• Korean Journal of Mathematics
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• 제18권1호
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• pp.21-28
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• 2010

In the unified field theory(UFT), many works on the solutions of Einstein's equation have been published. The main goal in the present paper is to obtain some geometric results on a particular solution of Einstein's equation under some condition in even-dimensional UFT $X_n$.

• 충청수학회지
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• 제23권2호
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• pp.185-195
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• 2010

In the unified field theory(UFT), in order to find a solution of the Einstein's equation it is necessary and sufficient to study the torsion tensor. The main goal in the present paper is to obtain, using a given torsion tensor (3.1), the complete representation of a particular solution of the Einstein's equation in terms of the basic tensor $g_{{\lambda}{\nu}}$ in even-dimensional UFT $X_n$.

• 충청수학회지
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• 제24권4호
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• pp.869-881
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• 2011

The main goal in the present paper is to obtain a necessary and sufficient condition for a new connection with zero torsion vector to be an Einstein's connection and derive some useful representation of the vector defining the Einstein's connection in even-dimensional UFT $X_n$.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.361-375
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• 2018

The object of the present paper is to study super quasi-Einstein manifolds. Some geometric properties of super quasi-Einstein manifolds have been studied. We also discuss $S(QE)_4$ spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a super quasi-Einstein spacetime.

• 충청수학회지
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• 제35권3호
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• pp.235-242
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• 2022

In this paper, we consider the existence of nonconstant warping functions on a warped product manifold M = B × _f² F, where B is a q(> 2)-dimensional base manifold with a nonconstant scalar curvature S_B(x) and F is a 3- dimensional fiber Einstein manifold and discuss that the resulting warped product manifold is an Einstein manifold, using the existence of the solution of some partial differential equation.

• 호남수학학술지
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• 제46권1호
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• pp.70-81
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• 2024

We consider the *-general critical equation on LP Sasakian manifolds, and show that such a manifold is generalized η-Einstein. After then, we consider LP Sasakian manifolds with *-conformally semisymmetric condition, and show that such manifolds are *-Einstein. Moreover, we show that the *-conformally semisymmetric LP Sasakian manifold is locally isometric to Eⁿ⁺¹(0) × Sⁿ(4).

• 한국수자원학회논문집
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• 제33권6호
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• pp.815-825
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• 2000

Einstein(1942)의 부유사량 산정식 유도과정에 있어 몇 가지 문제점들을 개선하였다. 수류조건을 판별하여 완난류 조건에서 유속의 영점높이를 산정하는 방법을 제시하고 부유사량 산정식을 일반화할 수 있는 무차원수를 도입하였다. 또한, 기준점 농도 산정의 정확성을 개선하기 위하여 최근에 개발된 소류사량 산정식으로부터 관련치를 추정하였으며, 수치적으로 또는 도표를 이용하여 해를 구해야 하는 수심적분치의 근사식을 개발하였다. Einstein의 기존 부유사량 산정식과 개선된 부유사량 산정식의 정확도를 검토하여 Brownlie(1981)가 수집한 자료에 대한 산정결과를 제시하였다.

• Korean Journal of Mathematics
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• 제13권1호
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• pp.1-11
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• 2005

The purpose of the present paper is to introduce a new concept of the E($^*{\kappa}$)-connection ${\Gamma}^{\nu}_{{\lambda}{\mu}}$, which is both Einstein and ($^*{\kappa}$)-connection, and to obtain a necessary and sufficient condition for the existence of the unique E($^*{\kappa}$)-connection in $n-^*g$-UFT. Next, under this condition, we shall obtain a surveyable tensorial representation of the unique E($^*{\kappa}$)-connection in $n-^*g$-UFT.

• 대한기계학회논문집
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• 제11권1호
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• pp.1-18
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• 1987

본 연구에서는 입자가 부상된 이상난류제트유동에 Einstein의 확산모형, Pes- kin모형, 3-방정식 모형, 4-방정식 모형, 대수응력모형 등을 적용하여 해석하고 각 모 형들의 결과를 비교 분석하였다. 이상난류유동의 수치해석에서 공기는 제1유체유동 으로 하고 첨가되는 고체분말의 흐름은 밀도(.rho.$_{p}$), 층류동점성계수(.nu.$_{p}$), 과점성계수(.nu.$_{pt}$ )를 갖는 제2유체유동의 흐름으로 간주하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권2호
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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.