• Title/Summary/Keyword: Complex Number

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USEFUL OPERATORS ON REPRESENTATIONS OF THE RATIONAL CHEREDNIK ALGEBRA OF TYPE 𝔰𝔩 n

  • Shin, Gicheol
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.421-433
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    • 2019
  • Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.

Matrix Pencil Method using Unitary Transform (Unitary 변환을 이용한 Matrix Pencil 방법)

  • Koh, Jin-Hwan;Zhou, WeiWei;Kim, Tae-Kon
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.44 no.2 s.314
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    • pp.102-107
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    • 2007
  • Since the Matrix Pencil (MP) method can be performed to estimate multiple DOAs by using only single snapshot, this method is suitable for short data length or when the environment is dynamic. As the number of array increases, the computational load increases due to complex number computation. This paper presents an approach based on a unitary matrix pencil (MP) algorithm to reduce the computational load. Unitary transformation for the MP method has been suggested and formulated successfully. The computer simulation shows that the error rate of proposed method agree with that of MP for different SNR values.

Determination of Effective Rainfall by US SCS Method and Regression Analysis (SCS방법 및 회귀분석에 의한 유출 강우량 결정)

  • 선우중호;윤용남
    • Water for future
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    • v.10 no.2
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    • pp.101-111
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    • 1977
  • The analysis performed here is aimed to increase the familiarity of hydrologic process especially for the small basins which are densely gaged. Kyung An and Mu Shim river basins are selected as a represectative basin according to the criteria which UNESCO has establisheed back in 1964 and being operated under the auspice of Ministry of Construction. The data exerted from these basins is utilized for the determination of the characteristics of precipitation and runoff phenomena for the small basin, which is considerred as a typical Korean samll watershed. The methodology developed by Soil Conservation Service, USA for determination of runoff value from precipitation is applied to find the suitability of the method to Korean River Basin. The soil cover complex number or runoff curve number was determined by considering the type of soil, soil cover, land use and other factor such as antecent moisture content. The averag values of CN for Kyung An and Mushim river basins were found to be 63.9 and 63.1 under AMC II, however, the values obtained from soil cover complex was less than those from total precipitation and effective precicpitation by 10-30%. It may be worth to note that an attention has to be paid in the application of SCS method lo Korean river basin by adjusting 10-30% increase to the value obtained from soil cover complex. Finally, the design flood hydrograph was consturcted by employing unit hydrograph technique to the dimensionless mass curve. Also a stepwise multiple regression was performed to find the relationship between runoff and API, evapotranspiration rate, 5 days antecedent precipitation and daily temperature.

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WEYL@S THEOREMS FOR POSINORMAL OPERATORS

  • DUGGAL BHAGWATI PRASHAD;KUBRUSLY CARLOS
    • Journal of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.529-541
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    • 2005
  • An operator T belonging to the algebra B(H) of bounded linear transformations on a Hilbert H into itself is said to be posinormal if there exists a positive operator $P{\in}B(H)$ such that $TT^*\;=\;T^*PT$. A posinormal operator T is said to be conditionally totally posinormal (resp., totally posinormal), shortened to $T{\in}CTP(resp.,\;T{\in}TP)$, if to each complex number, $\lambda$ there corresponds a positive operator $P_\lambda$ such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P_{\lambda}^{\frac{1}{2}}(T-{\lambda}I)|^{2}$ (resp., if there exists a positive operator P such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P^{\frac{1}{2}}(T-{\lambda}I)|^{2}\;for\;all\;\lambda)$. This paper proves Weyl's theorem type results for TP and CTP operators. If $A\;{\in}\;TP$, if $B^*\;{\in}\;CTP$ is isoloid and if $d_{AB}\;{\in}\;B(B(H))$ denotes either of the elementary operators $\delta_{AB}(X)\;=\;AX\;-\;XB\;and\;\Delta_{AB}(X)\;=\;AXB\;-\;X$, then it is proved that $d_{AB}$ satisfies Weyl's theorem and $d^{\ast}_{AB}\;satisfies\;\alpha-Weyl's$ theorem.

