase. In accord with experiment in nonpolar solvents, the two lowest π → π* excited singlet valence states are predicted to be located at 4.7 and 5.1 eV. The latter is expected to shift to the red in aqueous solutions. A satisfactory interpretation of the electronic spectra above 5.5 eV is obtained if the experimental data are assumed to consist of the superposition…
On Boundary Value Problems for ϕ-Laplacian on the Semi-Infinite Interval
2017
The Dirichlet problem and the problem with functional boundary condition for ϕ-Laplacian on the semi-infinite interval are studied as well as solutions between the lower and upper functions.
Positive solutions for singular (p, 2)-equations
2019
We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.
An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities
2005
AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.
New isoperimetric estimates for solutions to Monge - Ampère equations
2009
Abstract We prove some sharp estimates for solutions to Dirichlet problems relative to Monge–Ampere equations. Among them we show that the eigenvalue of the Dirichlet problem, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result falls in the class of affine isoperimetric inequalities and shows that the eigenvalue of the Monge–Ampere operator behaves just the contrary of the first eigenvalue of the Laplace operator.
Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian
2021
The paper focuses on a Dirichlet problem driven by the (Formula presented.) -Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.
Using Wave Propagation Simulations and Convolutional Neural Networks to Retrieve Thin Film Thickness from Hyperspectral Images
2021
Ill-posed inversion problems are one of the major challenges when there is a need to combine measurements with the theory and numerical model. In this study, we demonstrate the use of wave propagation simulations to train a convolutional neural network (CNN) for retrieving sub-wavelength thickness profiles of thin film coatings from hyperspectral images. The simulations are produced by solving numerically one-dimensional wave equation with a method based on Discrete Exterior Calculus (DEC). This approach provides a powerful tool to produce large sets of training data for the neural network. CNN was verified by simulated verification sets and measured reflectance spectra, both of which showe…
Dirichlet Forms, Poincaré Inequalities, and the Sobolev Spaces of Korevaar and Schoen
2004
We answer a question of Jost on the validity of Poincare inequalities for metric space-valued functions in a Dirichlet domain. We also investigate the relationship between Dirichlet domains and the Sobolev-type spaces introduced by Korevaar and Schoen.
L 2-topological invariants of 3-manifolds
1995
We give results on theL2-Betti numbers and Novikov-Shubin invariants of compact manifolds, especially 3-manifolds. We first study the Betti numbers and Novikov-Shubin invariants of a chain complex of Hilbert modules over a finite von Neumann algebra. We establish inequalities among the Novikov-Shubin invariants of the terms in a short exact sequence of chain complexes. Our algebraic results, along with some analytic results on geometric 3-manifolds, are used to compute theL2-Betti numbers of compact 3-manifolds which satisfy a weak form of the geometrization conjecture, and to compute or estimate their Novikov-Shubin invariants.