• Title/Summary/Keyword: convex domain

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Eigenvalue Analysis of Arbitrarily Shaped, Concave Membranes With a Deep Groove Using a Sub-domain Method (영역 분할법을 이용한 깊은 홈을 가진 임의 형상 오목 멤브레인의 고유치 해석)

  • Kang, S.W.;Yoon, J.I.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.10
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    • pp.1069-1074
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    • 2009
  • A sub-domain method for free vibration analysis of arbitrarily shaped, concave membranes with a deep groove is proposed in the paper. The proposed method divides the concave membrane of interest into two convex regions. The vibration displacement(approximate solution) of each convex region is assumed by linearly superposing plane waves generated at edges of the region. A sub-system matrix for each convex region is extracted by applying a provisional boundary condition to the approximate solution. Finally, a system matrix, which of the determinant gives eigenvalues of the concave membrane, is made by considering the fixed boundary condition(displacement zero condition) at edges and the compatibility condition(the condition of continuity in displacement and slope) at the interface between the two regions. Case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed are compared to those by NDIF method, FEM, or the exact method.

GLOBAL SHAPE OF FREE BOUNDARY SATISFYING BERNOULLI TYPE BOUNDARY CONDITION

  • Lee, June-Yub;Seo, Jin-Keun
    • Journal of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.31-44
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    • 2000
  • We study a free boundary problem satisfying Bernoulli type boundary condition along which the gradient of a piecewise harmonic solution jumps zero to a given constant value. In such problem, the free boundary splits the domain into two regions, the zero set and the harmonic region. Our main interest is to identify the global shape and the location of the zero set. In this paper, we find the lower and the upper bound of the zero set. In a convex domain, easier estimation of the upper bound and faster disk test technique are given to find a rough shape of the zero set. Also a simple proof on the convexity of zero set is given for a connected zero set in a convex domain.

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Univalent Functions Associated with the Symmetric Points and Cardioid-shaped Domain Involving (p,q)-calculus

  • Ahuja, Om;Bohra, Nisha;Cetinkaya, Asena;Kumar, Sushil
    • Kyungpook Mathematical Journal
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    • v.61 no.1
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    • pp.75-98
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    • 2021
  • In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.

DEFORMATION SPACES OF CONVEX REAL-PROJECTIVE STRUCTURES AND HYPERBOLIC AFFINE STRUCTURES

  • Darvishzadeh, Mehdi-Reza;William M.Goldman
    • Journal of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.625-639
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    • 1996
  • A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

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SOME NEW BONNESEN-STYLE INEQUALITIES

  • Zhou, Jiazu;Xia, Yunwei;Zeng, Chunna
    • Journal of the Korean Mathematical Society
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    • v.48 no.2
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    • pp.421-430
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    • 2011
  • By evaluating the containment measure of one domain to contain another, we will derive some new Bonnesen-type inequalities (Theorem 2) via the method of integral geometry. We obtain Ren's sufficient condition for one domain to contain another domain (Theorem 4). We also obtain some new geometric inequalities. Finally we give a simplified proof of the Bottema's result.

Development of a Modified NDIF Method for Extracting Highly Accurate Eigenvalues of Arbitrarily Shaped Acoustic Cavities (임의 형상 음향 공동의 고정밀도 고유치 추출을 위한 개선된 NDIF법 개발)

  • Kang, S.W.;Yon, J.I.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.22 no.8
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    • pp.742-747
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    • 2012
  • A modified NDIF method using a sub-domain approach is introduced to extract highly accurate eigenvalues of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex cavities. It was revealed that the solution of the NDIF method is very inaccurate or is not suitable for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave domain into several convex domains. Finally, the validity of the proposed method is verified in two case studies, which indicate that eigenvalues obtained by the proposed method are more accurate compared to the exact method, the NDIF method, or FEM(ANSYS).

Development of the NDIF Method Using a Sub-domain Approach for Extracting Highly Accurate Natural Frequencies of Arbitrarily Shaped Plates (임의 형상 평판의 고정밀도 고유진동수 추출을 위한 분할영역법 기반 NDIF법 개발)

  • Kang, S.W.;Yon, J.I.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.22 no.9
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    • pp.830-836
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    • 2012
  • The NDIF method based on a sub-domain technique is introduced to extract highly accurate natural frequencies of arbitrarily shaped plates with the simply-supported boundary condition. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped plates with various boundary conditions, has the feature that it yields highly accurate natural frequencies thanks to its effective theoretical formulation, compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex plates. It was revealed that the NDIF method offers very inaccurate natural frequencies or no solution for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave plate into several convex domains. Finally, the validity of the proposed method is verified in various case studies, which indicate that natural frequencies obtained by the proposed method are very accurate compared to the exact method and FEM(ANSYS).

PROJECTIVE DOMAINS WITH NON-COMPACT AUTOMORPHISM GROUPS I

  • Yi, Chang-Woo
    • Journal of the Korean Mathematical Society
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    • v.45 no.5
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    • pp.1221-1241
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    • 2008
  • Most of domains people have studied are convex bounded projective (or affine) domains. Edith $Soci{\acute{e}}$-$M{\acute{e}}thou$ [15] characterized ellipsoid in ${\mathbb{R}}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.

LQ-Servo PI Controller Design Using LMI (LMI를 이용한 LQ-서보형 PI제어기 설계)

  • 김상엽;서병설
    • Proceedings of the IEEK Conference
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    • 1999.11a
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    • pp.728-731
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    • 1999
  • This paper concerns a development of LQ-servo PI controller design on the basis of time-domain approach. This is because the previous design techniques developed on the frequency-domain is not well suited to meet the time-domain design specifications. Our development techniques used in this paper is based on the convex optimization methods including Lagrange multiplier, dual concept, semidefinite programming.

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MEROMOR0PHIC UNIVALENT HARMONIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Jahangiri, Jay M.;Silverman, Herb
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.763-770
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    • 1999
  • The purpose of this paper is to give sufficient coefficient conditions for a class of univalent harmonic functions that map each $$\mid$z$\mid$$ = r >1 onto a curve that bounds a domain that is starlike with respect to origin. Furthermore, it is shown that these conditions are also necessary when the coefficients are negative. Extreme points for these classes are also determined. Finally, comparable results are given for the convex analgo.

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