THE MAXIMAL VALUE OF POLYNOMIALS WITH RESTRICTED COEFFICIENTS

  • Dubicks, Arturas;Jankauskas, Jonas
    • Journal of the Korean Mathematical Society
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    • v.46 no.1
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    • pp.41-49
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    • 2009
  • Let $\zeta$ be a fixed complex number. In this paper, we study the quantity $S(\zeta,\;n):=mas_{f{\in}{\Lambda}_n}\;|f(\zeta)|$, where ${\Lambda}_n$ is the set of all real polynomials of degree at most n-1 with coefficients in the interval [0, 1]. We first show how, in principle, for any given ${\zeta}\;{\in}\;{\mathbb{C}}$ and $n\;{\in}\;{\mathbb{N}}$, the quantity S($\zeta$, n) can be calculated. Then we compute the limit $lim_{n{\rightarrow}{\infty}}\;S(\zeta,\;n)/n$ for every ${\zeta}\;{\in}\;{\mathbb{C}}$ of modulus 1. It is equal to 1/$\pi$ if $\zeta$ is not a root of unity. If $\zeta\;=\;\exp(2{\pi}ik/d)$, where $d\;{\in}\;{\mathbb{N}}$ and k $\in$ [1, d-1] is an integer satisfying gcd(k, d) = 1, then the answer depends on the parity of d. More precisely, the limit is 1, 1/(d sin($\pi$/d)) and 1/(2d sin($\pi$/2d)) for d = 1, d even and d > 1 odd, respectively.

ON THE ADJOINT LINEAR SYSTEM

  • Kwan, Shin-Dong
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.15-23
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    • 1994
  • Throughout this paper, we are working on the complex number field C. The aim of this paper is to explain the applications of Theorem 2 in .cint. 1. In the surface theory, the adjoint linear system has played important roles and many tools have been developed to understand it. In the cases of higher dimensional varieties, we don't have any useful tools so far. Theorem 2 implies that it is enough to compute the dimension of the adjoint linear system to check the birationality. We can compute, somehow, the dimension of the adjoint linear system. For example, we can get an information about $h^{0}$ (X, $O_{x}$( $K_{x}$ + D)) from Euler characteristic of vertical bar $K_{X}$ + D vertical bar and some vanishing theorems. We are going to show the applications of Theorem 2 to smooth three-folds and smooth fourfold, specially, of general type with a nef canonical divisor, smooth Fano variety, and Calabi-Yau manifold. Our main results are Theorem A and Theorem B. Most of birationality problems in Theorem A and Theorem B have been studied. (see Ando [1] and Matsuki [4] for the detail matters.) But Theorem 2 gives short and easy proofs in the cases of dimension 3 and improves the previously known results in the cases of dimension 4.4. 4.4.

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An Analysis of the Sound Stopband in Periodically Corrugated 2-D Ducts (반복 주름을 갖는 이차원 덕트의 음파차단 해석)

  • Kim, Hyun-Sil;Kim, Jae-Seung;Kim, Bong-Ki;Kim, Sang-Ryul;Lee, Seong-Hyun
    • The Journal of the Acoustical Society of Korea
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    • v.31 no.1
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    • pp.11-18
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    • 2012
  • In this paper, the occurrence of a stopband phenomenon when an acoustic wave propagates through periodically corrugated ducts is discussed using theoretical and BEM analyses. A 2-D duct with sinusoidally corrugated upper and lower walls is considered. When the magnitude of the sinusoidal corrugation is sufficiently small compared to the duct's height, the wave equation is solved with the multiple scaling perturbation method. Then stopbands for Bragg and non-Bragg resonances are computed from the condition where frequency becomes a complex number. A 2-D BEM analysis is performed to compute insertion loss of the duct, and stopbands are confirmed as predicted by analytical analysis.

