• Title/Summary/Keyword: $Z_2$

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HARMONIC MAPPING RELATED WITH THE MINIMAL SURFACE GENERATED BY ANALYTIC FUNCTIONS

  • JUN, SOOK HEUI
    • Korean Journal of Mathematics
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    • v.23 no.3
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    • pp.439-446
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    • 2015
  • In this paper we consider the meromorphic function G(z) with a pole of order 1 at -a and analytic function F(z) with a zero -a of order 2 in $\mathbb{D}=\{z :{\mid}z{\mid}<1\}$, where -1 < a < 1. From these functions we obtain the regular simply-connected minimal surface $S=\{(u(z),\;{\nu}(z),\;H(z)):z{\in}\mathbb{D}\}$ in $E^3$ and the harmonic function $f=u+i{\nu}$ defined on $\mathbb{D}$, and then we investigate properties of the minimal surface S and the harmonic function f.

Comparison of the Output Current THDi of Single-Phase Embedded Typical Z-Source Inverter and Embedded Quasi Z-Source Inverter (단상 임베디드 Typical Z-소스 인버터와 임베디드 Quasi Z-소스 인버터의 출력전류 THDi 비교)

  • Oh, Seung-Yeol;Kim, Se-Jin;Jung, Young-Gook;Park, Hee-Jae;Lim, Young-Cheol
    • Proceedings of the KIPE Conference
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    • 2012.11a
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    • pp.207-208
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    • 2012
  • 본 논문에서는 임베디드 Z-소스 컨버터 2대를 병렬 연결하여 승압 및 강압 기능을 가지는 단상 인버터의 THDi를 비교 분석하였다. 임베디드 Z-소스 인버터는 임베디드 Typical Z-소스 인버터와 임베디 Quasi Z-소스 인버터로 구분되며 각 인버터의 단락비에 따른 출력전류 THDi를 비교하였다. THDi의 비교를 위해 실험 세트를 구성하고 실험 데이터 이용해 비교 분석 하였다.

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Pharmacognostical Studies on the ‘Cho Pi Na Mu’ (초피나무의 생약학적 연구)

  • Park, Jong-Hee;Park, Seong-Su;Kim, Jeong-Myo
    • Korean Journal of Pharmacognosy
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    • v.33 no.2 s.129
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    • pp.75-80
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    • 2002
  • The Korean folk medicine 'Cho Pi Na Mu' has been used orally to tuberculosis, neuralgia, acute and chronic gastritis and arthritis. In order to clarify the botanical origin this crude drug, comparative anatomical studies were made on the branches of Zanthoxylum species growing wild in Korea, i.e. Z. coreanum, Z. piperitum, Z. piperitum var. pubescens, Z. planispinum, Z. schinifolium, Z. schinifolium var. inermis, Z. schinifolium var. microphyllum. As a result, it was clarified that 'Cho Pi Na Mu' was the branch of Z. piperitum.

SOME RESULTS ON UNIQUENESS OF MEROMORPHIC SOLUTIONS OF DIFFERENCE EQUATIONS

  • Gao, Zong Sheng;Wang, Xiao Ming
    • Communications of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.959-970
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    • 2017
  • In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.

CRITERIA OF NORMALITY CONCERNING THE SEQUENCE OF OMITTED FUNCTIONS

  • Chen, Qiaoyu;Qi, Jianming
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1373-1384
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    • 2016
  • In this paper, we research the normality of sequences of meromorphic functions concerning the sequence of omitted functions. The main result is listed below. Let {$f_n(z)$} be a sequence of functions meromorphic in D, the multiplicities of whose poles and zeros are no less than k + 2, $k{\in}\mathbb{N}$. Let {$b_n(z)$} be a sequence of functions meromorphic in D, the multiplicities of whose poles are no less than k + 1, such that $b_n(z)\overset{\chi}{\Rightarrow}b(z)$, where $b(z({\neq}0)$ is meromorphic in D. If $f^{(k)}_n(z){\neq}b_n(z)$, then {$f_n(z)$} is normal in D. And we give some examples to indicate that there are essential differences between the normal family concerning the sequence of omitted functions and the normal family concerning the omitted function. Moreover, the conditions in our paper are best possible.

Postmortem Changes in Z-disk Domain of Titin in the Chicken Muscle (계육의 숙성 중 Titin의 Z선 영역(Zeugmatin)의 변화)

  • 안동현;박선미
    • Food Science of Animal Resources
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    • v.18 no.4
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    • pp.292-300
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    • 1998
  • This study was undertaken to determine the influence in the Z-disk domain of titin on the tenderization of meat by the structure change of myofibrillar Z-disks during post-mortem aging. After weakening the structure of Z-disks, the Z-disk region was splitted. As the results, myofibrils were fragmented by mechanical strength. Using indirect immunofluorescence microscopy, we show that the Z-disk domain of titin was disappeared from myofibrils in this period. There phenomenon were also shown by treating myofibrils with a solution containing 0.1mM $Ca^{2+}$. We conclude that change in Z-disk domain of titin is directly effected on the tenderization of meat during post-mortem aging and these change is due to manily calcium ions.

