• Journal of The Korean Astronomical Society
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• v.9 no.1
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• pp.9-14
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• 1976

Godel models of the universe filled with fluid are studied in the framework of the Einstein-Cartan theory of gravitation. It is assumed that the models admit a group of motions simply transitive on space-time. The combined effects of spin and rotation(vorticity) are studied with a particular attention to whether the held equations impose any restriction on alignement of spin direction (a polarized spin distribution). The solutions are found explicitly in a closed form, which show that spin components are vanishingly small except in the direction of z-axis (the compass of inertia) in which they can assume an arbitrary distribution.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.789-799
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• 2022

We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a locally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two distinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Alías and Meléndez in [4] for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.

• Journal of Astronomy and Space Sciences
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• v.29 no.2
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• pp.191-194
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• 2012

The observed distribution of a blending-corrected sample of Einstein ring crossing times, $t_E$, for microlensing events toward the galactic bulge/bar are analyzed. An inspection of the distribution of crossing times suggests that it may be bimodal, indicating that two populations of lenses could be responsible for observed microlensing events. Given the possibility that microlensing in this direction can be due to the two most common classes of stars, main-sequence and white dwarf, we analyze and show via Monte Carlo simulations that the observed bimodality of $t_E$ can be derived from their accepted mass functions, and the density distributions of both stellar populations in the galactic disk and bulge/bar, with a transverse velocity distribution that is consistent with the density distribution. Kolmogorov-Smirnov (KS) one sample tests shows that a white dwarf population of about 25% of all stars in the galaxy agrees well with the observed bimodality with a KS significance level greater than 97%. This is an expanded and updated version of a previous investigation (Wickramasinghe, Neusima, & Struble, in Mao 2008). A power-point version of the talk, with introductory figures, is found at: https://sites.google.com/site/rhkochconference/agenda-1/program.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.108-120
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• 2022

We considered qualitative behaviour of the generalization of Einstein's model of Brownian motion when the key parameter of the time interval of free jump degenerates. Fluids will be characterised by number of particles per unit volume (density of fluid) at point of observation. Degeneration of the phenomenon manifests in two scenarios: a) flow of the fluid, which is highly dispersing like a non-dense gas and b) flow of fluid far away from the source of flow, when the velocity of the flow is incomparably smaller than the gradient of the density. First, we will show that both types of flows can be modeled using the Einstein paradigm. We will investigate the question: What features will particle flow exhibit if the time interval of the free jump is inverse proportional to the density and its gradient ? We will show that in this scenario, the flow exhibits localization property, namely: if at some moment of time t₀ in the region, the gradient of the density or density itself is equal to zero, then for some T during time interval [t₀, t₀ + T] there is no flow in the region. This directly links to Barenblatt's finite speed of propagation property for the degenerate equation. The method of the proof is very different from Barenblatt's method and based on the application of Ladyzhenskaya - De Giorgi iterative scheme and Vespri - Tedeev technique. From PDE point of view it assumed that solution exists in appropriate Sobolev type of space.

• Journal of The Korean Astronomical Society
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• v.55 no.5
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• pp.173-194
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• 2022

We complete the survey for finite-source/point-lens (FSPL) giant-source events in 2016-2019 KMTNet microlensing data. The 30 FSPL events show a clear gap in Einstein radius, 9 𝜇as < 𝜃_E < 26 𝜇as, which is consistent with the gap in Einstein timescales near t_E ~ 0.5 days found by Mróz et al. (2017) in an independent sample of point-source/point-lens (PSPL) events. We demonstrate that the two surveys are consistent. We estimate that the 4 events below this gap are due to a power-law distribution of free-floating planet candidates (FFPs) dN_FFP/d log M = (0.4 ± 0.2) (M/38 M_⊕)^-p/star, with 0.9 ≲ p ≲ 1.2. There are substantially more FFPs than known bound planets, implying that the bound planet power-law index 𝛾 = 0.6 is likely shaped by the ejection process at least as much as by formation. The mass density per decade of FFPs in the Solar neighborhood is of the same order as that of 'Oumuamua-like objects. In particular, if we assume that 'Oumuamua is part of the same process that ejected the FFPs to very wide or unbound orbits, the power-law index is p = 0.89 ± 0.06. If the Solar System's endowment of Neptune-mass objects in Neptune-like orbits is typical, which is consistent with the results of Poleski et al. (2021), then these could account for a substantial fraction of the FFPs in the Neptune-mass range.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.293-304
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• 2018

In this paper, we study ${\varphi}$-recurrent almost cosymplectic (${\kappa},{\mu}$)-space and prove that it is an ${\eta}$-Einstein manifold with constant coefficients. Next, we show that a three-dimensional locally ${\varphi}$-recurrent almost cosymplectic (${\kappa},{\mu}$)-space is the space of constant curvature.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.39-50
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• 2014

In this paper, we study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection, whose structure vector field ${\zeta}$ is tangent to M. The main result is a classification theorem for such Einstein half lightlike submanifolds of a Lorentzian space form admitting a semi-symmetric non-metric connection.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.999-1006
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• 1997

We proved that if a fibred Riemannian space $\tilde{M}$ with cosymplectic structure is conformally flat, then $\tilde{M}$ is the locally product manifold of locally Euclidean spaces, that is locally Euclidean. Moreover, we investigated the fibred Riemannian space with cosymplectic structure when the Riemannian metric $\tilde{g}$ on $\tilde{M}$ is Einstein.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1199-1207
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• 2022

In the present paper, a Riemannian submersion 𝜋 between Riemannian manifolds such that the total space of 𝜋 endowed with a torse-forming vector field 𝜈 is studied. Some remarkable results of such a submersion whose total space is Ricci soliton are given. Moreover, some characterizations about any fiber of 𝜋 or the base manifold B to be an almost quasi-Einstein are obtained.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1035-1047
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• 2004

In this paper, we study the unit tangent sphere bundles T$_1$M(4c) of complex space forms M(4c) with constant holomorphic sectional curvature 4c. In particular, we determine T$_1$M(4c) whose Ricci tensors satisfy the Einstein-like conditions.