• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.155-171
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• 1997

Let $M^n$ be a connected subminifold of a Euclidean space $E^m$, equipped with the induced metric. Denoty by $\Delta$ the Laplacian operator of $M^n$ and by x the position vector. A well-known T. Takahashi's theorem [13] says that $\delta x = \lambda x$ for some constant $\lambda$ if and only if $M^n$ is either minimal subminifold of $E^m$ or minimal submanifold in a hypersphere of $E^m$. In [9], O. Garay studied the hypersurfaces $M^n$ in $E^{n+1}$ satisfying $\delta x = Dx$, where D is a diagonal matrix, and he classified such hypersurfaces. Garay's condition can be seen as a generalization of T.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.197-206
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• 2019

We consider the extended generalized Hecke groups ${\bar{H}}_{3,q}$ generated by $X(z)=-(z-1)^{-1}$, $Y(z)=-(z+{\lambda}_q)^{-1}$ with ${\lambda}_q=2\;cos({\frac{\pi}{q}})$ where $q{\geq}3$ an integer. In this work, we study the generalized Pell sequences in ${\bar{H}}_{3,q}$. Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group ${\bar{H}}_{3,3}$ can be written by using Pell, Pell-Lucas and modified-Pell numbers.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.63 no.3
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• pp.200-205
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• 2014

In this paper, 5.8GHz band $4{\times}4$ Butler matrix is designed using easily accessible commercial $90^{\circ}$ hybrid coupler and semirigid coaxial cable as a transmission line. This Butler matrix is very flexible to changes of antenna system specification like a frequency band because $90^{\circ}$ hybrid coupler changing is all to do. The result of design is the distance of $2{\times}2$ array antenna element is $\sqrt{2}{\lambda}/4$, the 4 beam directions are diagonal of array antenna and phase shifter is not necessary. The beam width is roughly $25^{\circ}$ narrower because of array antenna geometry and the side lobe is about 10dB higher partially than theoretical beam pattern. But the overall beam pattern is similar with theoretical beam. This Butler matrix can be applied to switching beam antenna of 5.8GHz band Wi-Fi and WAVE system.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.211-222
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• 2017

In this paper, we consider three inverse eigenvalue problems for a special type of acyclic matrices. The acyclic matrices considered in this paper are described by a graph called a broom on n + m vertices, which is obtained by joining m pendant edges to one of the terminal vertices of a path on n vertices. The problems require the reconstruction of such a matrix from given partial eigen data. The eigen data for the first problem consists of the largest eigenvalue of each of the leading principal submatrices of the required matrix, while for the second problem it consists of an eigenvalue of each of its trailing principal submatrices. The third problem has an eigenvalue and a corresponding eigenvector of the required matrix as the eigen data. The method of solution involves the use of recurrence relations among the leading/trailing principal minors of ${\lambda}I-A$, where A is the required matrix. We derive the necessary and sufficient conditions for the solutions of these problems. The constructive nature of the proofs also provides the algorithms for computing the required entries of the matrix. We also provide some numerical examples to show the applicability of our results.

• JSTS:Journal of Semiconductor Technology and Science
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• v.14 no.6
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• pp.760-767
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• 2014

This paper describes a high-radix crossbar switch design with low latency and power dissipation for Network-on-Chip (NoC) applications. The reduction in latency and power is achieved by employing a folded-clos topology, implementing the switch organized as three stages of low-radix switches connected in cascade. In addition, to facilitate the uniform placement of wires among the sub-switch stages, this paper proposes a Mux-Matrix-Mux structure, which implements the first and third switch stages as multiplexer-based crossbars and the second stage as a matrix-type crossbar. The proposed 256-radix, 8-bit crossbar switch designed in a 65nm CMOS has the simulated power dissipation of 1.92-W and worst-case propagation delay of 0.991-ns while operating at 1.2-V supply and 500-MHz frequency. Compared with the state-of-the-art designs in literature, the proposed crossbar switch achieves the best energy-delay-area efficiency of $0.73-fJ/cycle{\cdot}ns{\cdot}{\lambda}^2$.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1829-1832
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• 2004

Closed loop stability of Extended Dynamic Matrix Control (EDMC) is investigated for limited sampling time. Linear approximation of the sensitivity functions is employed in the derivation of the stability condition. It is shown that the closed loop system will be stable if the control moves suppression coefficient ${\lambda}$ is taken arbitrarily large. Special cases such as M=P=1 and M=1, P>1 are discussed in more details.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.623-630
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• 2003

Recently, Tanaka(1988) derived two influence functions related to an eigenvalue problem $(A-\lambda_sI)\upsilon_s=0$ of real symmetric matrix A and used them for sensitivity analysis in principal component analysis. In this paper, we deal with the perturbation expansions up to quadratic terms of the same functions and discuss the application to sensitivity analysis in principal component regression analysis(PCRA). Numerical example is given to show how the approximation improves with the quadratic term.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.715-736
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• 2012

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type ${\lambda}$ > 0. We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals I of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard $k$-algebras R/I, where R is the polynomial ring $R=k[v_0,v_1,{\ldots},v_m]$ over a field $k$ with indeterminates $v_i$ and deg $v_i=1$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.3
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• pp.910-932
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• 1996

A problem of determining the effective conductivity of a useful model of sphere-matrix type, disordered three-phase composite media is considered. Specifically, a three-phase media in which two-phase composite spheres, consisting of spheres of conductivity $k_2$((phase 2) and concentric shells of conductivity $k_3$(phase 3), are randomly distributed in a matrix of conductivity $k_1$( (phase 1) is considered. As for the structure models configuring three-phase composite media, three different structure models of PCS, PS-1 and PS-2 models are defined, which are analogous to well-established PCS, PS structure models of two-phase composite media. Futhermore, a generalized PS-PCS structure model is proposed to incorporate thesee three different models in one. Effective condectivity $k^{\ast}$of multiphaes composite media is greatly influenced by the phase connectivity of each disspersed phase material, as well as phase conductivities and phase volume fractions. Phase connectivity of three-phase PCS, PS-1, PS-2 composite media is quantified by the impentrability parameter $\lambda$. Mathematically rigorous first-order cluster bounds on $k^{\ast}$ are derived for these models of three-phase composite media, and as computation examples, first-order cluster bounds on $k^{\ast}$ for three-phase composites consisting of largely different phase conductivities are computed and compared as function of concnectivity parpmeter $\lambda$. Results and discussions are given.

• Bulletin of the Korean Chemical Society
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• v.32 no.2
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• pp.477-482
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• 2011

The structural analysis of polytrimethylene terephthalate (PTT) and characterization of the hydrolytic degradation products after acid hydrolysis were performed using MALDI-TOF mass spectrometry. Mass spectra of the PTT samples were analyzed using a self-calibration method as well as an internal calibration method with standard materials of known masses. PTT structures constituting the samples were determined from the analyses of the spectra, and their relative compositions were estimated. The MALDI-TOF mass spectra of the acid-hydrolyzed PTT sample showed three main series of oligomer products with different end groups in accordance with the hydrolysis schemes. From the spectra of both $Na^+$ and $K^+$ adducts, it was concluded that the PTT samples have higher affinity for $Na^+$ compared with $K^+$ and therefore show higher ionization efficiency with sodium ions when dithranol is used as a matrix. Two different wavelength laser beams ($\lambda$ = 337 nm and 355 nm) were tested and it was observed that the 355 nm beam was more efficient in obtaining the MALDI spectra of PTT using dithranol as a matrix under our experimental conditions.