• Title/Summary/Keyword: ODD

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FURTHER LOG-SINE AND LOG-COSINE INTEGRALS

  • Choi, Junesang
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.4
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    • pp.769-780
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    • 2013
  • Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. Very recently, Choi [6] presented explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function. In the present sequel to the investigation [6], we evaluate the log-sine and log-cosine integrals involved in more complicated integrands than those in [6], by also using the Beta function.

COHOMOLOGY GROUPS OF CIRCULAR UNITS

  • Kim, Jae-Moon;Oh, Seung-Ik
    • Journal of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.623-631
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    • 2001
  • Let $\kappa$ be a real abelian field of conductor f and $\kappa$(sub)$\infty$ = ∪(sub)n$\geq$0$\kappa$(sub)n be its Z(sub)p-extension for an odd prime p such that płf$\phi$(f). he aim of this paper is ot compute the cohomology groups of circular units. For m>n$\geq$0, let G(sub)m,n be the Galois group Gal($\kappa$(sub)m/$\kappa$(sub)n) and C(sub)m be the group of circular units of $\kappa$(sub)m. Let l be the number of prime ideals of $\kappa$ above p. Then, for mm>n$\geq$0, we have (1) C(sub)m(sup)G(sub)m,n = C(sub)n, (2) H(sup)i(G(sub)m,n, C(sub)m) = (Z/p(sup)m-n Z)(sup)l-1 if i is even, (3) H(sup)i(G(sub)m,n, C(sub)m) = (Z/P(sup)m-n Z)(sup l) if i is odd (※Equations, See Full-text).

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ON THE STABILITY OF A MIXED TYPE FUNCTIONAL EQUATION

  • Lee, Sang-Baek;Park, Won-Gil;Bae, Jae-Hyeong
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.1
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    • pp.69-77
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    • 2006
  • The generalized Hyers-Ulam stability problems of the mixed type functional equation $$f\({\sum_{i=1}^{4}xi\)+\sum_{1{\leq}i<j{\leq}4}f(x_i+x_j)=\sum_{i=1}^{4}f(x_i)+\sum_{1{\leq}i<j<k{\leq}4}f(x_i+X_j+x_k)$$ is treated under the approximately even(or odd) condition and the behavior of the quadratic mappings and the additive mappings is investigated.

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A REMARK OF SOME IMAGINARY QUADRATIC FIELDS WITH ODD CLASS NUMBERS

  • Kim, Hyun;Lee, Keumyeon;Cheong, Cheoljo;Park, Hwasin
    • Honam Mathematical Journal
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    • v.36 no.1
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    • pp.147-155
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    • 2014
  • Let D be a square-free positive integer and let $K_D=\mathbb{Q}(\sqrt{-D})$ be the imaginary quadratic field. And let $h_D$ be the class number of the number field $K_D$. In this paper, we show the following: If D=l or 4l, where l is a prime number with $l{\equiv}3$ (mod 4), then $h_D$ is odd.

A Method of Selecting Filter Coefficient for Robust Data to Clock Equalizer in Optical Disc Drive (광 디스크 드라이브의 강인한 데이터-클럭 등화기 필터계수 선정)

  • Yeom, Dong-Hae;Kim, Jin-Kyu;Joo, Young-Hoon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.59 no.4
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    • pp.793-796
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    • 2010
  • The equalizer compensates a signal distorted by transmission lines and amplifying stages, so the signal can have uniform characteristics over all frequency range. The equalizer in ODD(Optical Disc Drive) improves the stability of the extracted clock from a received signal and the readability of an inserted disc by suppressing noise and ISI(Inter-Symbol Inference). The length of marks-spaces and track pitch on discs becomes shorter as the recording density of an optical media is higher, which causes noise and ISI. And, the sensitivity about the fluctuation of physical systems is higher as the optical devices become more complicate. This paper proposes a method to select the coefficient of built-in equalizer of ODD in order to maintain the quality of signals against noise and ISI caused by system fluctuation.

Variation of Relative Power Characteristics in EEG while Inducing Human Errors (인간과오 유발 상황에서 뇌파 상대파워 특성의 변화)

  • Lim, Hyeon-Kyo
    • Journal of the Korean Society of Safety
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    • v.23 no.3
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    • pp.65-70
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    • 2008
  • Electroencephalogram(EEG) would be the most objective psychophysiological research technique on human errors though few research has been taken yet. This study aimed to get characteristics of human error while committing simple Odd-Ball tasks by utilizing the power spectrum technique of EEG data. Each experiment was composed of 3 tasks with different rules, and three young undergraduate students participated in this study as paid subjects. The result showed that subject and the interaction of subject and task factors were statistically significant on variation of power of $\alpha$ and $\beta$ bands which implied there would exist groups with homogeneity in their response. And though the variation of band powers due to task factors were not so great as to get statistical significance, it implied that the task requiring decoding process would be more strange to human beings than the task merely requiring psychological recall process.

Analysis of Amplitude Distortion in Super Wide-Band AM Signal Transmission (초광대역 AM 신호전송에서의 진폭왜율해석)

  • 이충웅
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.8 no.3
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    • pp.27-32
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    • 1971
  • This paper presents the analysis of the amplitude distortion occurring in the transmission of super wideband AM signal when the amplitude and phase variations of the upper and lower sidebands of the AM signal are symmetrical, and odd symmetrical with respect to the carrier. It is shown that the case where the amplitude variations of the upper and lower sidebands of AM signal are symmetrical with respect to the carrier while the phase variations of the upper and lower sidebands are odd symmetrical with respect to the carrier induce, no amplitude distortion in AM signal transmission.

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STABLE SPLITTINGS OF BG FOR GROUPS WITH PERIODIC COHOMOLOGY AND UNIVERSAL STABLE ELEMENTS

  • Lim, Pyung-Ki
    • Bulletin of the Korean Mathematical Society
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    • v.26 no.2
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    • pp.109-114
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    • 1989
  • This paper deals with the classifying spaces of finite groups. To any finite group G we associate a space BG with the property that .pi.$_{1}$(BG)=G, .pi.$_{i}$ (BG)=0 for i>1. BG is called the classifying space of G. Consider the problem of finding a stable splitting BG= $X_{1}$$^{V}$ $X_{1}$$^{V}$..$^{V}$ $X_{n}$ localized at pp. Ideally the $X_{i}$ 's are indecomposable, thus displaying the homotopy type of BG in the simplest terms. Such a decomposition naturally splits $H^{*}$(BG). The main purpose of this paper is to give the classification theorem in stable homotopy theory for groups with periodic cohomology i.e. cyclic Sylow p-subgroups for p an odd prime and to calculate some universal stable element. In this paper, all cohomology groups are with Z/p-coefficients and p is an odd prime.prime.

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Design of Swing Arm Type's Actuator for Small-sized ODD (초소형 광디스크 드라이브를 위한 스윙암 타입 액추에이터 설계)

  • Oh, Jeseung;Park, Se-June;Lee, Dong-Ju;Jung, Ho-Seop;Park, No-Cheol;Park, Young-Pil
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.6 s.99
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    • pp.660-666
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    • 2005
  • Recently, the need for subminiature storage systems has increased with the diversification of portable devices. An actuator for small optical disk drives has to satisfy performance requirements such as higher access speed, lower power consumption, and smaller size. In this paper, we proposed the miniaturized rotary type VCM actuator that had an effective focusing mechanism and secured sufficient bandwidth for small form factor (SFF) optical disk drive (ODD). Initial model was designed by electromagnetic (EM) and structural analyses. Such a model was improved using design of experiments (DOE) procedure based on a Blu-ray disk (BD) 1x specifications.