• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제28권2호
• /
• pp.59-70
• /
• 2024

In this paper we present the approximation method of the circular helix by G² cubic polynomial curves. The approximants are G¹ Hermite interpolation of the circular helix and their approximation order is four. We obtain numerical examples to illustrate the geometric continuity and the approximation order of the approximants. The method presented in this paper can be extended to approximating the elliptical helix. Using the property of affine transformation invariance we show that the approximant has G² continuity and the approximation order four. The numerical examples are also presented to illustrate our assertions.

• 대한수학회논문집
• /
• 제10권2호
• /
• pp.483-490
• /
• 1995

A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

• Journal of Electrical Engineering and Technology
• /
• 제10권2호
• /
• pp.676-687
• /
• 2015

Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

• Structural Engineering and Mechanics
• /
• 제3권2호
• /
• pp.121-133
• /
• 1995

It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories. These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.

• East Asian mathematical journal
• /
• 제19권2호
• /
• pp.241-249
• /
• 2003

In [11] the feeble continuity is introduced and then the weak and strong forms of feeble(or, equivalently $\alpha$-continuity) continuity are studied. In this note, we introduce a type of function called a slightly $\alpha$-continuous function and study several properties of it

• East Asian mathematical journal
• /
• 제18권2호
• /
• pp.183-193
• /
• 2002

The aim of this paper is to prove a common fixed point theorem from the class of compatible maps to larger class of weakly compatible maps without appeal to continuity in fuzzy metric spaces.

• Kyungpook Mathematical Journal
• /
• 제51권1호
• /
• pp.87-91
• /
• 2011

In this paper we obtain a Voronvskaya type theorem for modi ed Post-Widde operators.

• 충청수학회지
• /
• 제19권3호
• /
• pp.213-218
• /
• 2006

The 2D g-Navier-Stokes equations are a certain modified Navier-Stokes equations and have the following form, $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla})u+{\nabla}p=f$$, in ${\Omega}$ with the continuity equation ${\nabla}{\cdot}(gu)=0$, in ${\Omega}$, where g is a suitable smooth real valued function. In this paper, we will derive 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In addition, we will see the relationship between two equations.

• 문화기술의 융합
• /
• 제9권6호
• /
• pp.57-66
• /
• 2023

이 연구는 예비교사들의 교육봉사지속성에 미치는 요인을 확인하기 위한 서술적 조사연구이다. 연구방법: 자료수집 기간은 2023년 3월 1일부터 30일까지 이루어졌다. G광역시 2개 대학 교직이수자 90명을 대상으로 자아효능감, 친사회성, 작업선호도, 교육봉사지속성을 조사하였다. 수집된 자료의 분석은 IBM SPSS/Win 26.0을 이용하였으며, 서술통계, ANOVA, Pearson 상관관계와 다중회귀분석을 하였다. 결과: 연구결과 연령과 전공에 따라 교육봉사지속성에 차이가 있음을 알 수 있었다(p<.05). 작업선호도, 자아효능감, 친사회성, 교육봉사지속성의 상관관계를 살펴본 결과 네 개 변인 모두 양의 상관관계를 갖고 있었다(p<.05). 어떤 변인이 교육봉사지속성에 영향을 끼쳤는지 알아보기 위해 다중회귀분석을 실시한 결과, 외적동기와 친사회성이 유의한 결과가 나타났으며 두 변인이 교육봉사지속성을 설명하는 설명력은 57.4%로 나타났다. 논의: 이 연구결과를 바탕으로 교육봉사지속성을 증가시키기 위해 외적동기와 친사회성을 강화할 수 있는 다양한 프로그램의 개발 및 적용방안이 마련되어야 할 것으로 생각된다.

• 대한수학회논문집
• /
• 제35권2호
• /
• pp.667-684
• /
• 2020

The objective of this paper is solving multidimensional backward stochastic differential equations with general time intervals, in L^p (p ≥ 1) sense, where the generator g satisfies a time-varying Osgood condition in y, a time-varying quasi-Hölder continuity condition in z, and its ith component depends on the ith row of z. Our result strengthens some existing works even for the case of finite time intervals.