• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

• Proceedings of the Korea Multimedia Society Conference
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• 2000.11a
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• pp.45-48
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• 2000

본 논문은 현재 고성능 가역압축 부호화의 표준이 되는 JPEG-LS의 예측오차에 대한 확률분포를 결정하는 컨텍스트 모델링(context modelling)에서 컨텍스트 정수의 결정 방법에 관해 기술한다. 먼저, 압축률 향상을 위해 낮은 대비(low contrast)를 적용하는 전처리 과정을 도입한다. 둘째로, 낮은 복잡도(low complexity)를 위해 주목화소와 주변화소 사이의 차분을 양자화하고, 그 값 Q$_1$,Q$_2$, Q$_3$로부터 컨텍스트 정수(Q)의 결정을 위해 우선 순위를 정한 후, 3차원 가상좌표 위로의 할당을 고려한다. 또한, 제안 방법과 JPEG-LS의 near-lossless부분을 비교하여, 다양한 영상에 대하여 적용시켜 본 결과, 제안한 방법의 압축률과 손실이득이 훨씬 좋음을 보인다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.11
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• pp.1735-1741
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• 1993

New family of frequency hopping patterns with long period and good Hamming autocorrelation and Hamming crosscorrelation properties which can be used for frequency hopped multiple access communication systems is introduced. Period of frequency hopping patterns is qk-1, the alphabet size of frequency hopping patterns is q, and the size of family of frequency hopping patterns is q, where k is arbitrary integer and q is power of prime number. The maximum value of out-of-Phase Hamming autocorrelation function of any frequency hopping pattern and Hamming crosscorrelation function of any two frequency hopping patterns in the family is qk-1, which corresponds to optima1 Hamming correlation properties. And the average number of hits per q*q square in one frequency hopping pattern and its time shifted version or two frequency hopping patterns in the frequency hopped multiple access communication systems is less than 1.

• Journal of Marine Bioscience and Biotechnology
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• v.2 no.2
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• pp.120-122
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• 2007

A $Q_{10}$-producing photosynthetic bacterium was isolated from the silt at Nakdong river. The isolate had 1.55 mg of $Q_{10}$ per gram of dry cell. By the 16s-rDNA sequence analysis, the isolate was found to be Rhodobacter sphaeroids with 100% similarity (Genbank Accession No.=AM696701).

• The Journal of Engineering Geology
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• v.16 no.3 s.49
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• pp.283-291
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• 2006

Shotcrete is used as a permanent lining in single shell tunnels even though shotcrete has been used as a temporary lining in NATM tunnels. Therefore, the accurate evaluation of strength parameters is very crucial because the reliable estimation of loads acting on the shotcretes is necessary to maintain the stability of tunnels. The evaluation of strength parameters of the ground far the single shell tunnels should be investigated to adapt the method in Korea because the geological condition of Korea is different from that of other country. Rock classification and strength parameters obtained from 25 tunnel sites were investigated for this study. Support types fur the different rock classes are suggested for the single shell tunnels in Korea based on the NMT because Q-system has been widely used in Korea. The support types in terms of both Q and RMR values are given based on the correlation of Q and RMR values obtained from the case studies.

• Proceedings of the Korean Vacuum Society Conference
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• 2003.02a
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• pp.191-191
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• 2003

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.2
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• pp.15-22
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• 2004

For an ElGamal-type signature scheme using a generate g of order q, it has been well-known that the message nonce should be chosen randomly in the interval (0, q-1) for each message to be signed. In (2), H. Kuwakado and H. Tanaka proposed a polynomial time algorithm that gives the private key of the signer if two signatures with message nonces 0＜$k_1$, $k_2$$\leq$Ο(equation omitted) are available. Recently, R. Gallant, R. Lambert, and S. Vanstone suggested a method to improve the efficiency of elliptic curve crytosystem using integer decomposition. In this paper, by applying the integer decomposition method to the algorithm proposed by Kuwakado and Tanaka, we extend the algorithm to work in the case when ｜$k_1$ ｜,｜$k_2$, ｜$\leq$Ο(equation mitted) and improve the efficiency and completeness of the algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.9
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• pp.759-764
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• 2013

We present a square root algorithm in $F_q$ which generalizes Atkin's square root algorithm [9] for finite field $F_q$ of q elements where $q{\equiv}5$ (mod 8) and Kong et al.'s algorithm [11] for the case $q{\equiv}9$ (mod 16). Our algorithm precomputes ${\xi}$ a primitive $2^s$-th root of unity where s is the largest positive integer satisfying $2^s|q-1$, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, M$\ddot{u}$ller and Kong et al.

• Journal of the Korea Society of Computer and Information
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• v.3 no.2
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• pp.183-188
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• 1998

This paper proposes an extended RSA public-key cryptosystem which extends a conventional one. The number of multiplication times has been increased by extending the modulus parameters p, q. This result shows the increase of computational complexity which required in cryptanalysis. It also improves the strength of RSA public key cryptosystem through this proof which is based on integral number theory.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.10
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• pp.507-511
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• 2005

We have derived the linear complexity of a binary sequence generated by a Feedback with Carry Shift Regiater(FCSR) under the following condition: q is a power of a prime such that $q=r^e,\;(e{\geq}2)$ and r=2p+1, where both r and p are 2-prime. Also, a summation generator creates sequence from addition with carry of LFSR(Linear Feedback Shift Register) sequences. Similarly, it is possible to generate keystream by bitwise exclusive-oring on two FCSR sequences. In this paper, we described the cryptographic properties of a sequence generated by the FCSRs in view of the linear complexity.