• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.455-463
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• 2010

The differentiable manifold with f - structure were studied by many authors, for example: K. Yano [7], Ishihara [8], Das [4] among others but thus far we do not know the geometry of manifolds which are endowed with special polynomial $F_{a(j){\times}(j)$-structure satisfying $$\prod\limits_{j=1}^{k}\;[F^2+a(j)F+\lambda^2(j)I]\;=\;0$$ However, special quadratic structure manifold have been defined and studied by Sinha and Sharma [8]. The purpose of this paper is to study the geometry of differentiable manifolds equipped with such structures and define special polynomial structures for all values of j = 1, 2,$\ldots$,$K\;\in\;N$, and obtain integrability conditions of the distributions $\pi_m^j$ and ${\pi\limits^{\sim}}_m^j$.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.37-51
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• 2002

Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z $\in$ C such that ∥z-T(z)∥<∥x-T(x)∥ for all x on the boundary of C, then the trajectory tlongrightarrowz$_{t}$$\in$C, t$\in$[0, 1) defined by the equation z$_{t}$ = tT(z$_{t}$)+(1-t)z is continuous and strongly converges to a fixed point of T as t longrightarrow 1￣.ow 1￣.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.275-285
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• 1997

Let E be a uniformly convex Banach space with a uniformly G$\hat{a}teaux differentiable norm, C a nonempty closed convex subset of $E, T : C \to E$ a nonexpansive mapping, and Q a sunny nonexpansive retraction of E onto C. For $u \in C$ and $t \in (0,1)$, let $x_t$ be a unique fixed point of a contraction $R_t : C \to C$, defined by $R_tx = Q(tTx + (1-t)u), x \in C$. It is proved that if ${x_t}$ is bounded, then the strong $lim_{t\to1}x_t$ exists and belongs to the fixed point set of T. Furthermore, the strong convergence of ${x_t}$ in a reflexive and strictly convex Banach space with a uniformly G$\hat{a}$teaux differentiable norm is also given in case that the fixed point set of T is nonempty.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.8
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• pp.842-847
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• 2008

This paper proposes a new sliding-surface-based tracking control system for nonholonomic mobile robots with disturbance. To design a robust controller, we consider the kinematic model and the dynamic model of mobile robots with disturbance. We also propose a new sliding surface to solve the problem of previous study. That is, since the new sliding surface is composed of differentiable functions unlike the previous study, we can obtain the control law for arbitrary trajectories without any constraints. From the Lyapunov stability theory, we prove that the position tracking errors and the heading direction error converge to zero. Finally, we perform the computer simulations to demonstrate the performance of the proposed control system.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1101-1121
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• 2008

One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.483-498
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• 2011

In this paper, we introduce a new class of uniformly point-wise R-subweakly commuting self-mappings and prove several common fixed point theorems and best approximation results for uniformly point-wise R-subweakly commuting asymptotically I-nonexpansive mappings in normed linear spaces. We also establish some results concerning strong convergence of nearest common fixed points of asymptotically I-non-expansive mappings in reflexive Banach spaces with a uniformly G$\^{a}$teaux differentiable norm. Our results unify and generalize various known results given by some authors to a more general class of noncommuting mappings.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.377-392
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• 2008

Let X be a real reflexive Banach space with a uniformly $G\hat{a}teaux$ differentiable norm, C a nonempty closed convex subset of X, T : C $\rightarrow$ X a continuous pseudocontractive mapping, and A : C $\rightarrow$ C a continuous strongly pseudocontractive mapping. We show the existence of a path ${x_t}$ satisfying $x_t=tAx_t+(1- t)Tx_t$, t $\in$ (0,1) and prove that ${x_t}$ converges strongly to a fixed point of T, which solves the variational inequality involving the mapping A. As an application, we give strong convergence of the path ${x_t}$ defined by $x_t=tAx_t+(1-t)(2I-T)x_t$ to a fixed point of firmly pseudocontractive mapping T.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.544-547
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• 2008

Navigation in 3D virtual environment(VE) is very difficult because the virtual environment is lack information than real 3D world. So navigation is import research subject in 3D VE. In this paper, we study tour path setting method using spline curve. The spline curve is augmented polynomial function. So the curve is differentiable. In particular, since the curves which are order of 2 and 3 are second order differentiable those are sufficiently smooth for using the computer graphics and CAD system.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.1-7
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• 1993

Vector optimization problems consist of two or more objective functions and constraints. Optimization entails obtaining efficient solutions. Geoffrion [3] introduced the definition of the properly efficient solution in order to eliminate efficient solutions causing unbounded trade-offs between objective functions. In 1974, Isermann [7] obtained a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with linear constraints and showed that every efficient solution is a properly efficient solution. Since then, many authors [1, 2, 4, 5, 6] have extended the Isermann's results. In particular, Gulati and Islam [4] derived a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with nonlinear constraints, under certain assumptions. In this paper, we consider the following nonlinear vector optimization problem (NVOP): (Fig.) where for each i, f$_{i}$ is a differentiable function from R$^{n}$ into R and g is a differentiable function from R$^{n}$ into R$^{m}$ .

• Annual Conference of KIPS
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• 2020.11a
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• pp.850-853
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• 2020

gradient decent 를 기반으로 한 Differentiable architecture search(DARTS)는 한 번의 Architecture Search 로 모든 후보 연산 중 가장 가중치가 높은 연산 하나를 선택한다. 이 때 비슷한 종류의 연산이 가중치를 나누어 갖는 "표의 분산"이 나타나, 성능이 더 좋은 연산이 선택되지 못하는 상황이 발생한다. 본 연구에서는 이러한 상황을 막기위해 Architecture Parameter 가중치의 gradient 를 기반으로 연산들을 클러스터링 하여 그룹화 한다. 그 후 그룹별로 가중치를 합산하여 높은 가중치를 갖는 그룹만을 사용하여 한 번 더 Architecture Search 를 진행한다. 각각의 Architecture Search 는 DARTS 의 절반 epoch 만큼 이루어지며, 총 epoch 이 같으나 두번째의 Architecture Search 는 선별된 연산 그룹을 사용하므로 DARTS 에 비해 더 적은 Search Cost 가 요구된다. "표의 분산"문제를 해결하고, 2 번으로 나뉜 Architecture Search 에 따라 CIFAR 10 데이터 셋에 대해 2.46%의 에러와 0.16 GPU-days 의 탐색시간을 얻을 수 있다.