Search results for "functions"
showing 10 items of 1066 documents
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...
A third integrating factor for indefinite integrals of special functions
2020
An integrating factor f ~ x is presented involving the terms in y ′ ′ x and q x y x of the general homogenous second-order linear ordinary differential equation. The new integrating factors obey se...
Approximating the solutions of differential inclusions driven by measures
2019
The matter of approximating the solutions of a differential problem driven by a rough measure by solutions of similar problems driven by “smoother” measures is considered under very general assumptions on the multifunction on the right-hand side. The key tool in our investigation is the notion of uniformly bounded $$\varepsilon $$-variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.
ON THE FUNDAMENTAL THEOREM OF CALCULUS FOR FRACTAL SETS
2015
The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock–Kurzweil type is introduced.
Defect interaction and local structural distortions in Mg-doped LaGaO3: A combined experimental and theoretical study
2017
A combined experimental and theoretical study of Mg-doped LaGaO3 electrolyte was carried out, with the aim to unveil the interaction between oxygen vacancy (Vo) and perovskite B site cations. LaGaO3 (LG) and LaGa0.875Mg0.125O2.938 (LGM0125) samples were comprehensively characterized by X-ray absorption spectroscopy (XAS) and X-ray diffraction, in order to investigate short- and long-range structures of both undoped and Mg-doped materials. XAS analysis evidenced a preferential Ga-Vo interaction in LGM0125, confirmed by periodic hybrid density functional theory calculations, which were combined with a symmetry-independent classes (SICs) approach in order to (a) obtain a detailed picture of th…
Comments on “Mean velocity and turbulent characteristics of flow over half-cycle cosine sharp-crested weirs” by Salehi S., Esmaili K., Azimi A.H.
2019
Abstract In this paper the stage-discharge equation of a half-cycle cosine weir is theoretically deduced applying the Π-Theorem of dimensional analysis and the self-similarity theory. The coefficients of the new stage-discharge relationships are estimated using the results of the experimental runs by Salehi et al..
Calculation of size‐intensive transition moments from the coupled cluster singles and doubles linear response function
1994
Coupled cluster singles and doubles linear response (CCLR) calculations have been carried out for excitation energies and dipole transition strengths for the lowest excitations in LiH, CH+, and C4and the results compared with the results from a CI-like approach to equation of motion coupled cluster (EOMCC). The transition strengths are similar in the two approaches for single molecule calculations on small systems. However, the CCLR approach gives size-intensive dipole transition strengths, while title EOMCC formalism does not. Thus, EOMCC calculations can give unphysically dipole transition strengths, e.g., in EOMCC calculations on a sequence of noninteracting LiH systems we obtained a neg…
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.
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.