Hybrid Closed-Form Solution for Wireless Localization with Range Measurements (거리정보 기반 무선위치추정을 위한 혼합 폐쇄형 해)

  • Cho, Seong Yun
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.7
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    • pp.633-639
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    • 2013
  • Several estimation methods used in the range measurement based wireless localization area have individual problems. These problems may not occur according to certain application areas. However, these problems may give rise to serious problems in particular applications. In this paper, three methods, ILS (Iterative Least Squares), DS (Direct Solution), and DSRM (Difference of Squared Range Measurements) methods are considered. Problems that can occur in these methods are defined and a simple hybrid solution is presented to solve them. The ILS method is the most frequently used method in wireless localization and has local minimum problems and a large computational burden compared with closed-form solutions. The DS method requires less processing time than the ILS method. However, a solution for this method may include a complex number caused by the relations between the location of reference nodes and range measurement errors. In the near-field region of the complex solution, large estimation errors occur. In the DSRM method, large measurement errors occur when the mobile node is far from the reference nodes due to the combination of range measurement error and range data. This creates the problem of large localization errors. In this paper, these problems are defined and a hybrid localization method is presented to avoid them by integrating the DS and DSRM methods. The defined problems are confirmed and the performance of the presented method is verified by a Monte-Carlo simulation.

Development of Optimal Design User Interface for Waveguide tee Junction using PSO Algorithm and VBA (PSO 알고리즘과 VBA를 이용한 Waveguide tee Junction의 최적설계 인터페이스 개발)

  • Park, Hyun-Soo;Byun, Jin-Kyu;Lee, Dal-Ho;Lee, Hyang-Beom
    • 한국정보통신설비학회:학술대회논문집
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    • 2009.08a
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    • pp.36-39
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    • 2009
  • We developed an optimal design interface based on VBA(Visual Basic Application) that takes advantage of API(Application Program Interface) function of commonly used EM analysis software. The developed interface is adopted for an optimal design of a septum in a waveguide tee junction using PSO(Particle Swarm Optimization) algorithm. The objective function of the optimal design is defined by $S_{11}$-parameter of the waveguide tee junction Design variables are established as position of the septum, that are changed to satisfy the design goal Using the developed design interface and PSO algorithm, the objective function converged to the smallest value, showing the validity of the proposed method. The design interface was developed using Microsoft Excel software, enabling easy control of design parameters for user. Also, various analysis parameters can be set in the Excel interface, including waveguide input mode and frequency. After completion of the design, field solutions at user-specified positrons can be extracted to the output files in complex number form.

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Damage detection of reinforced concrete columns retrofitted with FRP jackets by using PZT sensors

  • Tzoura, Efi A.;Triantafillou, Thanasis C.;Providakis, Costas;Tsantilis, Aristomenis;Papanicolaou, Corina G.;Karabalis, Dimitris L.
    • Structural Monitoring and Maintenance
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    • v.2 no.2
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    • pp.165-180
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    • 2015
  • In this paper lead zirconate titanate transducers (PZT) are employed for damage detection of four reinforced concrete (RC) column specimens retrofitted with carbon fiber reinforced polymer (CFRP) jackets. A major disadvantage of FRP jacketing in RC members is the inability to inspect visually if the concrete substrate is damaged and in such case to estimate the extent of damage. The parameter measured during uniaxial compression tests at random times for known strain values is the real part of the complex number of the Electromechanical Admittance (Conductance) of the sensors, obtained by a PXI platform. The transducers are placed in specific positions along the height of the columns for detecting the damage in different positions and carrying out conclusions for the variation of the Conductance in relation to the position the failure occurred. The quantification of the damage at the concrete substrate is achieved with the use of the root-mean-square-deviation (RMSD) index, which is evaluated for the corresponding strain values. The experimental results provide evidence that PZT transducers are sensitive to damage detection from an early stage of the experiment and that the use of PZT sensors for monitoring and detecting the damage of FRP-retrofitted reinforced concrete members, by using the Electromechanical Admittance (EMA) approach, can be a highly promising method.