Search results for "Basis"
showing 10 items of 760 documents
H-He collision-induced satellite in the Lyman alpha profile of DBA white dwarf stars
2020
The spectra of helium-dominated white dwarf stars with hydrogen in their atmosphere present a distinctive broad feature centered around 1160~\AA\/ in the blue wing of the Lyman-$\alpha$ line. It is extremely apparent in WD 1425+540 recently observed with HST COS. With new theoretical line profiles based on ab initio atomic interaction potentials we show that this feature is a signature of a collision-induced satellite due to an asymptotically forbidden transition. This quasi-molecular spectral satellite is crucial to understanding the asymmetrical shape of Lyman-$\alpha$ seen in this and other white dwarf spectra. Our previous work predicting this absorption feature was limited by molecular…
Nuclear anapole moment interaction in BaF from relativistic coupled-cluster theory
2018
We present high accuracy relativistic coupled cluster calculations of the P-odd interaction coefficient $W_A$ describing the nuclear anapole moment effect on the molecular electronic structure. The molecule under study, BaF, is considered a promising candidate for the measurement of the nuclear anapole moment, and the preparation for the experiment is now underway [Altunas et al., Phys. Rev. Lett. 120, 142501 (2018)]. Influence of various computational parameters (size of the basis set, treatment of relativistic effects, and treatment of electron correlation) on the calculated $W_A$ coefficient is investigated and a recommended value of 147.7 Hz with an estimated uncertainty of 1.5% is prop…
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…
Reply to comment on “A MRCI PS and CASSCF study of the ground state MgO dissociation energy”
1993
To compute the dissociation energy of MgO, the relationship among the size of the active space in CASSCF wavefunctions, the computed De and the continuity of ∂E/∂r is studied. Basis set influence is also considered. Finally, it is concluded that the dissociation energy of MgO referred to ground state atoms is 2.32±0.1 eV.
Distributed BOLD-response in association cortex vector state space predicts reaction time during selective attention.
2006
Human cortical information processing is thought to be dominated by distributed activity in vector state space (Churchland, P.S., Sejnowski, T.J., 1992. The Computational Brain. MIT Press, Cambridge.). In principle, it should be possible to quantify distributed brain activation with independent component analysis (ICA) through vector-based decomposition, i.e., through a separation of a mixture of sources. Using event-related functional magnetic resonance imaging (fMRI) during a selective attention-requiring task (visual oddball), we explored how the number of independent components within activated cortical areas is related to reaction time. Prior to ICA, the activated cortical areas were d…
The History of Algebra in Mathematics Education
2006
In this chapter, we analyse key issues in algebra history from which some lessons can be extracted for the future of the teaching and learning of algebra. A comparative analysis of two types of pre-Vietan languages (before 16th century), and of the corresponding methods to solve problems, leads to conjecture the presence of didactic obstacles of an epistemological origin in the transition from arithmetic to algebraic thinking. This illustrates the value of historic and critical analysis for basic research design in mathematics education. Analysing the interrelationship between different evolution stages of the sign system of symbolic algebra and vernacular language supports the inference th…
An Overview on Algebraic Structures
2016
This chapter recaps and formalizes concepts used in the previous sections of this book. Furthermore, this chapter reorganizes and describes in depth the topics mentioned at the end of Chap. 1, i.e. a formal characterization of the abstract algebraic structures and their hierarchy. This chapter is thus a revisited summary of concepts previously introduced and used and provides the mathematical basis for the following chapters.
On difference of operators with different basis functions
2019
In the recent years several researchers have studied problems concerning the difference of two linear positive operators, but all the available literature on this topic is for operators having same basis functions. In the present paper, we deal with the general quantitative estimate for the difference of operators having different basis functions. In the end we provide some examples. The estimates for the differences of two operators can be obtained also using classical result of Shisha and Mond. Using numerical examples we will show that for particular cases our result improves the classical one.
On Extensional Fuzzy Sets Generated by Factoraggregation
2014
We develop the concept of a general factoraggregation operator introduced by the authors on the basis of an equivalence relation and applied in two recent papers for analysis of bilevel linear programming solving parameters. In the paper this concept is generalized by using a fuzzy equivalence relation instead of the crisp one. We show how the generalized factoraggregation can be used for construction of extensional fuzzy sets and consider approximations of arbitrary fuzzy sets by extensional ones.
Vectors and Vector Fields
2012
The purpose of this book is to explain in a rigorous way Stokes’s theorem and to facilitate the student’s use of this theorem in applications. Neither of these aims can be achieved without first agreeing on the notation and necessary background concepts of vector calculus, and therein lies the motivation for our introductory chapter.