• 충청수학회지
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• 제21권4호
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.

• JSTS:Journal of Semiconductor Technology and Science
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• 제14권4호
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• pp.391-406
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• 2014

The performance of General-Purpose computation on Graphics Processing Units (GPGPU) is heavily dependent on the memory access behavior. This sensitivity is due to a combination of the underlying Massively Parallel Processing (MPP) execution model present on GPUs and the lack of architectural support to handle irregular memory access patterns. Application performance can be significantly improved by applying memory-access-pattern-aware optimizations that can exploit knowledge of the characteristics of each access pattern. In this paper, we present an algorithmic methodology to semi-automatically find the best mapping of memory accesses present in serial loop nest to underlying data-parallel architectures based on a comprehensive static memory access pattern analysis. To that end we present a simple, yet powerful, mathematical model that captures all memory access pattern information present in serial data-parallel loop nests. We then show how this model is used in practice to select the most appropriate memory space for data and to search for an appropriate thread mapping and work group size from a large design space. To evaluate the effectiveness of our methodology, we report on execution speedup using selected benchmark kernels that cover a wide range of memory access patterns commonly found in GPGPU workloads. Our experimental results are reported using the industry standard heterogeneous programming language, OpenCL, targeting the NVIDIA GT200 architecture.

• 제어로봇시스템학회논문지
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• 제15권2호
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• pp.155-162
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• 2009

In walking guide robot, a guide vehicle detects an obstacle distribution in the walking space using range sensors, and generates a 3D grid map to map the obstacle information and the tactile display. And the obstacle information is transferred to a blind pedestrian using tactile feedback. Based on the obstacle information a user plans a walking route and controls the guide vehicle. The algorithm for 3D detection of an obstacle distribution and the method of mapping the generated obstacle map and the tactile display device are proposed in this paper. The experiment for the 3D detection of an obstacle distribution using ultrasonic sensors is performed and estimated. The experimental system consisted of ultrasonic sensors and control system. In the experiment, the detection of fixed obstacles on the ground, the moving obstacle, and the detection of down-step are performed. The performance for the 3D detection of an obstacle distribution and space mapping is verified through the experiment.

• 한국게임학회 논문지
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• 제19권5호
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• pp.39-52
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• 2019

최근 체감형 스포츠 게임은 시각적 자극 통한 콘텐츠 몰입을 위해 다양한 연구가 진행되고 있다. 그 중 미디어 콘텐츠의 다면 영상 기술은 넓은 시야에 영상을 투사하여 몰입시키기에 적절하지만 캘리브레이션과 시야에 맞는 매핑 작업을 따로 거쳐야한다는 어려움이 있다. 본 논문은 누구나 쉽게 적용 가능한 캘리브레이션 매핑 기술을 개발하고, CAVE 형태의 체감형 필드아처리 게임 공간에 적용한다. 그 결과 콘텐츠의 해상도를 유지하고 왜곡 없는 영상을 통해 체험자에게 공간감 제공이 가능하다는 것을 확인하였다. 본 논문에서 개발한 기술은 소방 훈련 콘텐츠와 같이 높은 몰입이 필요한 훈련 및 교육 분야에도 활용 가능할 것으로 기대한다.

• 한국융합학회논문지
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• 제12권11호
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• pp.207-220
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• 2021

최근 센서 경험을 위한 새로운 매체들의 발전은 프로젝션맵핑, 가상현실과 같은 비디오 설치 미술의 시각적 표현을 더욱 확장시키고 있다. 예술가들은 새로운 매체들들 통해 새로운 시각적 표현 기법을 개발하고 발전시킬 수 있다. 프로젝션맵핑 기술은 지속적으로 미디어아트 작품의 시각적 표현에 다양한 가능성을 부여하고 있다. 본 논문은 프로젝션맵핑 기술에 기반한 시각 표현이 인간의 감각 체험으로 전이되고 확장되는 과정을 연구하기 위해서, 매체가 갖는 '복제성,' '전파성,' '가상성' 그리고 '인터랙션'의 특징을 분석함으로써 시각적 표현을 정의하고 의미를 기술하였다. 작품 분석을 통해 '반복과 중첩,' '시뮬라이크롬과 은유,' '치환과 전환'의 시각적 표현 기법에 대해 분석하고, 프로젝션맵핑 작품인 에 적용함으로써 시각 표현 기법이 인간의 감각 체험으로 확장되는 과정을 연구하였다. 시각적 표현의 확장성 연구는 작품을 제작하는 예술가들이나 관람하는 관객들에게 작품의 의미를 전달하거나 해석하는데 필요한 핵심 요소이다.

• International Journal of Control, Automation, and Systems
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• 제2권1호
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• pp.107-117
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• 2004

A new algorithm for planning a collision-free path based on an algebraic curve as well as the concept of path space is developed. Robot path planning has so far been concerned with generating a single collision-free path connecting two specified points in a given robot workspace with appropriate constraints. In this paper, a novel concept of path space (PS) is introduced. A PS is a set of points that represent a connection between two points in Euclidean metric space. A geometry mapping (GM) for the systematic construction of path space is also developed. A GM based on the 2$^{nd}$ order base curve, specifically Bezier curve of order two is investigated for the construction of PS and for collision-free path planning. The Bezier curve of order two consists of three vertices that are the start, S, the goal, G, and the middle vertex. The middle vertex is used to control the shape of the curve, and the origin of the local coordinate (p, $\theta$) is set at the centre of S and G. The extreme locus of the base curve should cover the entire area of actual workspace (AWS). The area defined by the extreme locus of the path is defined as quadratic workspace (QWS). The interference of the path with obstacles creates images in the PS. The clear areas of the PS that are not mapped by obstacle images identify collision-free paths. Hence, the PS approach converts path planning in Euclidean space into a point selection problem in path space. This also makes it possible to impose additional constraints such as determining the shortest path or the safest path in the search of the collision-free path. The QWS GM algorithm is implemented on various computer systems. Simulations are carried out to measure performance of the algorithm and show the execution time in the range of 0.0008 ~ 0.0014 sec.

• 대한수학회보
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• 제44권3호
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• pp.537-545
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• 2007

Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in the setup of certain metrizable topological vector spaces are obtained. As applications, related results on best approximation are derived. Our results extend, generalize and unify various known results in the literature.

• 호남수학학술지
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• 제30권2호
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• pp.299-310
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• 2008

The notion of interval-valued fuzzy ${\alpha}$-continuous mappings and interval-valued fuzzy contra ${\alpha}$-continuous mappings is introduced, and their characterizations are investigated.

• East Asian mathematical journal
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• 제27권1호
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• pp.11-21
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• 2011

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

• 충청수학회지
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• 제30권2호
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• pp.239-249
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• 2017

In this paper, we approximate a fuzzy almost cubic function by a cubic function in a fuzzy sense. Indeed, we investigate solutions of the following cubic functional equation $$3f(kx+y)+3f(kx-y)-kf(x+2y)-2kf(x-y)-3k(2k^2-1)f(x)+6kf(y)=0$$. and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.