• Honam Mathematical Journal
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• v.32 no.4
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• pp.711-738
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• 2010

We list two kinds of gradation of openness and we study in the sense of the followings: (i) We give the definition of IVGO of fuzzy sets and obtain some basic results. (ii) We give the definition of interval-valued gradation of clopeness and obtain some properties. (iii) We give the definition of a subspace of an interval-valued smooth topological space and obtain some properties. (iv) We investigate some properties of gradation preserving (in short, IVGP) mappings.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.243-267
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• 2013

This paper is dedicated to study a new class of general nonlinear random A-maximal $m$-relaxed ${\eta}$-accretive (so called (A, ${\eta}$)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in $q$-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal $m$-relaxed ${\eta}$-accretive mappings due to Lan et al. and Chang's lemma [13], some new iterative algorithms with mixed errors for finding the approximate solutions of the aforesaid class of nonlinear random equations are constructed. The convergence analysis of the proposed iterative algorithms under some suitable conditions are also studied.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1023-1036
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• 2015

Let {Xn; $n{\succeq}1$} be a field of martingale differences taking values in a p-uniformly smooth Banach space. The paper provides conditions under which the series ${\sum}_{i{\preceq}n}\;Xi$ converges almost surely and the tail series {$Tn={\sum}_{i{\gg}n}\;X_i;n{\succeq}1$} satisfies $sup_{k{\succeq}n}{\parallel}T_k{\parallel}=\mathcal{O}p(b_n)$ and ${\frac{sup_{k{\succeq}n}{\parallel}T_k{\parallel}}{B_n}}{\rightarrow\limits^p}0$ for given fields of positive numbers {bn} and {Bn}. This result generalizes results of A. Rosalsky, J. Rosenblatt [7], [8] and S. H. Sung, A. I. Volodin [11].

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1053-1064
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• 2012

For a double array of random elements $\{X_{mn};m{\geq}1,n{\geq}1\}$ in a $p$-uniformly smooth Banach space, $\{b_{mn};m{\geq}1,n{\geq}1\}$ is an array of positive numbers, convergence of double random series ${\sum}^{\infty}_{m=1}{\sum}^{\infty}_{n=1}X_{mn}$, ${\sum}^{\infty}_{m=1}{\sum}^{\infty}_{n=1}b^{-1}_{mn}X_{mn}$ and strong law of large numbers $$b^{-1}_{mn}\sum^m_{i=1}\sum^n_{j=1}X_{ij}{\rightarrow}0$$ as $$m{\wedge}n{\rightarrow}{\infty}$$ are established.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.41-53
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• 2008

Polynomials are one of most important and widely used numerical tools in dealing with a smooth function on a bounded domain and trigonometric functions work for smooth periodic functions. However, they are not the best choice if a function has a bounded support in space and in frequency domain. The Prolate Spheroidal wave function (PSWF) of order zero has been known as a best candidate as a basis for band-limited functions. In this paper, we review some basic properties of PSWFs defined as eigenfunctions of bounded Fourier transformation. We also propose numerical inversion schemes based on PSWF and present some numerical examples to show their feasibilities as signal processing tools.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.131-136
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• 2012

If one can find a control Lyapunov function (CLF) for a given nonlinear system, the control input stabilizing the system can be easily obtained. To find a CLF, the time derivative of an energy function should be negative definite. This procedure frequently requires a control input which is a rational function or includes an inverse function. The control input is not defined on the specific state-space where the denominator of the rational function is equal to 0 or the inverse function does not exist. In this region with singularities, the trajectory of the control system cannot be generated, which is one of the most important reasons why it is hard to make the origin of a nonlinear system be globally asymptotically stable. In this paper, we propose a smooth control law ensuring the globally asymptotic stability by means of cancelling the singularity in the control input.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2534-2536
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• 2003

Color는 다른 물체로부터 하나의 물체를 특정짓기 위한 효과적이고 강인한 실마리이므로 color clustering이 많은 주목을 받고 있다. 그러나 불규칙한 조명변화에 의한 color 변이 때문에 color segmentation은 매우 어렵다. 이 논문은 B-spline 곡선을 이용한, HSI color space에서의 intensity 정보를 포함한 신뢰할 수 있는 color modeling 방법을 제안한다. 이것은 비록 HS 평균임에도 불구하고 단색 물체의 color 분포가 조명이 변함에따라 변한다는 사실에 기반한다. 이 접근법을 사용하면 피부색을 가진 영역의 color clustering이 불규칙한 조명변화에 적응될 수 있다.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.43.2-43.2
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• 2019

In many astrophysical systems, smooth large-scale variations coexist with small-scale fluctuations. For example, a large-scale velocity or density gradient can exist in molecular clouds that have small-scale fluctuations by turbulence. In redshifted 21cm observations, we also have two types of signals - the Galactic foreground emissions that change smoothly and the redshifted 21cm signals that fluctuate fast in frequency space. In many cases, the large-scale variations make it difficult to extract information on small-scale fluctuations. We propose a simple technique to remove smooth large-scale variations. Our technique relies on multi-point structure functions and can obtain the magnitudes of small-scale fluctuations. It can also be used to design filters that can remove large-scale variations and retrieve small-scale data. We discuss how to apply our technique to irregularly spaced data, such as rotation measure observations toward extragalactic radio point sources.

• The Journal of Korea Robotics Society
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• v.17 no.3
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• pp.303-307
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• 2022

This paper proposes a method that can generate a smooth trajectory from the discontinuous trajectory in kinematic, dynamic, and task-space trajectory constraints. The problem is defined as the minimization of kinetic energy, and then the simulation is performed by using the MATLAB. Kinematic and inverse kinematic equations are derived for the simulation of the 6-DOF robotic arm. The simulation results showed that the trajectory of each joint is generated while satisfying the constraints without any discontinuity. There are small errors in the Cartesian trajectory, but unnecessary deceleration and acceleration can be eliminated. In addition, it is possible to quickly switch between the robotic tasks by applying the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1281-1285
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• 2004

There are numerous emotions in the human world. Human expresses and recognizes their emotion using various channels. The example is an eye, nose and mouse. Particularly, in the emotion recognition from facial expression they can perform the very flexible and robust emotion recognition because of utilization of various channels. Hybrid-feature extraction algorithm is based on this human process. It uses the geometrical feature extraction and the color distributed histogram. And then, through the independently parallel learning of the neural-network, input emotion is classified. Also, for the natural classification of the emotion, advancing two-dimensional emotion space is introduced and used in this paper. Advancing twodimensional emotion space performs a flexible and smooth classification of emotion.