• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.235-246
• /
• 2005

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original(in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.

• Journal of the Korean Data and Information Science Society
• /
• v.15 no.3
• /
• pp.689-694
• /
• 2004

We investigate the test for model adequacy in nonlinear regression. We can expect the usual likelihood ratio statistic to be unaffected by any parametric- effect curvature; only the effect of intrinsic curvature needs to be considered. Multiplicative correction factor is derived for the limiting distribution of test statistic, which is a function of the intrinsic curvature arrays.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.461-477
• /
• 2016

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

• Journal of the Chungcheong Mathematical Society
• /
• v.34 no.4
• /
• pp.379-385
• /
• 2021

We consider the local uniqueness of a catenoid under the condition for the Gaussian curvature analogous to Bianchi surfaces. More precisely, if a nonplanar minimal surface in ℝ³ has the Gaussian curvature $K={\frac{1}{(U(u)+V(v))^2}}$ for any functions U(u) and V (v) with respect to a line of curvature coordinate system (u, v), then it is part of a catenoid. To do this, we use the relation between a conformal line of curvature coordinate system and a Chebyshev coordinate system.

• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.893-900
• /
• 2023

In the present study, we consider some curvature properties of generalized B-curvature tensor on Kenmotsu manifold. Here first we describe certain vanishing properties of generalized B curvature tensor on Kenmostu manifold. Later we formulate generalized B pseudo-symmetric condition on Kenmotsu manifold. Moreover, we also characterize generalized B ϕ-recurrent Kenmotsu manifold.

• Honam Mathematical Journal
• /
• v.38 no.3
• /
• pp.593-611
• /
• 2016

This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.

• Journal of Energy Engineering
• /
• v.8 no.2
• /
• pp.293-297
• /
• 1999

Direct comparisons are made between curvature-corrected eddy viscosity models and the present experimental data. The results show that the curvature effects can be quantified through a curvature parameter R$\sub$c/ or S$\sub$c/ and a non-equilibrium value of p/$\varepsilon$. The data reveal a significant dependence of the eddy viscosity on the curvature and strain history for a fluid in a stabilizing curvature field, S$\sub$c/>1.0. Especially, experimental result shows that the eddy viscosity coefficient ratio at S$\sub$c/=3 changes from 10 to -10 although shear rate preserved constant. It is therefore suggested that proper curvature modifications, particularly the strain history effect, must be introduced into current eddy viscosity models for their application to turbulent flows subjected to curvature straining field for a non-negligible period of time.

• Journal of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.829-845
• /
• 2013

In this paper, we firstly establish a family of curvature invariant conditions lying between the well-known 2-nonnegative curvature operator and nonnegative curvature operator along the Ricci flow. These conditions are defined by a set of inequalities involving the first four eigenvalues of the curvature operator, which are named as 3-parameter ${\lambda}$-nonnegative curvature conditions. Then a related rigidity property of manifolds with 3-parameter ${\lambda}$-nonnegative curvature operators is also derived. Based on these, we also obtain a strong maximum principle for the 3-parameter ${\lambda}$-nonnegativity along Ricci flow.

• Journal of the Optical Society of Korea
• /
• v.19 no.6
• /
• pp.658-664
• /
• 2015

Lens designers generally refer to flat image fields and attempt to minimize the field curvature. Present-day CMOS image sensors for mobile phone cameras, however, are not flat, but curved. Sometimes it is necessary to generate an intentional field curvature according to the degree and direction of the CMOS image-sensor’s curvature. This paper presents the degree of curvature of a CMOS image sensor measured using an interferometer, and proposes an effective compensation method that minimizes the net field curvature through optimizing the air gap between lens elements, which is demonstrated using simulations and experiments.

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