• Korean Journal of Mathematics
• /
• v.22 no.1
• /
• pp.207-216
• /
• 2014

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to study the algebraic geometric structures of 3-dimensional $^*g-ESX_3$. Particularly, in 3-dimensional $^*g-ESX_3$, we derive a new set of powerful recurrence relations in the first class.

• Korean Journal of Mathematics
• /
• v.24 no.3
• /
• pp.319-330
• /
• 2016

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unied eld tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to study the algebraic geometric structures of 5-dimensional $^*g-ESX_5$. Particularly, in 5-dimensional $^*g-ESX_5$, we derive a new set of powerful recurrence relations in the first class.

• Korean Journal of Mathematics
• /
• v.25 no.1
• /
• pp.127-135
• /
• 2017

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 5-dimensional $^*g-ESX_5$ and to display a surveyable tnesorial representation of 5-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.

• Korean Journal of Mathematics
• /
• v.23 no.2
• /
• pp.313-321
• /
• 2015

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 3-dimensional $^*g-ESX_3$ and to display a surveyable tnesorial representation of 3-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.

• Korean Journal of Mathematics
• /
• v.21 no.1
• /
• pp.91-100
• /
• 2013

This paper is a direct continuation of [1] and [2]. In this paper we investigate some properties of ES-curvature tensor and contracted ES-curvature tensor of g - $ESX_n$. Also, we study the field equations in the n-dimensional ES manifold g - $ESX_n$.

• Korean Journal of Mathematics
• /
• v.26 no.1
• /
• pp.43-51
• /
• 2018

The manifold $^{\ast}g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^{\ast}g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to derive a new set of powerful recurrence relations and to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 5-dimensional $^{\ast}g-ESX_5$ and to display a surveyable tnesorial representation of 5-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the second class.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.133-139
• /
• 2010

The manifold $g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $g_{{\lambda}{\mu}}$ through the ES-connection which is both Einstein and semi-symmetric. In this paper, we investigate the properties of the vectors $X_{\lambda}$, $S_{\lambda}$ and $U_{\lambda}$ of $g-ESX_n$, with main emphasis on the derivation of several useful generalized identities involving it.

• Korean Journal of Mathematics
• /
• v.19 no.4
• /
• pp.381-390
• /
• 2011

This paper is a direct continuation of [1]. In this paper we derive tensorial representations of contracted ES curvature tensors of $g-ESX_n$ and prove several generalized identities involving them. In particular, a variation of the generalized Bianchi's identity in $g-ESX_n$, which has a great deal of useful physical applications, is proved in Theorem (2.9).

• Korean Journal of Mathematics
• /
• v.19 no.1
• /
• pp.25-32
• /
• 2011

This paper is a direct continuation of [1]. In this paper we investigate some properties of ES-curvature tensor of g - $ESX_n$, with main emphasis on the derivation of several useful generalized identities involving it. In this subsequent paper, we are concerned with contracted curvature tensors of g - $ESX_n$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in g - $ESX_n$, which has a great deal of useful physical applications.

• Journal of Aerospace System Engineering
• /
• v.9 no.2
• /
• pp.34-40
• /
• 2015

Staged combustion cycle engines are well known to have high combustion efficiencies and specific impulse. In this study, design of mixing head part of combustion chamber for 8tonf class staged combustion cycle rocket engine (ES-08) was performed. Structural stability of the mixing head part of the combustion chamber is very important design factor because it is loaded by high temperature and high pressure of fuel and oxidizer as well as by thrust load simultaneously. Uniformity of flow distributions of the propellants to the injectors is also important factor. First, a basic configuration for the ES-08 mixing head part was designed on the basis of the structural design requirements. And then, the structural analyses were performed on the basic configuration as well as some of reinforced configurations. As the structural analyses results, the most stable configuration was selected for the ES-08 mixing head part. In order to examine the uniformity of the flow distributions of the propellants through the manifold of the mixing head, flow analysis was performed based on the selected configuration. The results of the flow analysis showed that the fuel and the oxidizer were uniformly supplied to the injector.