• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.899-912
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• 2011

We introduce ${\varphi}$-frames in $L^2$(G), as a generalization of a-frames defined in [8], where G is a locally compact Abelian group and ${\varphi}$ is a topological automorphism on G. We give a characterization of ${\varphi}$-frames with regard to usual frames in $L^2$(G) and show that ${\varphi}$-frames share several useful properties with frames. We define the associated ${\varphi}$-analysis and ${\varphi}$-preframe operators, with which we obtain criteria for a sequence to be a ${\varphi}$-frame or a ${\varphi}$-Bessel sequence. We also define ${\varphi}$-Riesz bases in $L^2$(G) and establish equivalent conditions for a sequence in $L^2$(G) to be a ${\varphi}$-Riesz basis.

• Korean Journal of Computational Design and Engineering
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• v.14 no.4
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• pp.217-224
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• 2009

Most divide-and-conquer implementations for Delaunay triangulation utilize quad-edge or winged-edge data structure since triangles are frequently deleted and created during the merge process. How-ever, the proposed divide-and-conquer algorithm utilizes the array based data structure that is much simpler than the quad-edge data structure and requires less memory allocation. The proposed algorithm has two important features. Firstly, the information of space partitioning is represented as a permutation vector sequence in a vertices array, thus no additional data is required for the space partitioning. The permutation vector represents adaptively divided regions in two dimensions. The two-dimensional partitioning of the space is more efficient than one-dimensional partitioning in the merge process. Secondly, there is no deletion of edge in merge process and thus no bookkeeping of complex intermediate state for topology change is necessary. The algorithm is described in a compact manner with the proposed data structures and operators so that it can be easily implemented with computational efficiency.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.3
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• pp.202-209
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• 2003

We succeeded to build a cost effective assistance robotic arm with a compact and lightweight body. The robotic arm has three joints, and the tip of robotic arm to install tools consists of a closed link mechanism, which consisted of two actuators and several links. The robotic arm has been made possible by the use of actuators typically used in radio control devices. The controller of the robotic arm consists of a single chip PIC only. The robotic arm has a friendly user interface, as the operators are aged and disabled in most cases. The operator can manipulate the robotic arm by voice commands or by pressing a push button. The robotic arm has been successfully prototyped and tested on an elderly patient to assist with eating. The results of field test were satisfactory.

• Korean Journal of Computational Design and Engineering
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• v.1 no.1
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• pp.1-19
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• 1996

Non-manifold topological representations can provide a single unified representation for mixed dimensional models or cellular models and thus have a great potential to be applied in many application areas. Various boundary representations for non-manifold topology have been proposed in recent years. These representations are mainly interested in describing the sufficient adjacency relationships and too redundant as a result. A model stored in these representations occupies too much storage space and is hard to be manipulated. In this paper, we proposed a compact hierarchical non-manifold boundary representation that is extended from the half-edge data structure for solid models by introducing the partial topological entities to represent some non-manifold conditions around a vertex, edge or face. This representation allows to reduce the redundancy of the existing schemes while full topological adjacencies are still derived without the loss of efficiency. To verify the statement above, the storage size requirement of the representation is compared with other existing representations and present some main procedures for querying and traversing the representation. We have also implemented a set of the generalized Euler operators that satisfy the Euler-Poincare formula for non-manifold geometric models.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.401-408
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• 2014

If A is a unital Banach algebra, then the spectrum can be viewed as a function ${\sigma}$ : 𝕬 ${\rightarrow}$ 𝕾, mapping each T ${\in}$ 𝕬 to its spectrum ${\sigma}(T)$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\mathbb{C}$. This paper is concerned with the continuity of the spectrum ${\sigma}$ via Browder's theorem. It is shown that ${\sigma}$ is continuous when ${\sigma}$ is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.109-114
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• 1998

Let H be a separable complex H be a space and let (equation omitted)(H) be the *-algebra of all bounded linear operators on H. An operator T in (equation omitted)(H) is said to be p-hyponormal if ($T^{\ast}T)^p - (TT^{\ast})^{p}\geq$ 0 for 0 ＜ p ＜ 1. If p = 1, T is hyponormal and if p = $\frac{1}{2}$, T is semi-hyponormal. In this paper, by using a technique introduced by S. K. Berberian, we show that the approximate point spectrum $\sigma_{\alpha p}(T) of a pure p-hyponormal operator T is empty, and obtains the compact perturbation of T.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.217-223
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• 2003

Let $\cal{K}$ be the extension Hilbert space of a Hilbert space $\cal{H}$ and let $\Phi$ be the faithful $\ast$-representation of $\cal{B}(\cal{H})$ on $\cal{k}$. In this paper, we show that if T is an irreducible ${\omega}-hyponormal$ operators such that $ker(T)\;{\subset}\;ker(T^{*})$ and $T^{*}T\;-\;TT^{\ast}$ is compact, then $\sigma_{e}(T)\;=\;\sigma_{e}(\Phi(T))$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.743-750
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• 2010

For several Banach spaces X and Y and operator ideal $\cal{U}$, if $\cal{U}$(X, Y) denotes the component of operator ideal $\cal{U}$; according to Freedman's definitions, it is shown that a necessary and sufficient condition for a closed subspace $\cal{M}$ of $\cal{U}$(X, Y) to have the alternative Dunford-Pettis property is that all evaluation operators $\phi_x\;:\;\cal{M}\;{\rightarrow}\;Y$ and $\psi_{y^*}\;:\;\cal{M}\;{\rightarrow}\;X^*$ are DP1 operators, where $\phi_x(T)\;=\;Tx$ and $\psi_{y^*}(T)\;=\;T^*y^*$ for $x\;{\in}\;X$, $y^*\;{\in}\;Y^*$ and $T\;{\in}\;\cal{M}$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.831-838
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• 2020

Let H be a complex Hilbert space and T : H → H be a bounded linear operator. Then T is said to be norm attaining if there exists a unit vector x₀ ∈ H such that ║Tx₀║ = ║T║. If for any closed subspace M of H, the restriction T|M : M → H of T to M is norm attaining, then T is called an absolutely norm attaining operator or 𝓐𝓝-operator. In this note, we discuss linear maps on B(H), which preserve the class of absolutely norm attaining operators on H.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1337-1358
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• 2018

In this paper, we study the solvability of the nonlinear Dirichlet problem with sum of the operators of independent non standard growths $$-div\({\mid}{\nabla}u{\mid}^{p_1(x)-2}{\nabla}u\)-\sum\limits^n_{i=1}D_i\({\mid}u{\mid}^{p_0(x)-2}D_iu\)+c(x,u)=h(x),\;{\in}{\Omega}$$ in a bounded domain ${\Omega}{\subset}{\mathbb{R}}^n$. Here, one of the operators in the sum is monotone and the other is weakly compact. We obtain sufficient conditions and show the existence of weak solutions of the considered problem by using monotonicity and compactness methods together.