• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.341-352
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• 2019

Let M be an n-dimensional closed Riemannian manifold with metric g, $d{\mu}=e^{-{\phi}(x)}d{\nu}$ be the weighted measure and ${\Delta}_{p,{\phi}}$ be the weighted p-Laplacian. In this article we will study the evolution and monotonicity for the first nonzero eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Yamabe flow on closed Riemannian manifolds. We find the first variation formula of it along the Yamabe flow. We obtain various monotonic quantities and give an example.

• 터널과지하공간
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• 제29권4호
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• pp.230-242
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• 2019

신속한 암반 및 암석 균열 조사를 위해서는 자동화된 조사기법이 필요하다. 그러나 자동 조사기법의 균열 지도가 수동으로 조사한 것과 얼마나 일치하는지 표기하는 단일 지표가 없어서 그 정확도를 평가하는데 어려움이 있다. 따라서 본 연구에서는 균열 지도 간의 일치도를 단일 값으로 표현하는 조사선 교차 일치도 (Scanline Intersection Similarity, SIS)라는 지표를 새롭게 제안하였다. 제안된 지표는 두 균열 지도의 균열 빈도를 다수의 조사선 상에서 비교하여 이들 간의 기하학적 일치도를 도출한다. 해당 지표의 적용성을 검토하기 위해 컴퓨터 비전 (Computer Vision) 분야에서 널리 사용하는 일치도 지표인 Intersection Over Union (IoU)과 비교분석하였다. IoU는 균열의 미시적 형태 차이를 과대평가하는 반면에, 제안된 지표의 경우 미시적 형태 차이보다 경사와 같은 거시적 형태 차이를 더 민감하게 반영하였다. 따라서 균열의 거시적 형태가 중요한 암반 공학적 관점에서, 제안된 지표가 IoU 보다 균열 지도의 일치도 지표로써 적합하였다. 더 나아가 제안된 지표를 딥러닝(Deep Learning)을 이용한 균열 조사기법에 적용해본 결과, 해당 기법의 정확도가 조사선 교차 일치도로 0.674 임을 확인하였다.

• 한국HCI학회:학술대회논문집
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• 한국HCI학회 2006년도 학술대회 1부
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• pp.355-361
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• 2006

In large scale environments like airport, museum, large warehouse and department store, autonomous mobile robots will play an important role in security and surveillance tasks. Robotic security guards will give the surveyed information of large scale environments and communicate with human operator with that kind of data such as if there is an object or not and a window is open. Both for visualization of information and as human machine interface for remote control, a 3D model can give much more useful information than the typical 2D maps used in many robotic applications today. It is easier to understandable and makes user feel like being in a location of robot so that user could interact with robot more naturally in a remote circumstance and see structures such as windows and doors that cannot be seen in a 2D model. In this paper we present our simple and easy to use method to obtain a 3D textured model. For expression of reality, we need to integrate the 3D models and real scenes. Most of other cases of 3D modeling method consist of two data acquisition devices. One for getting a 3D model and another for obtaining realistic textures. In this case, the former device would be 2D laser range-finder and the latter device would be common camera. Our algorithm consists of building a measurement-based 2D metric map which is acquired by laser range-finder, texture acquisition/stitching and texture-mapping to corresponding 3D model. The algorithm is implemented with laser sensor for obtaining 2D/3D metric map and two cameras for gathering texture. Our geometric 3D model consists of planes that model the floor and walls. The geometry of the planes is extracted from the 2D metric map data. Textures for the floor and walls are generated from the images captured by two 1394 cameras which have wide Field of View angle. Image stitching and image cutting process is used to generate textured images for corresponding with a 3D model. The algorithm is applied to 2 cases which are corridor and space that has the four wall like room of building. The generated 3D map model of indoor environment is shown with VRML format and can be viewed in a web browser with a VRML plug-in. The proposed algorithm can be applied to 3D model-based remote surveillance system through WWW.

• 호남수학학술지
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• 제35권4호
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• pp.551-564
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• 2013

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica, 24(5) (2008), 867-876] introduced the notion of occasionally weakly compatible mappings in metric spaces. In this paper, we prove some common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using an implicit relation. We also give an illustrative example to support our main result.

• 충청수학회지
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• 제28권4호
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• pp.647-651
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• 2015

Let (X, d) be a compact metric space, and let $f:X{\rightarrow}X$ be a continuous map. We consider that if a positively continuum-wise expansiveness continuous map f has the positively shadowing property in the nonwandering set, then the topological entropy is positive.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권1호
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• pp.29-37
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• 2017

A general optimal recovery problem is to approximate a value of a linear operator on a subset (class) in linear space from a value of another linear operator (called information), measured with an error in given metric. We use this formulation to investigate the classical computerized tomography problem of inversion of the noisy Radon transform.

• 대한수학회논문집
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• 제22권4호
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• pp.575-586
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• 2007

We introduce here notions of chain recurrent sets, attractors and its basins for general dynamical systems and prove important properties including (i) the chain recurrent set CR(f) of f on a metric space (X, d) is the complement of the union of sets B(A) -A as A varies over the collection of attractors and (ii) genericity of general dynamical systems.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2001년도 추계학술발표회 논문집
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• pp.137-141
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• 2001

We can obtain SLLN's for fuzzy random variables with respect to the new metric $d_s$ on the space F(R) of fuzzy numbers in R. In this paper, we obtain a SLLN for convex tight random elements taking values in F(R).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권1호
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• pp.9-16
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• 1995

D. Dubois and H. Prade introduced the notions of fuzzy numbers and defined its basic operations [3]. R. Goetschel, W. Voxman, A. Kaufmann, M. Gupta and G. Zhang [4,5,6,9] have done much work about fuzzy numbers. Let $\mathbb{R}$ the set of all real numbers and $F^{*}(\mathbb{R})$ all fuzzy subsets defined on $\mathbb{R}$. G. Zhang [8] defined the fuzzy number $\tilde{a}\;\in\;F^{*}(\mathbb{R})$ as follows : (omitted)

• 충청수학회지
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• 제13권1호
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• pp.131-138
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• 2000

Let D be the open unit disk in the complex plane $\mathbb{C}$. For any q > 0, the operator $Q_q$ defined by $$Q_qf(z)=q\int_{D}\frac{f(\omega)}{(1-z{\bar{\omega}})^{1+q}}d{\omega},\;z{\in}D$$. maps $L^{\infty}(D)$ boundedly onto $B_q$ for each q > 0. In this paper, weighted Bloch spaces $\mathcal{B}_q$ (q > 0) are considered on the open unit ball in $\mathbb{C}^n$. In particular, we will investigate the possibility of extension of this operator to the Weighted Bloch spaces $\mathcal{B}_q$ in $\mathbb{C}^n$.