• Title/Summary/Keyword: fractional division

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A SIMPLE PROOF OF HILBERT BASIS THEOREM FOR *ω-NOETHERIAN DOMAINS

  • Lim, Jung Wook;Oh, Dong Yeol
    • Korean Journal of Mathematics
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    • v.21 no.2
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    • pp.197-201
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    • 2013
  • Let D be an integral domain with quotient field K, * a star-operation on D, $GV^*(D)$ the set of nonzero finitely generated ideals J of D such that $J_*=D$, and $*_{\omega}$ a star-operation on D defined by $I_{*_{\omega}}=\{x{\in}K{\mid}Jx{\subseteq}I\;for\;some\;J{\in}GV^*(D)\}$ for all nonzero fractional ideals I of D. In this article, we give a simple proof of Hilbert basis theorem for $*_{\omega}$-Noetherian domains.

Analysis of Nonlinear Behavior in Fractional Van der Pol Equation with Periodic External Force (주기적인 외력을 가진 Van der Pol 발진기에서의 비선형 거동 해석)

  • Bae, Young-Chul
    • The Journal of the Korea institute of electronic communication sciences
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    • v.11 no.1
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    • pp.87-92
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    • 2016
  • Van der Pol's oscillators is non-conservative oscillator that having nonlinear damping phenomena. The energy of its system is dissipative at a high amplitude whereas its system creates the energy at low amplitude. In order to identify another behaviors in the Van der Pol oscillator, the periodic external force applied in the Van der Pol oscillator. This paper confirms the pattern of variation for the limit cycle according to parameter variation in order to identify another behaviors in the Van der Pol oscillator.

A Study on the New Method by EMPLUX for Soil-Remediation(1) (토양오염 복원을 위한 EMPLUX를 사용한 새로운 방법에 대한 연구)

  • Kim, Jung-Sung
    • Journal of Environmental Science International
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    • v.16 no.12
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    • pp.1325-1335
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    • 2007
  • The utility of soil-gas surveys is directly proportional to their accuracy in reflecting and representing changes in the subsurface concentrations of source compounds. Passive soil-gas vapor-phase is merely a fractional trace of the source, so, as a matter of convenience, the units used in reporting detection values from EMFLUX surveys are smaller than those employed for source-compound concentrations. According to the Leaking Underground Storage Tank(LUST) Program Annual Report, approximately 16 U.S. million dollars were spent for environmental site investigations at over 1,600 Underground Storage Tank(UST) sites and approximately over 1,000 acres of land was characterized and remediated in the State of Illinois in the year of 2003 alone. The main purpose of this study is to propose an idea to significantly reduce the site investigation cost by utilizing a passive soil-gas survey and conventional intrusive drilling method and to fully define the three dimensional characteristics of subsurface contamination from two industrial drycleaning facilities.

Measures for Evaluating the Orthogonal Array of Strength 3 (강도 3의 직교대열을 평가하기 위한 측도)

  • Jang Dae-Heung
    • The Korean Journal of Applied Statistics
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    • v.18 no.3
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    • pp.617-625
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    • 2005
  • We usually use orthogonal designs-orthogonal array of strength 2 as orthogonal arrays. It was shown that fractional factorial plaits represented by orthogonal arrays of strength 3 are universally optimal under the additive motels that includes the mean, all main effects and all two-factor interactions. Therefore, we need the measure for evaluating the orthogonal array of strength 3. We can extend this measure as the measure for evaluating the orthogonal array of strength t($\ge$ 2).

Materials Properties of Nickel Electrodeposits as a Function of the Current Density, Duty Cycle, Temperature and pH

  • Kim, Dong-Jin;Kim, Myung Jin;Kim, Joung Soo;Kim, Hong Pyo
    • Corrosion Science and Technology
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    • v.5 no.5
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    • pp.168-172
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    • 2006
  • Alloy 600 having a superior resistance to a corrosion is used as a steam generator tubing in nuclear power plants. In spite of its high corrosion resistance, there are many tubings which experience corrosion problems such as a SCC under the high temperature and high pressure environments of nuclear power plants. The Alloy 600 tubing can be repaired by using a Ni electroplating having an excellent SCC resistance. In order to carry out a successful Ni electrodeposition inside a steam generator tubing, the effects of various parameters on the material properties of the electrodeposit should be elucidated. Hence this work deals with the effects of an applied current density, duty cycle($T_{on}/(T_{on}+T_{off})$) of a pulse current, bath temperature and solution pH on the material properties of Ni electrodeposit obtained from a Ni sulphamate bath by analyzing the current efficiency, potentiodynamic curve, hardness and stress-strain curve. Hardness, YS(yield strength) and TS(tensile strength) decreased whereas the elongation increased as the applied current density increased. This was thought to be by a concentration depletion at the interface of the electrodeposit/solution, and a fractional decrease of the hydrogen reduction reaction. As the duty cycle increased, the hardness, YS and TS decreased while the elongation increased. During an off time at a high duty cycle, the concentration depletion could not be recovered sufficiently enough to induce a coarse grain sized electrodeposit. With an increase of the solution temperature and pH, the YS and TS increased while the elongation decreased. The experimental results of the hardness and the stress-strain curves can be supplemented by the results of the potentiodynamic curve.

