• Title/Summary/Keyword: $\phi$ -q-n

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The analysis of partial discharge signals according to particle states in GIS (GIS내 파티클의 상태에 따른 부분방전 신호의 분석)

  • 김경화;이동준;곽희로
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.14 no.1
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    • pp.67-74
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    • 2000
  • This paper presents the analysis of partial discharge signals according to the particle states in GIS, for preventing the insulation failure and recognizing the particle states. In this paper, four states of particle (particle on electrode, particle on enclosure, particle on spacer and crossing particle) were simulated. And $\Phi$-Q-N distribution of partial discharge signals was analyzed and the statistical operator of the $\Phi$-Q distribution was analyzed. As a result, it was found that the states of particle were distinguished by analysis of the $\Phi$-Q-N distribution and the statistical operator of the $\Phi$-Q distribution.

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Partial Discharge Pattern Recognition using Neural Network (뉴우럴 네트워크에 의한 부분방전 패턴 인식)

  • Lee, June-Ho;Hozumi, Naohiro;Okamoto, Tatsuki
    • Proceedings of the KIEE Conference
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    • 1995.07c
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    • pp.1304-1306
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    • 1995
  • In this study, a neural network algorithm through a data standardization method was developed to discriminate the phase-shifted partial discharge(PD) patterns such as a $\phi$-q-n pattern. Considering the PD measurement in the field, it is not so easy to acquire absolute phase angles of PD pulses. As a consequence, one of the significant problems to be solved in applying the neural network algorithm to practical systems is to develop a method that can discriminate phase-shifted $\phi$-q-n patterns. Therefore, authors established a new method which could convert phase-shifted $\phi$-q-n patterns to a standardized $\phi$-q-n pattern which was not influenced by phase shifting. This new standardization method improved the recognition performance of a neural network for the phase-shifted $\phi$-q-n patterns considerably.

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A 2kβ Algorithm for Euler function 𝜙(n) Decryption of RSA (RSA의 오일러 함수 𝜙(n) 해독 2kβ 알고리즘)

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.19 no.7
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    • pp.71-76
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    • 2014
  • There is to be virtually impossible to solve the very large digits of prime number p and q from composite number n=pq using integer factorization in typical public-key cryptosystems, RSA. When the public key e and the composite number n are known but the private key d remains unknown in an asymmetric-key RSA, message decryption is carried out by first obtaining ${\phi}(n)=(p-1)(q-1)=n+1-(p+q)$ and then using a reverse function of $d=e^{-1}(mod{\phi}(n))$. Integer factorization from n to p,q is most widely used to produce ${\phi}(n)$, which has been regarded as mathematically hard. Among various integer factorization methods, the most popularly used is the congruence of squares of $a^2{\equiv}b^2(mod\;n)$, a=(p+q)/2,b=(q-p)/2 which is more commonly used then n/p=q trial division. Despite the availability of a number of congruence of scares methods, however, many of the RSA numbers remain unfactorable. This paper thus proposes an algorithm that directly and immediately obtains ${\phi}(n)$. The proposed algorithm computes $2^k{\beta}_j{\equiv}2^i(mod\;n)$, $0{\leq}i{\leq}{\gamma}-1$, $k=1,2,{\ldots}$ or $2^k{\beta}_j=2{\beta}_j$ for $2^j{\equiv}{\beta}_j(mod\;n)$, $2^{{\gamma}-1}$ < n < $2^{\gamma}$, $j={\gamma}-1,{\gamma},{\gamma}+1$ to obtain the solution. It has been found to be capable of finding an arbitrarily located ${\phi}(n)$ in a range of $n-10{\lfloor}{\sqrt{n}}{\rfloor}$ < ${\phi}(n){\leq}n-2{\lfloor}{\sqrt{n}}{\rfloor}$ much more efficiently than conventional algorithms.