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FUNCTIONAL EQUATIONS IN THREE VARIABLES

  • Boo, Deok-Hoon;Park, Chun-Gil;Wee, Hee-Jung
    • Journal of the Chungcheong Mathematical Society
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    • v.17 no.2
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    • pp.169-190
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    • 2004
  • Let r, s be nonzero real numbers. Let X, Y be vector spaces. It is shown that if a mapping f : $X{\rightarrow}Y$ satisfies f(0) = 0, and $$sf(\frac{x+y{\pm}z}{r})+f(x)+f(y){\pm}f(z)=sf(\frac{x+y}{r})+sf(\frac{y{\pm}z}{r})+sf(\frac{x{\pm}z}{r})$$, or $$sf(\frac{x+y{\pm}y}{r})+f(x)+f(y){\pm}f(z)=f(x+y)+f(y{\pm}z)+f(x{\pm}z)$$ for all x, y, $z{\in}X$, then there exist an additive mapping A : $X{\rightarrow}Y$ and a quadratic mapping Q : $X{\rightarrow}Y$ such that f(x) = A(x) + Q(x) for all $x{\in}X$. Furthermore, we prove the Cauchy-Rassias stability of the functional equations as given above.

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THE CHOW RING OF A SEQUENCE OF POINT BLOW-UPS

  • Daniel Camazon Portela
    • Communications of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.563-574
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    • 2024
  • Given a sequence of point blow-ups of smooth n-dimensional projective varieties Zi defined over an algebraically closed field $k,\,Z_s\,{\overset{{\pi}_s}{\longrightarrow}}\,Z_{s-1}\,{\overset{{\pi}_{s-1}}{\longrightarrow}}\,{\cdots}\,{\overset{{\pi}_2}{\longrightarrow}}\,Z_1\,{\overset{{\pi}_1}{\longrightarrow}}\,Z_0$, with Z0 ≅ ℙn, we give two presentations of the Chow ring A(Zs) of its sky. The first one uses the classes of the total transforms of the exceptional components as generators and the second one uses the classes of the strict transforms ones. We prove that the skies of two sequences of point blow-ups of the same length have isomorphic Chow rings. Finally we give a characterization of the final divisors of a sequence of point blow-ups in terms of some relations defined over the Chow group of zero-cycles A0(Zs) of its sky.

Effect of Nitrogen Treatment on the Structure and Magnetic Properties of $RuSr_2(EuCe)Cu_2O_z$ Compound (질소 열처리에 따른 $RuSr_2(EuCe)Cu_2O_z$ 계의 구조 및 자기적 특성)

  • Lee, H.K.;Kim, Y.I.;Kim, Y.C.
    • Progress in Superconductivity
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    • v.13 no.3
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    • pp.178-183
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    • 2012
  • Two $RuSr_2(EuCe)Cu_2O_z$ samples (as prepared and after $N_2$ treatment) have been investigated by thermogravimetric (TC) analysis, high-resolution x-ray powder diffraction and magnetization measurements. TG measurements which were carried out in $H_2/Ar$ atmosphere showed that the $N_2$ treatment of the as-prepared sample at $650^{\circ}C$ for 2h leads to a decrease in the oxygen content z by about 0.25. This oxygen depletion was accompanied by an increase in the magnetic transition temperature from 54.0 K to 114.9 K. This magnetic behavior is discussed in connection with the results of Rietveld analysis of the x-ray diffraction data which showed that the $N_2$ treatment resulted in both a significant increase in the rotation angle of the $RuO_6$ octahedra and a decrease in c-lattice parameter of the sample.

Characteristics of Rustling Sound of Laminated Fabric Utilizing Nano-web (나노웹을 이용한 라미네이트소재의 마찰음 특성)

  • Jeong, Tae-Young;Lee, Eu-Gene;Lee, Seung-Sin;Cho, Gil-Soo
    • Fashion & Textile Research Journal
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    • v.15 no.4
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    • pp.620-629
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    • 2013
  • This study examines the rustling sound characteristics of electrospun nanofiber web laminates according to layer structures. This study assesses mechanical properties and frictional sounds (such as SPL); in addition, Zwicker's psychoacoustic parameters (such as Loudness (Z), Sharpness (Z), Roughness (Z), and Fluctuation strength (Z)) were calculated using the Sound Quality Program (ver.3.2, B&K, Denmark). The result determined how to control these characteristics and minimize rustling sounds. A total of 3 specimens' frictional sound (generated at 0.63 m/s) was recorded using a Simulator for Frictional Sound of Fabrics (Korea Patent No. 10-2008-0105524) and SPLs were analyzed with a Fast Fourier Transformation (FFT). The mechanical properties of fabrics were measured with a KES-FB system. The SPL value of the sound spectrum showed 6.84~58.47dB at 0~17,500Hz. The SPL value was 61.2dB for the 2-layer PU nanofiber web laminates layered on densely woven PET(C1) and was the highest at 65.1dB for the 3-layer PU nanofiber web laminates (C3). Based on SPSS 18.0, it was shown that there is a correlation between mechanical properties and psychoacoustic characteristics. Tensile properties (LT), weight (T), and bending properties (2HB) showed a high correlation with psychoacoustic characteristics. Tensile linearity (LT) with Loudness (Z) showed a negative correlation coefficient; however, weight (T) with Sharpness (Z) and Roughness (Z), and bending hysteresis (2HB) with Roughness (Z) indicated positive correlation coefficients, respectively.