The effect of algebraic thinking-based instruction on problem solving in fraction division (분수의 나눗셈에 대한 대수적 사고 기반 수업이 문제해결에 미치는 영향)

  • Park, Seo Yeon;Chang, Hyewon
    • Education of Primary School Mathematics
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    • v.27 no.3
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    • pp.281-301
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    • 2024
  • Many students have experienced difficulties due to the discontinuity in instruction between arithmetic and algebra, and in the field of elementary education, algebra is often treated somewhat implicitly. However, algebra must be learned as algebraic thinking in accordance with the developmental stage at the elementary level through the expansion of numerical systems, principles, and thinking. In this study, algebraic thinking-based classes were developed and conducted for 6th graders in elementary school, and the effect on the ability to solve word-problems in fraction division was analyzed. During the 11 instructional sessions, the students generalized the solution by exploring the relationship between the dividend and the divisor, and further explored generalized representations applicable to all cases. The results of the study confirmed that algebraic thinking-based classes have positive effects on their ability to solve fractional division word-problems. In the problem-solving process, algebraic thinking elements such as symbolization, generalization, reasoning, and justification appeared, with students discovering various mathematical ideas and structures, and using them to solve problems Based on the research results, we induced some implications for early algebraic guidance in elementary school mathematics.

An Empirical Study for the Existence of Long-term Memory Properties and Influential Factors in Financial Time Series (주식가격변화의 장기기억속성 존재 및 영향요인에 대한 실증연구)

  • Eom, Cheol-Jun;Oh, Gab-Jin;Kim, Seung-Hwan;Kim, Tae-Hyuk
    • The Korean Journal of Financial Management
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    • v.24 no.3
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    • pp.63-89
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    • 2007
  • This study aims at empirically verifying whether long memory properties exist in returns and volatility of the financial time series and then, empirically observing influential factors of long-memory properties. The presence of long memory properties in the financial time series is examined with the Hurst exponent. The Hurst exponent is measured by DFA(detrended fluctuation analysis). The empirical results are summarized as follows. First, the presence of significant long memory properties is not identified in return time series. But, in volatility time series, as the Hurst exponent has the high value on average, a strong presence of long memory properties is observed. Then, according to the results empirically confirming influential factors of long memory properties, as the Hurst exponent measured with volatility of residual returns filtered by GARCH(1, 1) model reflecting properties of volatility clustering has the level of $H{\approx}0.5$ on average, long memory properties presented in the data before filtering are no longer observed. That is, we positively find out that the observed long memory properties are considerably due to volatility clustering effect.

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Performance Comparison of the OFDM/SFH and OFDM/DS Systems in the Jamming Channel (OFDM/SFH와 OFDM/DS 시스템의 Jamming 채널에서 성능비교)

  • 박종현;김상우;유흥균;이상태
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.14 no.11
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    • pp.1149-1155
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    • 2003
  • OFDM/SFH(orthogonal frequency division multiplexing/slow frequency hopping) system is the combination of OFDM communication system with frequency hopping(FH) method and OFDM/DS(orthogonal frequency division multiplexing/direct sequence) system combines the OFDM communication system with direct sequence(DS) method in terms of PN(pseudo noise) sequence. These two systems are also can be used for anti-jamming. In this study we analyze performances of OFDM/SFH system and OFDM/DS system with the equal information rate in partial band jamming and tone jamming channel. We find BER(bit error rate) in the variation of JFR(jamming fractional ratio) and JSR(jamming to signal power ratio) of the partial band jamming. Also, BER is found in the several JSR of the single tone or multi tone jamming. OFDM/DS system shows better performance than OFDM/SFH system in partial band jamming environment. OFDM/DS system has about 2.5 ㏈ SNR(signal to noise power ratio) gains than OFDM/SFH system when JFR=4/16 and JSR=0 ㏈ to meet BER=10$\^$-3/. However, OFDM/SFH system has about 3 ㏈ SNR gains than OFDM/DS system at single tone jamming of JSR=5 ㏈. In multi tone jamming, performance of OFDM/SFH system is considerably degraded than OFDM/DS system.

Novel Integer Frequency Offset Detection Method for OFDM Systems (OFDM 시스템을 위한 새로운 정수 주파수 옵셋 검파 기법)

  • Song, Chong-Han;Yoon, Tae-Ung;Lee, Myung-Soo;Lee, Young-Yoon;Kim, Sang-Hun;Yoon, Seok-Ho
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.34 no.6C
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    • pp.656-663
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    • 2009
  • Recently, frequency offset estimation method for orthogonal frequency division multiplexing has been proposed by Ren et al. (REA). The method can estimate an frequency offset independently from training symbol structure. In REA method, however, the detection probability of integer frequency offset is varying according to fractional frequency offset. In this paper, we first analysis REA frequency offset estimation method, and define new detection criteria suitable for the method. Then, we propose efficient integer frequency offset estimation method based on the new detection criteria and maximum likelihood method. The proposed method still has the advantages of REA method, while overcome the drawback. The numerical results demonstrate that the proposed methods outperform the REA method, in terms of integer frequency offset detection probability.