Search results for " Function"
showing 10 items of 9395 documents
Size-consistent ab initio calculation of the electric quadrupole moment of Cl2
2003
Abstract The molecular electric quadrupole moment ( Θ ) of Cl 2 has been calculated using SDCI, and (SC) 2 -SDCI wave functions as well as CCSD, CCSD(T), and CC3 methods. All these correlation methods are single reference. All of them, but SDCI, are free of the size-extensivity error. The variation of Θ from the separated atoms to the equilibrium region is reported. The present results leads to an estimated value of 2.3520 a.u. (10.55 × 10 −40 Cm 2 ) corresponding to a CC(3) calculation at the CBS approach and including the ro-vibrational and thermal averaging corrections. This value is compatible with two experimental values and points to one of them as slightly more reliable.
Modeling of defects and surfaces in perovskite ferroelectrics
2002
The results of electronic structure calculations for different terminations of SrTiO3 (100) and (110) perovskite thin films are discussed. These calculations are based on the ab initio Hartree-Fock (HF) method and Density Functional Theory (DFT). Results are compared with previous ab initio plane-wave LDA and classical Shell Model (SM) calculations. Calculated considerable increase of the Ti – O chemical bond covalency nearby the surface is confirmed by experimental data. Our quantum chemical calculations performed by means of the intermediate neglect of differential overlap (INDO) method confirm the existence of self-trapped electrons in KNbO3, KTaO3 and BaTiO3 crystals. The relevant latti…
Ab Initio Study on the Mechanism of the Reactions of the Nitrate Radical with Haloalkenes: 1,2-Dichloroethene, 1,1-Dichloroethene, Trichloroethene, …
2000
A general mechanism for the reactions of the NO3 radical with 1,2-dichloroethene, 1,1-dichloroethene, trichloroethene, and tetrachloroethene is proposed from ab initio DFT calculations. The calculated mechanism shows three main parallel reaction pathways. For the systems where the two carbon atoms are differently substituted, the study includes both the attacks with Markownikoff and contra-Markownikoff orientation. The first reaction pathway leads to the formation of an epoxide along with the NO2 radical, the second one to the formation of carbonyl compounds, and the third one leads, through the cleavage of the C−C bond, to the formation of carbonyl compounds with a lower number of carbon a…
Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds
2017
We study ray transforms on spherically symmetric manifolds with a piecewise $C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2$ functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a $C^{1,1}$ metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.
Indefinite integrals involving the incomplete elliptic integrals of the first and second kinds
2016
ABSTRACTA substantial number of indefinite integrals are presented for the incomplete elliptic integrals of the first and second kinds. The number of new results presented is about three times the total number to be found in the current literature. These integrals were obtained with a Lagrangian method based on the differential equations which these functions obey. All results have been checked numerically with Mathematica. Similar results for the incomplete elliptic integral of the third kind will be presented separately.
Indefinite integrals involving the incomplete elliptic integral of the third kind
2016
ABSTRACTA substantial number of new indefinite integrals involving the incomplete elliptic integral of the third kind are presented, together with a few integrals for the other two kinds of incomplete elliptic integral. These have been derived using a Lagrangian method which is based on the differential equations which these functions satisfy. Techniques for obtaining new integrals are discussed, together with transformations of the governing differential equations. Integrals involving products combining elliptic integrals of different kinds are also presented.
A note on a generalization of Françoise's algorithm for calculating higher order Melnikov functions
2004
In [J. Differential Equations 146 (2) (1998) 320–335], Françoise gives an algorithm for calculating the first nonvanishing Melnikov function M of a small polynomial perturbation of a Hamiltonian vector field and shows that M is given by an Abelian integral. This is done under the condition that vanishing of an Abelian integral of any polynomial form ω on the family of cycles implies that the form is algebraically relatively exact. We study here a simple example where Françoise’s condition is not verified. We generalize Françoise’s algorithm to this case and we show that M belongs to the C[log t, t, 1/t] module above the Abelian integrals. We also establish the linear differential system ver…
A generalization of Françoise's algorithm for calculating higher order Melnikov functions
2002
Abstract In [J. Differential Equations 146 (2) (1998) 320–335], Francoise gives an algorithm for calculating the first nonvanishing Melnikov function Ml of a small polynomial perturbation of a Hamiltonian vector field and shows that Ml is given by an Abelian integral. This is done under the condition that vanishing of an Abelian integral of any polynomial form ω on the family of cycles implies that the form is algebraically relatively exact. We study here a simple example where Francoise's condition is not verified. We generalize Francoise's algorithm to this case and we show that Ml belongs to the C [ log t,t,1/t] module above the Abelian integrals. We also establish the linear differentia…
Automorphisms of hyperelliptic GAG-codes
2009
Abstract We determine the n –automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.
Picard and the Italian Mathematicians: The History of Three Prix Bordin
2016
It is usually said that in the transition period between 19th and 20th centuries, French scholars (mainly Picard and Humbert) as well as Italian scholars (mainly Castelnuovo, Enriques and Severi) were interested in the study of algebraic surfaces, though using different methods.