Search results for "Names"
showing 10 items of 6843 documents
Indefinite integrals involving Jacobi polynomials from integrating factors
2020
A method was presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many special f...
Indefinite integrals of special functions from hybrid equations
2019
Elementary linear first and second order differential equations can always be constructed for twice differentiable functions by explicitly including the function's derivatives in the definition of ...
Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method
2015
ABSTRACTA method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear…
A generalized integration formula for indefinite integrals of special functions
2020
An integration formula for generating indefinite integrals which was presented in Conway JT [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec...
Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach
2011
Fractional power-law nonlinear drift arises in many applications of engineering interest, as in structures with nonlinear fluid viscous–elastic dampers. The probabilistic characterization of such structures under external Gaussian white noise excitation is still an open problem. This paper addresses the solution of such a nonlinear system providing the equation governing the evolution of the characteristic function, which involves the Riesz fractional operator. An efficient numerical procedure to handle the problem is also proposed.
Gaussian and non-Gaussian stochastic sensitivity analysis of discrete structural systems
2000
Abstract The derivatives of the response of a structural system with respect to the system parameters are termed sensitivities. They play an important role in assessing the effect of uncertainties in the mathematical model of the system and in predicting changes of the response due to changes of the design parameters. In this paper, a time domain approach for evaluating the sensitivity of discrete structural systems to deterministic, as well as to Gaussian or non-Gaussian stochastic input is presented. In particular, in the latter case, the stochastic input has been assumed to be a delta-correlated process and, by using Kronecker algebra extensively, cumulant sensitivities of order higher t…
Extremal solutions and strong relaxation for nonlinear multivalued systems with maximal monotone terms
2018
Abstract We consider differential systems in R N driven by a nonlinear nonhomogeneous second order differential operator, a maximal monotone term and a multivalued perturbation F ( t , u , u ′ ) . For periodic systems we prove the existence of extremal trajectories, that is solutions of the system in which F ( t , u , u ′ ) is replaced by ext F ( t , u , u ′ ) (= the extreme points of F ( t , u , u ′ ) ). For Dirichlet systems we show that the extremal trajectories approximate the solutions of the “convex” problem in the C 1 ( T , R N ) -norm (strong relaxation).
Thermodynamic approach of supercontinuum generation
2009
International audience; This paper is aimed at providing an overview on recent theoretical and experimental works in which a thermodynamic description of the incoherent regime of supercontinuum generation has been formulated. On the basis of the wave turbulence theory, we show that this highly nonlinear and quasi-continuous-wave regime of supercontinuum generation is characterized by two different phenomena. (i) A process of optical wave thermalization ruled by the four-wave mixing effects: The spectral broadening inherent to supercontinuum generation is shown to result from the natural tendency of the optical field to reach its thermodynamic equilibrium state, i. e., the state of maximum n…
High-pressure crystal structure, lattice vibrations, and band structure of BiSbO4
2016
The high-pressure crystal structure, lattice-vibrations HP crystal structure, lattice vibrations, and band , and electronic band structure of BiSbO4 were studied by ab initio simulations. We also performed Raman spectroscopy, infrared spectroscopy, and diffuse-reflectance measurements, as well as synchrotron powder X-ray diffraction. High-pressure X-ray diffraction measurements show that the crystal structure of BiSbO4 remains stable up to at least 70 GPa, unlike other known MTO4-type ternary oxides. These experiments also give information on the pressure dependence of the unit-cell parameters. Calculations properly describe the crystal structure of BiSbO4 and the changes induced by pressur…
Ambient-temperature high-pressure-induced ferroelectric phase transition in CaMnTi2O6
2017
The ferroelectric to paraelectric phase transition of multiferroic ${\mathrm{CaMnTi}}_{2}{\mathrm{O}}_{6}$ has been investigated at high pressures and ambient temperature by second-harmonic generation (SHG), Raman spectroscopy, and powder and single-crystal x-ray diffraction. We have found that ${\mathrm{CaMnTi}}_{2}{\mathrm{O}}_{6}$ undergoes a pressure-induced structural phase transition ($P{4}_{2}mc\ensuremath{\rightarrow}P{4}_{2}/nmc$) at $\ensuremath{\sim}7\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ to the same paraelectric structure found at ambient pressure and ${T}_{c}=630\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The continuous linear decrease of the SHG intensity that disappears at 7 …