• International Journal of CAD/CAM
• /
• 제7권1호
• /
• pp.11-20
• /
• 2007

A topology optimization methodology, named "smooth boundary topology optimization," is proposed to overcome the shortcomings of cell-based methods. Material boundary is represented by B-spline curves and their control points are considered as design variables. The design is improved by either creating a hole or moving control points. To determine which is more beneficial, a selection criterion is defined. Once determined to create a hole, it is represented by a new B-spline and recognized as a new boundary. Because the proposed method deals with the control points of B-spline as design variables, their total number is much smaller than cell-based methods and it ensures smooth boundaries. Differences between our method and level set method are also discussed. It is shown that our method is a natural way of obtaining smooth boundary topology design effectively combining computer graphics technique and design sensitivity analysis.

• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.81-105
• /
• 2003

This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small ｜t｜ and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small ｜t｜.

• 대한산업공학회지
• /
• 제21권4호
• /
• pp.571-580
• /
• 1995

Medial axis transformation is an important concept used in many engineering applications. We propose a new approach to medial axis transformation of 2D objects with smooth boundary. Our approach differs from the traditional ones: we construct the medial axis starting from the inside points, while the previous algorithms started from the boundary points. As a result, previous algorithms are highly sensitive to the small irregularities of the object's boundary curve, while our approach is robust.

• 대한수학회지
• /
• 제49권1호
• /
• pp.17-30
• /
• 2012

Let D be an arbitrary domain in $\mathbb{C}^n$, n > 1, and $M{\subset}{\partial}D$ be an open piece of the boundary. Suppose that M is connected and ${\partial}D$ is smooth real-analytic of finite type (in the sense of D'Angelo) in a neighborhood of $\bar{M}$. Let f : $D{\rightarrow}\mathbb{C}^n$ be a holomorphic correspondence such that the cluster set $cl_f$(M) is contained in a smooth closed real-algebraic hypersurface M' in $\mathbb{C}^n$ of finite type. It is shown that if f extends continuously to some open peace of M, then f extends as a holomorphic correspondence across M. As an application, we prove that any proper holomorphic correspondence from a bounded domain D in $\mathbb{C}^n$ with smooth real-analytic boundary onto a bounded domain D' in $\mathbb{C}^n$ with smooth real-algebraic boundary extends as a holomorphic correspondence to a neighborhood of $\bar{D}$.

• 정보처리학회논문지B
• /
• 제12B권3호
• /
• pp.223-232
• /
• 2005

본 논문에서는 블록 기반으로 부호화된 영상에 대하여 블록 경계 영역 특성에 따른 적응적 필터링을 이용한 양자화 잡음 제거 알고리즘을 제안하였다 제안한 방법에서는 블록 경계에 인접한 네 개 화소들의 통계적 특성을 이용하여 각 블록 경계 영역을 평탄 부영역(smooth sub-region)과 복잡 부영역(complex sub-region)으로 분류한 후, 인접 블록간 영역 특성을 이용하여 서로 다른 블록간 필터링을 수행한다. 먼저 인접 블록 모두 평탄 부영역인 경우에는 평탄 블록 경계 영역 중 블록화 현상이 발생하지 않은 영역도 존재하기 때문에 계산량을 줄이기 위하여 평탄 영역 중 블록화 현상이 발생한 영역만을 검출하여 필터링을 수행한다. 그리고, 두 부영역이 서로 다른 부영역인 경우에 대하여서는 기존의 방법들과는 달리 실제 에지 성분을 보존하면서 블록화 현상과 에지 주위에서 발생하는 링잉 현상을 동시에 제거하기 위하여 인접 블록의 영역 특성에 따라 적응적으로 일차원 필터링을 수행한다. 두 부영역이 모두 복잡 부영역일 경우에는 블록화 현상을 제거하면서 실제 에지를 보존하기 위하여 블록화 강도 및 양자화 파라미터에 따라 블록 경계 영역의 두 화소에 대하여 필터링을 수행한다. 모의실험 결과를 통하여 제안한 방법이 객관적 화질 및 주관적 화질 측면에서 기존의 방법보다 그 성능이 우수함을 확인하였다.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2005년도 창립60주년 기념 추계 학술대회
• /
• pp.214.2-214.2
• /
• 2005

• 대한수학회지
• /
• 제44권6호
• /
• pp.1417-1428
• /
• 2007

We obtain weighted $L^p$ estimates $(1{\leq}p<{\infty})\;for\;\bar{\partial}$ on convex domains with piecewise smooth boundaries in $\mathbb{C}^2$ by using explicit formulas of solutions introduced by Berndtsson and Andersson.

• 대한수학회지
• /
• 제33권2호
• /
• pp.333-346
• /
• 1996

Let $A(\zeta, \partial)$ be a second order uniformly elliptic operator $$ A(\zeta, \partial )u = -\sum_{j, k = 1}^{n} \frac{\partial\zeta_i}{\partial}(a_{jk}(\zeta)\frac{\partial\zeta_k}{\partial u}) + \sum_{j = 1}^{n}b_j(\zeta)\frac{\partial\zeta_j}{\partial u} + c(\zeta)u $$ with real, smooth coefficients $a_{j, k}, b_j$, c defined on $\zeta \in \Omega, \Omega$ a bounded domain in $R^n$ with a sufficiently smooth boundary $\Gamma$.

• 대한수학회지
• /
• 제41권5호
• /
• pp.875-882
• /
• 2004

Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{p}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.

• 대한수학회보
• /
• 제52권1호
• /
• pp.85-103
• /
• 2015

We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.