Gravitational lens on de-Sitter background

Gravitational lenses are examined in de-Sitter (dS) background, for which the existence of the dS horizon is taken into account and hyperbolic trigonometry is used together with the hyperbolic angular diameter distance. Spherical trigonometry is used to discuss a gravitational lens in anti-de Sitter (AdS) background. The difference in the form among the dS/AdS lens equations and the exact lens equation in Minkowski background begins at the third order, when a small angle approximation is used in terms of lens and source planes. The angular separation of lensed images is decreased by the third-order deviation in the dS lens equation, while it is increased in AdS. In the present framework on the dS/AdS backgrounds, we discuss also the deflection angle of light, which does not include any term of purely the cosmological constant. Despite the different geometry, the deflection angle of light rays in hyperbolic and spherical geometry can take the same form. Through a coupling of the cosmological constant with lens mass, the separation angle of multiple images is larger (smaller) in dS (AdS) than in the flat case, for a given mass, source direction, and angular diameter distances among the lens, receiver and source.Comment: 12 pages, 8 figures, typos corrected, 2 references added, accepted for PR

Gravitational lens on an optical constant-curvature background: Its application to Weyl gravity model

We describe the gravitational lens on a constant-curvature background by using an optical constant-curvature (OCC) approach that allows to explicitly take into account a global geometry of the background space. First, light rays are curves in the space described by an optical metric. The OCC approach focuses on the case that the optical metric for the background spacetime has a constant curvature, for which the exact lens equation on an OCC background [Phys. Rev. D 105, 084022 (2022)] can be used. As a concrete example, next we discuss the gravitational lens in Mannheim-Kazanas (MK) solution, which include Rindler and de Sitter terms. By fully taking into account a background dependence of the light deflection, the deflection angle of light consistent with the OCC approach is well defined at large distance. In the OCC approach, finally, we examine the global behavior of the deflection angle and the gravitational lens observables in the Weyl gravity.Comment: 11 pages, 4 figure

Equivalence between definitions of the gravitational deflection angle of light for a stationary spacetime

The Gibbons-Werner-Ono-Ishihara-Asada method for gravitational lensing in a stationary spacetime has been recently reexamined [Huang and Cao, arXiv:2306.04145], in which the gravitational deflection angle of light based on the Gauss-Bonnet theorem can be rewritten as a line integral of two functions $H$ and $T$. The present paper proves that the Huang-Cao line integral definition and the Ono-Ishihara-Asada one [Phys. Rev. D 96, 104037 (2017)] are equivalent to each other, whatever asymptotic regions are. A remark is also made concerning the direction of a light ray in a practical use of these definitions.Comment: 4 pages, 1 figure, text improved, accepted for PR

Implementation and design of new functions for a web-based E-Learning system to stimulate learners motivation

Due to the opportunities provided by the Internet, people are taking advantage of e-learning courses and during the last few years enormous research efforts have been dedicated to the development of e-learning systems. So far, many e-learning systems are proposed and used practically. However, in these systems the e-learning completion rate is low. One of the reasons is the low study desire and motivation. In our previous work, we implemented a e-learning system that is able to increase the learning efficiency by stimulating learners motivation. In this work, we designed and implemented new functions to improve the system performancePeer ReviewedPostprint (published version

Book Recommendation Based on Library Loan Records and Bibliographic Information

AbstractIn order to show the effectiveness of using (a) library loan records and (b) information about book contents as a basis for book recommendations, we entered various data into a support vector machine (SVM), used it to recommend books to subjects, and asked them for evaluations of the recommendations that were given. The data that we used were (1) confidence and support with an association rule that was based on the loan records, (2) similarities between book titles, (3) matches/mismatches between the Nippon Decimal Classification (NDC) categories of the books, and (4) similarities between the outlines of the books in the BOOK Database. The subjects were 32 students who belonged to T University. The books that we recommended and the loan records that we used were obtained from the T University Library. The results showed that the combinations of (1), (2), (3) and (1), (2) were rated more favorably by the subjects than the other combinations. However, the books that were recommended by Amazon were rated even more favorably by the subjects. This is a topic for further research