• Title/Summary/Keyword: even and odd numbers

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A Study on the Stress Analysis ofAxi-symetric Body with N on-symetric Load and N on-symetric Given Displacements (비대칭 하중을 받고 비대칭 변위가 주어진 축대칭 물체의 응력해석에 관한 연구)

  • 전효중;왕지석;최순열
    • Journal of Advanced Marine Engineering and Technology
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    • v.14 no.4
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    • pp.46-56
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    • 1990
  • Stress analysis of axi-symetric body with non-symetric loading and non-symetric given displacements is investigated in this paper using the finite element method. As the non-symetric load and non-symetric given displacements of axi-symetric body are generally periodic functions of angle .theta., the nodal forces and nodal displacements can be expanded in cosine and sine series, that is, Fourier series. Furthermore, using Euler's formula, the cosine and sine series can be converted into exponential series and it is prooved that the related calculus become more clear. Substituting the nodal displacements expanded in Fourier series into the strain components of cylindrical coordinates system, the element strains are expressed in series form and by the principal of virtual work, the element stiffness martix and element load vector are obtained for each order. It is also showed that if the non-symetric loads are even or odd functions of angle ${\theta}$ the stiffness matrix and load vector of the system are composed with only real numbers and relatively small capacity fo computer memory is enough for calculation.

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Optical Implementation of Perceptron Learning Model using the Polarization Property of Commercial LCTV (상용 LCTV의 편광 특성을 이용한 Perceptron 학습 모델의 광학적 구현)

  • 한종욱;용상순;김동훈;김성배;박일종;김은수
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.27 no.8
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    • pp.1294-1302
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    • 1990
  • In this paper, optical implementation of single layer perceptron to discriminate the even and odd numbers using commericla LCTV spatial light modulator is described. In order to overcome the low dynamic range of gray levels of LCTV, nonlinear quantized perceptron model is introduced, which is analyzed to have faster convergent time with small gray levels through the computer simulation. And the analog weights containing positive and negative values of single layer perceptron is represented by using the polarization-based encoding method. Finally, optical implementation of the nonlinear quantized perceptron learning model based on polarization property of the commercial LCTV is proposed and some experimental results are given.

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A Study on the Introduction of the National Point Number for Advanced Location-Finding (위치찾기 선진화를 위한 국가지점번호 도입방안 연구)

  • Yang, Sungchul
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.31 no.2
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    • pp.151-157
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    • 2013
  • The law for indicating the address based on the street name has taken effect in 1997. The address based on land-lot number will be changed to the address based on the street name giving odd numbers to the buildings situated on the left side and even numbers to the buildings situated on the right side per street. Searching locations by street name addresses is possible for residential areas, on the other hand, the system of finding locations is insufficient for farmlands, mountains and others, so it is unable to cope with crimes and emergency rescue. In order to make up for the weak points of street name address, the national point number, grid reference system was introduced for finding location of non-residential areas. Therefore, the purpose of this paper is to help the introduction the national point number. In this paper, we proposed a territory-oriented control point and grid range for the national point number. Numbering scheme of grid zone shall be alphanumeric, a two-letter pair Hangul and the grid coordinates in terms of Easting and Northing. We also proposed the notice area for the national point number and location of signs, application about the public and private sector.

SPN Block cipher SSB having same structure in encryption and decryption (암호와 복호가 동일한 SPN 블록 암호 SSB)

  • Cho, Gyeong-Yeon
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.15 no.4
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    • pp.860-868
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    • 2011
  • Feistel and SPN are the two main structures in a block cipher. Feistel is a symmetric structure which has the same structure in encryption and decryption, but SPN is not a symmetric structure. In this paper, we propose a SPN block cipher so called SSB which has a symmetric structure in encryption and decryption. The proposed SSB is composed of the even numbers of N rounds. Each round consists of a round key addition layer, a subsitution layer, a byte exchange layer and a diffusion layer. The subsitution layer of the odd round is inverse function of one of the even round. And the diffusion layer is a MDS involution matrix. The differential and linear attack probability of SSB is $2^{-306}$ which is same with AES. The proposed symmetric SPN block cipher SSB is believed to construct a safe and efficient cipher in Smart Card and RFID environments which is in limited hardware and software resources.

Biodegradation of crude oil hydrocarbons by Acinetobacter sp. isolated from activated sludge (활성슬러지에서 단리한 Acinetobacter sp.에 의한 원유탄화수소분해)

  • Dong-Hyuk CHOI;Dong Hoon LEE
    • Journal of Korea Soil Environment Society
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    • v.5 no.1
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    • pp.97-108
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    • 2000
  • A Gram-type negative bacteria that can utilize crude oil as the sole source of carbon and energy was isolated from an activated sludge of a local sewage treatment plant and identified tentatively as belonging to the genus Acinetobacter. The isolate could degrade n-alkanes and unidentified hydrocarbons in crude oil and utilize n-alkanes, hydrophobic substrates, as sole carbon and energy sources. n-Alkanes from tridecane (Cl3) to triacontane (C30) in crude oil were degraded simultaneously with no difference in degradation characteristics between the two close odd and even numbered alkanes in carbon numbers. The linear growth of the isolate and the degradation characteristics of Pr-alkanes suggested that the transport of substrates from the oil phase to the site where the substrates undergo the initial oxidation in microorganism might be the rate limiting in the biodegradation process of crude oil constituents. The remainder fraction of substrates after cultivation was considered to reflect the hydrocarbon inclusions in the cell mass, characteristics in Acinetobacter species, and to control the transport of substrates from crude oil phase. On the basis of the results, the isolate was considered to play an important role in the degradation study of hydrophobic environmental pollutants.

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Analyses of the precision and strategies for representing the magnitude of fractions and decimals on the number line among 6th graders (초등학교 6학년의 분수와 소수의 크기에 대한 수직선 표상의 정확성 및 사용 전략 분석)

  • Jinyoung Heo;Soo-hyun Im
    • The Mathematical Education
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    • v.63 no.3
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    • pp.393-409
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    • 2024
  • The number line model, which intuitively marks numerical magnitudes in space, is widely utilized to help in understanding the magnitudes that fractions and decimals represent. The study analyzed 6th graders' understanding of fractions and decimals, their problem solving strategies, and whether individual differences in the flexibility of various strategy uses are associated with the accuracy of numerical representation, calculation fluency, and overall mathematical achievement. As a result of the study, students showed relatively lower accuracy in representing fractions and decimals on a number line compared to natural numbers, especially for fractions with odd denominators compared to even denominators, and for two-digit decimals compared to three-digit decimals. Regarding strategy use, students primarily used benchmark, segmentation, and approximation strategies for fractions, and benchmark, rounding, and transformation strategies for decimals sequentially. Lastly, as students used various representation strategies for fractions, their accuracy in representing fractions and their overall mathematical achievement scores showed significantly better outcomes. Taken together, we suggest the need for careful instruction on different interpretations of fractions, the place value of decimals, and the meaning of zero in decimal places. Moreover, we discuss instructional methods that integrate the number line model and its diverse representation strategies to enhance students' understanding of fractions and decimals.