Numerical solution of Dalgarno-Lewis equations by a mapped Fourier grid method

Cohen, S.; Themelis, Spyros I.

doi:10.1063/1.2185639

Cited by 22 publications

(31 citation statements)

References 40 publications

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“…Large scale calculations using fully correlated Hylleraas basis sets can attain a degree of precision not possible for calculations based on orbital basis sets [19,24,25]. There have been many calculations of the dynamic polarizability for Li [18,[26][27][28][29][30][31][32], but fewer for Be + [28,30]. The present calculation is by far the most precise calculation of the dynamic polarizability that is based upon a solution of the non-relativistic Schrödinger equation.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic dipole polarizabilities of the Li atom and the Be+ion

et al. 2010

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The dynamic dipole polarizabilities for the Li atom and the Be + ion in the 2 2 S and 2 2 P states are calculated using the variational method with a Hylleraas basis. The present polarizabilities represent the definitive values in the non-relativistic limit. Corrections due to relativistic effects are also estimated. Analytic representations of the polarizabilities for frequency ranges encompassing the n = 3 excitations are presented. The recommended polarizabilities for 7 Li and 9 Be + were 164.11 ± 0.03 a 3 0 and 24.489 ± 0.004 a 3 0 .

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Section: Introductionmentioning

confidence: 99%

“…There have been many calculations of the static polarizabilities of the ground and excited states of the Li atom and the Be + ion [17][18][19][20][21][22][23]. The most precise calculations on Li and Be + are the Hylleraas calculations by Tang and collaborators [17,23].…”

Section: Introductionmentioning

confidence: 99%

Dynamic dipole polarizabilities of the Li atom and the Be+ion

et al. 2010

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“…Degenerate energies must be excluded from the calculation of polarizabilities. By projecting out the degenerate state [7], Eq. (6) is modified into…”

Section: Polarizabilities Of the Hydrogen Atommentioning

confidence: 99%

“…They are a useful testing ground for numerical techniques [6,7], in particular because of the similarity of simple models of alkali atoms with hydrogen. However, contrary to the alkali case, the hydrogen atom polarizabilities are unrealistic in the sense that degenerate states must be excluded.…”

Section: Introductionmentioning

confidence: 99%

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Exact nonrelativistic polarizabilities of the hydrogen atom with the Lagrange-mesh method

Baye

2012

Phys. Rev. A

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Exact analytical expressions of the dipole polarizabilities of the non-relativistic hydrogen atom in spherical coordinates are derived with the help of the Lagrange-mesh numerical method. This method can provide exact energies and wave functions for well chosen conditions of calculation.Exact dipole polarizabilities are obtained after an unambiguous rounding up to at least principal quantum numbers around n = 30. The scalar polarizability of any nl level is given by n 4 [4n 2 + 14 + 7l(l + 1)]/4 and its tensor polarizability by −n 4 [3n 2 − 9 + 11l(l + 1)]l/4(2l + 3), which allow calculating the polarizability of any hydrogen state nlm.

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Hybrid-patent classification based on patent-network analysis

Liu

Shih

2010

J. Am. Soc. Inf. Sci.

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Effective patent management is essential for organizations to maintain their competitive advantage. The classification of patents is a critical part of patent management and industrial analysis. This study proposes a hybrid-patent-classification approach that combines a novel patent-network-based classification method with three conventional classification methods to analyze query patents and predict their classes. The novel patent network contains various types of nodes that represent different features extracted from patent documents. The nodes are connected based on the relationship metrics derived from the patent metadata. The proposed classification method predicts a query patent's class by analyzing all reachable nodes in the patent network and calculating their relevance to the query patent. It then classifies the query patent with a modified k -nearest neighbor classifier. To further improve the approach, we combine it with content-based, citation-based, and metadata-based classification methods to develop a hybrid-classification approach. We evaluate the performance of the hybrid approach on a test dataset of patent documents obtained from the U.S. Patent and Trademark Office, and compare its performance with that of the three conventional methods. The results demonstrate that the proposed patent-network-based approach yields more accurate class predictions than the patent network-based approach. IntroductionPatents are valuable intellectual property and therefore require effective management to ensure that an organization maintains its competitive advantage (Guan & Gao, 2009;Su, Lai, Sharma, & Kuo, 2009). Because of developments in various technologies, the number of patents has increased rapidly in recent years. How to manage the constantly growing volume of patents is thus becoming an important issue. Patent classification is a key part of patent management; however, as the task is usually performed by patent analysts, categorizing new patent documents correctly is a laborious process. Hence, there is a pressing need for an effective patent-classification approach.Basically, patent classification can be regarded as a textcategorization problem that involves assigning a patent document to a particular class. Most existing studies have considered information content to classify patent documents, and several classification algorithms have been developed based on different content features (e.g., He & Lo, 2008;Fall, Torcsvari, Benzineb, & Karetka, 2003, 2004Kim & Choi, 2007;Larkey, 1999;Loh, He, & Shen, 2006;Trappey, Hsu, Trappey, & Lin, 2006). In addition, some approaches have utilized citation relationships to improve the performance of patent classification (Lai & Wu, 2005; Li, Chen, Zang, & Lie, 2007) while others have employed patent metadata (e.g., the inventor's name) to achieve improvements in the classification performance (Richter & MacFarlane, 2005).Since patent metadata provides rich information that can be used to infer possible relationships between patent documents, there exists the poten...

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Numerical solution of Dalgarno-Lewis equations by a mapped Fourier grid method

Cited by 22 publications

References 40 publications

Dynamic dipole polarizabilities of the Li atom and the Be+ion

Dynamic dipole polarizabilities of the Li atom and the Be+ion

Exact nonrelativistic polarizabilities of the hydrogen atom with the Lagrange-mesh method

Hybrid-patent classification based on patent-network analysis

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