• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.399-416
• /
• 2017

In this paper, we study a class of Finsler metrics called general (${\alpha},{\beta}$)-metrics, which are defined by a Riemannian metric ${\alpha}$ and a 1-form ${\beta}$. We show that every general (${\alpha},{\beta}$)-metric with isotropic Berwald curvature is either a Berwald metric or a Randers metric. Moreover, a lot of new isotropic Berwald general (${\alpha},{\beta}$)-metrics are constructed explicitly.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.867-871
• /
• 2013

It has been conjectured that, on a compact 3-dimensional orientable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker $s^{\prime}^*_g{\neq}0$, which generalizes the previous partial results.

• Communications for Statistical Applications and Methods
• /
• v.18 no.1
• /
• pp.131-136
• /
• 2011

The original Bates-Watts framework applies only to the complete parameter vector. Thus, guidelines developed in that framework can be misleading when the adequacy of the linear approximation is very different for different subsets. The subset curvature measures appear to be reliable indicators of the adequacy of linear approximation for an arbitrary subset of parameters in nonlinear models. Given the specific mean shift outlier model, the standard approaches to obtaining test statistics for outliers are discussed. The accuracy of outlier tests is investigated using subset curvatures.

• 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).

• 한국전산유체공학회:학술대회논문집
• /
• 1997.10a
• /
• pp.131-135
• /
• 1997

Effect of wall curvature on flow characteristics is studied for mildly and strongly curved duct flows. The ducts are S-shaped, and the flow is partially blocked at the rear of the downstream. The presence of blockage in combination with curvature generates secondary flows on the concave surface; the magnitude of the secondary flow being dependent on the degree of wall curvature. Objectives are to compare the flow structures for mild and strong cases and to illuminate the changes in flow structure as the flow turns. Sensitivity on numerical solutions due to different inflow boundary conditions is also examined.

• The Pure and Applied Mathematics
• /
• v.20 no.3
• /
• pp.199-206
• /
• 2013

We present a 4-dimensional nil-manifold as the first example of a closed non-K$\ddot{a}$hlerian symplectic manifold with the following property: a function is the scalar curvature of some almost K$\ddot{a}$hler metric iff it is negative somewhere. This is motivated by the Kazdan-Warner's work on classifying smooth closed manifolds according to the possible scalar curvature functions.

• Journal of the Korean Data and Information Science Society
• /
• v.24 no.1
• /
• pp.179-187
• /
• 2013

Bates and Watts (1981) have discussed the problems of reparameterizing nonlinear models in obtaining accurate linear approximation confidence regions for the parameters. A similar problem exists with computing confidence curves for fitted values or predictions. The statistical behavior of fitted values does not depend on the parameterization. Thus, as long as the intrinsic curvature is small, standard Wald intervals for fitted values are likely to be sufficient. Accuracy of linear approximation for fitted values is investigated using confidence curves.

• Communications of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.245-249
• /
• 2010

We show that on a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ (dim $M^{2n}\;=\;2n\;{\geq}\;4$), $M^{2n}$ is K$\ddot{a}$hler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of $M^{2n}$ everywhere. As a consequence, if a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ is both conformally flat and scalar flat, then $M^{2n}$ is K$\ddot{a}$hler. In contrast with the compact case, we show that there exists a locally conformal K$\ddot{a}$hler manifold with k equal to s, which is not K$\ddot{a}$hler.

• Journal of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.147-157
• /
• 2006

In this paper, we study complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an antide Sitter space $H_1^4(-1)$. It is proved that complete maximal spacelike hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space $H_1^4(-1)$ are isometric to the hyperbolic cylinder $H^2(c1){\times}H^1(c2)$ with S = 3 or they satisfy $S{\leq}2$, where S denotes the squared norm of the second fundamental form.

• The Journal of Korea CHUNA Manual Medicine
• /
• v.5 no.1
• /
• pp.151-161
• /
• 2004

Objectives : To investigate and compare the curvature of the cervical spine of the patients with whiplash and insidious onset neck pain. Method : Clinical study carried out in 33 insidious onset neck pain outpatients and 34 whiplash onset neck pain inpatients in Conmaul Oriental Hospital. Cervical spine curvature was measured using five measuring Methods. Type of cervical spine curvature was analyzed by Jochumsen method. Ishihara Index. T-test was used to compare the cervical spine angle of the two groups. Results : The prevalence of 'straight' and 'kyphotic' cervical spines was 46.5% in the insidious onset cases and 26.47% in the whiplash onset cases. In Jackson's angle, Jochumsen method, Ishihara Index, and Park's method, angle of the Cervical spine curvature was significantly lower in the insidious onset cases. (P<0.01) Conclusion : The results suggest that the cervical spine of neck pain patients is 'straight' and 'kyphotic' and more significant in insidious onset cases.