Reverse Baby-step 2k-ary Adult-step Method for 𝜙((n) Decryption of Asymmetric-key RSA (비대칭키 RSA의 𝜙(n) 해독을 위한 역 아기걸음- 2k-ary 성인걸음법)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.14 no.6
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    • pp.25-31
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    • 2014
  • When the public key e and the composite number n=pq are disclosed but not the private key d in an asymmetric-key RSA, message decryption is carried out by obtaining ${\phi}(n)=(p-1)(q-1)=n+1-(p+q)$ and subsequently computing $d=e^{-1}(mod{\phi}(n))$. The most commonly used decryption algorithm is integer factorization of n/p=q or $a^2{\equiv}b^2$(mod n), a=(p+q)/2, b=(q-p)/2. But many of the RSA numbers remain unfactorable. This paper therefore applies baby-step giant-step discrete logarithm and $2^k$-ary modular exponentiation to directly obtain ${\phi}(n)$. The proposed algorithm performs a reverse baby-step and $2^k$-ary adult-step. As a results, it reduces the execution time of basic adult-step to $1/2^k$ times and the memory $m={\lceil}\sqrt{n}{\rceil}$ to l, $a^l$ > n, hence obtaining ${\phi}(n)$ by executing within l times.

Polynomials satisfying f(x-a)f(x)+c over finite fields

  • Park, Hong-Goo
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.277-283
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    • 1992
  • Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

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Partial Discharge Distribution Analysis on Interlace Defects of Cable Joint using K-means Clustering (K-means 클러스터링을 이용한 케이블 접속재 계면결함의 부분방전 분포 해석)

  • Cho, Kyung-Soon;Hong, Jin-Woong
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.20 no.11
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    • pp.959-964
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    • 2007
  • To investigate the influence of partial discharge(PD) distribution characteristics due to various defects on the power cable joints interface, we used the K-means clustering method. As the result of PD number(n) distribution analyzing on $\Phi-n$ graph, the phase angle($\Phi$) of cluster centroid shifted to $0^{\circ}\;and\;180^{\circ}$ increasing with applying voltage. It was confirmed that the PD quantify(q) and euclidean distance of centroid were increased with applying voltage from the centroid distribution analyzing of $\Phi-q$ plane. The dispersion degree was increased with calculated standard deviation of the $\Phi-q$ cluster centroid. The PD number and mean value on $\Phi-q$ graph were some different by electric field concentration with defect types.

LIPSCHITZ TYPE CHARACTERIZATION OF FOCK TYPE SPACES

  • Hong Rae, Cho;Jeong Min, Ha
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.6
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    • pp.1371-1385
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    • 2022
  • For setting a general weight function on n dimensional complex space ℂn, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.

ON A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALS

  • ZHANG, BIN;ZHOU, YU
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1911-1924
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    • 2015
  • A cyclotomic polynomial ${\Phi}_n(x)$ is said to be ternary if n = pqr for three distinct odd primes p < q < r. Let A(n) be the largest absolute value of the coefficients of ${\Phi}_n(x)$. If A(n) = 1 we say that ${\Phi}_n(x)$ is flat. In this paper, we classify all flat ternary cyclotomic polynomials ${\Phi}_{pqr}(x)$ in the case $q{\equiv}{\pm}1$ (mod p) and $4r{\equiv}{\pm}1$ (mod pq).

SEMI-CYCLOTOMIC POLYNOMIALS

  • LEE, KI-SUK;LEE, JI-EUN;Kim, JI-HYE
    • Honam Mathematical Journal
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    • v.37 no.4
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    • pp.469-472
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    • 2015
  • The n-th cyclotomic polynomial ${\Phi}_n(x)$ is irreducible over $\mathbb{Q}$ and has integer coefficients. The degree of ${\Phi}_n(x)$ is ${\varphi}(n)$, where ${\varphi}(n)$ is the Euler Phi-function. In this paper, we define Semi-Cyclotomic Polynomial $J_n(x)$. $J_n(x)$ is also irreducible over $\mathbb{Q}$ and has integer coefficients. But the degree of $J_n(x)$ is $\frac{{\varphi}(n)}{2}$. Galois Theory will be used to prove the above properties of $J_n(x)$.

Sobolev orthogonal polynomials and second order differential equation II

  • Kwon, K.H.;Lee, D.W.;Littlejohn, L.L.
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.135-170
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    • 1996
  • Recently many people have studied the Sobolev orthogonal polynomials, that is, polynomials which are orthogonal relative to a symmetric bilinear form $\phi(\cdot,\cdot)$ defined by $$ (1.1) $\phi(p,q) := (p,q)_N = \sum_{k=0}^{N} \int_{R}p^(k) (x)q^(k) (x) d\mu_k, $$ where each $d\mu_k$ is a signed Borel measure on the real line $R$ with finite moments of all orders. For the brief history on this subject, we refer to the survey article Ronveaux [13] and Marcellan and et al [10].

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