• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.235-242
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• 2023

In this paper, we studied several geometrical aspects of a perfect fluid spacetime admitting a Ricci ρ-soliton and an η-Ricci ρ-soliton. Beside this, we consider the velocity vector of the perfect fluid space time as a gradient vector and obtain some Poisson equations satisfied by the potential function of the gradient solitons.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.201-210
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• 2024

This paper is concerned with the study of spacetimes satisfying div 𝓜 = 0, where "div" denotes the divergence and 𝓜 is the m-projective curvature tensor. We establish that a perfect fluid spacetime with div 𝓜 = 0 is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with div 𝓜 = 0 represents a generalized Robertson-Walker spacetime.

• Genomics & Informatics
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• v.11 no.4
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• pp.277-281
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• 2013

RNA analysis has become a reliable method of body fluid identification for forensic use. Previously, we developed a combination of four multiplex quantitative PCR (qRT-PCR) probes to discriminate four different body fluids (blood, semen, saliva, and vaginal secretion). While those makers successfully identified most body fluid samples, there were some cases of false positive and negative identification. To improve the accuracy of the identification further, we tried to use multiple markers per body fluid and adopted the NanoString nCounter system instead of a multiplex qRT-PCR system. After measuring tens of RNA markers, we evaluated the accuracy of each marker for body fluid identification. For body fluids, such as blood and semen, each body fluid-specific marker was accurate enough for perfect identification. However, for saliva and vaginal secretion, no single marker was perfect. Thus, we designed a logistic regression model with multiple markers for saliva and vaginal secretion and achieved almost perfect identification. In conclusion, the NanoString nCounter is an efficient platform for measuring multiple RNA markers per body fluid and will be useful for forensic RNA analysis.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.271-277
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• 2010

We prove the global (in time) vorticity existence for the 2-D Euler equations of a perfect incompressible fluid in $B^0_{{\infty},1}({\mathbb{R}}^2){\cap}L^p({\mathbb{R}}^2)$ with 1 < p < 2. Moreover, we prove that the particle trajectory map X(x, t) satisfies the following estimate: for some positive constant C $${\parallel}X^{\pm1}(\cdot,\;t)-id(\cdot){\parallel}_{B^1_{\infty,1}}{\leq}Ce^{e^{Ct}}$$, where id represents the identity map on ${\mathbb{R}}^2$.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.571-580
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• 2018

The object of the present paper is to prove the non-existence of pseudo projective Ricci symmetric spacetimes $(PW\;RS)_4$ with different types of energy momentum tensor. We also discuss whether a fluid $(PW\;RS)_4$ spacetime with the basic vector field as the velocity vector field of the fluid can admit heat flux. Next we consider perfect fluid and dust fluid $(PW\;RS)_4$ spacetimes respectively. Finally we construct an example of a $(PW\;RS)_4$ spacetime.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.911-920
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• 2019

In this paper we characterize semiconformally flat spacetimes and a spacetime with harmonic semiconformal curvature tensor. At first in a semiconformally flat perfect fluid spacetime we obtain a state equation and prove that in particular for dimension n = 4, the spacetime represents a model for incoherent radiation. Next we prove that perfect fluid spacetime with harmonic semiconformal curvature tensor is of Petrov type I, D or O and the spacetime is a GRW spacetime. As a consequence we obtain several corollaries.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.391-413
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• 2018

In this paper we introduce a new tensor named semi-projective curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds $(PSPS)_n$ which recover some known results of Chaki [5]. We provide several interesting results. Among others we prove that in a $(PSPS)_n$ if the associated vector field ${\rho}$ is a unit parallel vector field, then either the manifold reduces to a pseudosymmetric manifold or pseudo projective symmetric manifold. Moreover we deal with semi-projectively flat perfect fluid and dust fluid spacetimes respectively. As a consequence we obtain some important theorems. Next we consider the decomposability of $(PSPS)_n$. Finally, we construct a non-trivial Lorentzian metric of $(PSPS)_4$.

• Journal of the Korean Society of Visualization
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• v.17 no.3
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• pp.39-45
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• 2019

A study on the sloshing flow of highly-viscous fluid in a rectangular box was made by both of theoretical approach and experimental visualization method. Assuming a smallness of external forcing to oscillate the container, it was investigated a linear sloshing flow of highly-viscous fluid utilizing asymptotic analysis by Taylor-series expansion as a small parameter R_e (≪1) in which R_e denotes Reynolds number. The theory predict that, during all cycles of sloshing, a linear shape of free surface will prevail in a bulk zone and it has confirmed in experiment. The relevance of perfect slip boundary condition, adopted in theoretical approach, to the bulk zone flow at the container wall was tested in experiment. It is found that quasi-steady coated thin film, which makes a lubricant layer between bulk flow and solid wall, is generated on the wall and the film makes a role to perfect slip boundary condition.

• Journal of the Korea Institute of Military Science and Technology
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• v.4 no.2
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• pp.202-214
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• 2001

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study quasi one-dimensional nozzle flow and axisymmetric sphere-cone($5^{\circ}$) flow for the perfect gas, the equilibrium and the nonequilibrium chemically reacting hypersonic flow. The effective gamma(${ \tilde{\gamma}}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The influences of the various altitude(30km, 50km) at Mach number(15.0, 20.0) were investigated. The equilibrium shock position was located farthest downstream when compared with those of perfect gas in a quasi one-dimensional nozzle. The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.669-689
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• 2011

The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic geometric properties of such a manifold are obtained. The applications of Lorentzian quasi-Einstein manifolds to the general relativity and cosmology are investigated. Theories of gravitational collapse and models of Supernova explosions [5] are based on a relativistic fluid model for the star. In the theories of galaxy formation, relativistic fluid models have been used in order to describe the evolution of perturbations of the baryon and radiation components of the cosmic medium [32]. Theories of the structure and stability of neutron stars assume that the medium can be treated as a relativistic perfectly conducting magneto fluid. Theories of relativistic stars (which would be models for supermassive stars) are also based on relativistic fluid models. The problem of accretion onto a neutron star or a black hole is usually set in the framework of relativistic fluid models. Among others it is shown that a quasi-Einstein spacetime represents perfect fluid spacetime model in cosmology and consequently such a spacetime determines the final phase in the evolution of the universe. Finally the existence of such manifolds is ensured by several examples constructed from various well known geometric structures.