• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.475-487
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• 2003

A generalized even-dimensional Riemannian manifold defined by the ME-connection which is both Einstein and of the form (3.3) is called an even-dimensional ME-manifold and we denote it by $MEX_{2n}$. The purpose of this paper is to study a necessary and sufficient condition that there is an ME-connection, to derive the useful properties of some tensors, and to investigate a representation of the ME-vector in $MEX_{2n}$.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.775-779
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• 2005

On a compact n-dimensional manifold $M^n$, a critical point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satifies the critical point equation (CPE), given by $Z_g\;=\;s_g^{1\ast}(f)$. It has been conjectured that a solution (g, f) of CPE is Einstein. The purpose of the present paper is to prove that every compact stable minimal hypersurface is in a certain hypersurface of $M^n$ under an assumption that Ker($s_g^{1\ast}{\neq}0$).

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.185-195
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• 2020

This paper aims to study the 𝒲^⁎-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time having a semi-symmetric 𝒲^⋆-curvature tensor is semi-symmetric, whereas the whereas the energy-momentum tensor T of a space-time having a divergence free 𝒲^⋆-curvature tensor is of Codazzi type. A space-time having a traceless 𝒲^⁎-curvature tensor is Einstein. A 𝒲^⁎-curvature flat space-time is Einstein. Perfect fluid space-times which admits 𝒲^⋆-curvature tensor are considered.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.507-519
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• 2023

The aim of this paper is to study the Fisher-Marsden conjucture in the frame work of f-cosymplectic and (k, µ)-cosymplectic manifolds. First we prove that a compact f-cosymplectic manifold satisfying the Fisher-Marsden equation R'^*_g = 0 is either Einstein manifold or locally product of Kahler manifold and an interval or unit circle S¹. Further we obtain that in almost (k, µ)-cosymplectic manifold with k < 0, the Fisher-Marsden equation has a trivial solution.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.57.5-58
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• 2015

We describe relations between modern cosmology and general relativity in the historical context. We reveal some ironies imbedded in Einstein's final correction of his gravitational field equation in the context of cosmology in 1917 which has apparently opened a new era of modern physical cosmology. The ugly (according to Einstein) correction term was introduced only to build a static cosmology which turns out to be in flat contradiction with observation. Somehow, however, it is the correction term which has saved the modern cosmology from the genuine creativity of nature continuously revealed by astronomical observations. Whether the present precision cosmology is also a correct one is often ignored by the practitioners but still a pressing open question left for future theoretical and observational pursuits.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.1
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• pp.1-7
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• 1988

Prediction performances by Einstein's equation of diffusivity, Peskin's model, Three-Equation model, Four-Equation model and Algebraic Stress Model, have been compared by analyzing twophase (air-solid) turbulent jet flow. Turbulent kinetic energy equation of dispersed phase was solved to investigate effects of turbulent kinetic energy on turbulent diffusivity. Turbulent kinetic energy dissipation rate of particles has been considered by solving turbulent kinetic energy dissipation rate equation of dispersed phase and applying it to turbulent diffusivity of dispersed phase. Results show that turbulent diffusivity of dispersed phase can be expressed by turbulent kinetic energy ratio between phases and prediction of turbulent kinetic energy was improved by considering turbulent kinetic energy dissipation rate of dispersed phase for modelling turbulent diffusivity. This investigation also show that Algebraic Stress Model is the most promising method in analyzing gas-solid two phases turbulent flow.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.645-660
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• 2021

This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.

• Journal of the Korean Geotechnical Society
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• v.19 no.4
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• pp.95-105
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• 2003

The existing design criteria f3r the estimation of ultimate bearing capacity of drilled shaft socketed into rock masses are mainly obtained from the ultimate pile load capacities, which are determined by inconsistent failure criteria. Therefore, these design criteria generally produce difffrent predictions even for drilled shaft in the same condition. In this paper, the accuracies of the existing design criteria are investigated to develop an optimized design process for drilled shaft socketed into rock masses. Reasonable and consistent ultimate capacities of drilled shafts socked into rock masses, necessary far the check of accuracies of predictions, are determined by applying a specific failure criterion to a total of 11 pile load test results. A comparison between the predicted and the measured load capacities shows that ultimate base load capacities calculated from Zhang and Einstein's equation and NAVFAC are close to the measured values. Rosenberg and Journeaux's equation produces satisfactory prediction f3r ultimate side load capacity.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.1
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• pp.79-92
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• 1984

The analysis of total load was carried out by using the theory of unit stseam power (USP). The dimensionless USP equation of $S_R$ which was the rate of suspended load and bed load was derived from the USP function by applying the Einstein's reference concentration and Stokes' fall velocity. And the R relationship between the water discharge and Reynolds number (Re) was discussed, and it was shown that USP was closely related with Re. The value of $S_R$ was determined from the experimental data of Han River downstream and Mantz. And it was tested to several observatories of Korean Rivers. A good correlation among USP, suspended load and $S_R$ was shown and USP was increased with the increment of the turbulent intensity. Judging from the above results, it is considered this study can be contributed to estimate the total load.

• Analytical Science and Technology
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• v.15 no.6
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• pp.496-501
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• 2002

The electrolyte cathode glow discharge (ELCAD) is a new optical system for direct determination of trace heavy metals in flowing water. ELCAD has been successfully developed for on-line monitoring of heavy metals in flowing water. The application of an atmospheric glow discharge between an electrolyte solution cathode and a platinum rod anode led to the development of stable discharge. The fundamental aspects of new plasma source have been investigated. The fundamental study of ELCAD system has been measured plasma temperature using Einstein-Boltzmann equation after searching Fe atomic emission lines. The spectrum of each elements such as Cu, Pb, Fe, Ni and Cr show only major elemental line and no ionic line possibly due to low temperature plasma source. The detection limits of each elements are also investigated. These informations show that this type of plasma may apply for monitoring of heavy metals in waste water which consists of complex matrix.