• East Asian mathematical journal
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• v.35 no.3
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• pp.285-288
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• 2019

Let $F_n$, $n{\in}{\mathbb{N}}$ be the n - th Fibonacci number, and let (p, q) be one of ordered pairs ($F_{n+2}$, $F_n$) or ($F_{n+1}$, $F_n$). Then we show that the multiplicative inverse of q mod p as well as that of p mod q are again Fibonacci numbers. For proof of our claim we make use of well-known Cassini, Catlan and dOcagne identities. As an application, we determine the number $N_{p,q}$ of nonzero term of a polynomial ${\Delta}_{p,q}(t)=\frac{(t^{pq}-1)(t-1)}{(t^p-1)(t^q-1)}$ through the Carlitz's formula.

• Journal of Intelligence and Information Systems
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• v.12 no.1
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• pp.107-123
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• 2006

We propose the Generalized Binary Second-order Recurrent Neural Networks(GBSRNNf) being equivalent to regular grammars and ?how the implementation of lexical analyzer recognizing the regular languages by using it. All the equivalent representations of regular grammars can be implemented in circuits by using GSBRNN, since it has binary-valued components and shows the structural relationship of a regular grammar. For a regular grammar with the number of symbols m, the number of terminals p, the number of nonterminals q, and the length of input string k, the size of the corresponding GBSRNN is $O(m(p+q)^2)$ and its parallel processing time is O(k) and its sequential processing time, $O(k(p+q)^2)$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1181-1188
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• 2010

q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)=[2]q \sum\limits_{n=0}^\infty\frac{(-1)^n\epsilon^nq^{sn}}{[n]_q}$$ where 0 < q < 1, $\mathfrak{R}$(s) > 1, $\varepsilon{\in}T_p$, which are compared with Euler q-zeta functions in the reference ([18]). Furthermore, we give the q-extensions of the above twisted Lerch type Euler zeta functions at negative integers which interpolate twisted q-Euler polynomials.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.843-867
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• 2022

Maynard proved that there exists an effectively computable constant q1 such that if q ≥ q1, then $\frac{{\log}\;q}{\sqrt{q}{\phi}(q)}Li(x){\ll}{\pi}(x;\;q,\;m)<\frac{2}{{\phi}(q)}Li(x)$ for x ≥ q8. In this paper, we will show the following. Let 𝛿1 and 𝛿2 be positive constants with 0 < 𝛿1, 𝛿2 < 1 and 𝛿1 + 𝛿2 > 1. Assume that L ≠ ℚ is a number field. Then there exist effectively computable constants c0 and d1 such that for dL ≥ d1 and x ≥ exp (326n𝛿1L(log dL)1+𝛿2), we have $$\|{\pi}_C(x)-\frac{{\mid}C{\mid}}{{\mid}G{\mid}}Li(x)\|\;{\leq}\;\(1-c_0\frac{1og\;d_L}{d^{7.072}_L}\)\;\frac{{\mid}C{\mid}}{{\mid}G{\mid}}Li(x)$$.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.391-410
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• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.2
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• pp.37-43
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• 2008

The performance and hardware complexity of LDPC decoders depend on the design parameters of quantization, the clipping threshold $c_{th}$ and the number of quantization bits q, and also on the maximum number of decoding iterations. In this paper, the BER performances of LDPC codes are evaluated according to the clipping threshold $c_{th}$ and the number of quantization bits q through the simulation studies. By comparing the quantized Min-Sum algorithm with the ideal Min-Sum algorithm, it is shown that the quantized case with $c_{th}=2.5$ and q=6 has the best performance, which approaches the idea case. The decoding complexities are calculated and the word error rates(WER) are estimated by using the pdf which is obtained through the statistical analyses on the iteration numbers. These results can be utilized to tradeoff between the decoding performance and the complexity in LDPC decoder design.

• Korean Journal of Plant Resources
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• v.30 no.2
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• pp.213-218
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• 2017

Rice is the staple food of at least half of the world's population. Due to global warming, the weather is difficult to forecast nowadays. Therefore, it is necessary to breed various breeding to respond to such changes in the environment. This study was conducted to analyze the QTL about plant form, culm length, ear number and ear length by using 120 lines by anther culture, a cross between the Indica variety Cheongcheong and Japonica variety Nagdong. DNA marker was selected on the QTLs gene, and the following results were obtained. CNDH (Cheongcheong Nagdong Doubled Haploid) lines frequency distribution table curves about culm length, ear number and ear length exhibited showed a continuous variation close to a normal distribution. QTL analysis result, on culm length qPlL1-1 and qPlL1-2 were detected on the chromosome 1 and qPlL5 was detected on the chromosome 5. However, on ear length qPL2, qPL3 and qPL10, were detected on the chromosome 2, 3 and 10, while on ear number qPN1-1 and qPN1-2 were detected on the chromosome 1, qPN9 was detected on the chromosome 9. The QTLs related to culm length was found to chromosomes 5 and LOD scores were 3.81. The QTLs related to ear length was found to chromosomes 2 and 3 LOD scores were 7.13 and 3.20. The QTLs related to ear number was found to chromosome 9 and LOD scores were 4.27. Twenty two (22) Japonica cultivars and 12 Indica cultivars were analyzed polymorphisms, using selected 9 markers from the result about plant form analysis. RM5311, RM555 and RM8111 about the culm length, the ear length and number of ear were selected on the standard of Cheongcheong and Nagdong. Each rate of concordances about the culm length, the ear length and number of ear are 44.11%, 41.17% and 44.11%.

• Korean Journal of Optics and Photonics
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• v.6 no.3
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• pp.245-256
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• 1995

Rugate filters of inhomogeneous refractive index were designed using the Fourier transform and the effect of reflectance, stop bandwidth, optical thickness, and Q function on the rugate filter was investigated. An iterative correction process using a merit function was employed to fit an initial design to the target spectrum. Three Q functions derived by Sossi, Bovard, and Fabricius, respectively, were compared in terms of the number of iteration, merit function, and optimum optical thickness. The result shows that after a number of iterations the Q functions by Bovard and Fabricius produce high rejection rugate filters closer to the target spectrum than the Sossi's Q function and the optimal optical thickness is determined by the stop-band width of the rugate filter. ilter.

• Journal of the Korean Institute of Landscape Architecture
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• v.21 no.2
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• pp.107-119
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• 1993

This study was conducted to increase to increase the plant species diversity, which was based on the analysis of plant community structure and the survey of human's disturbance degree in Mt. Yongma and Mt. Acha urban nature park, Seoul. The plant community were divided into four groups by TWINSPAN and DCA. These groups were Pinus rigida-P. densiflora community, Quercus mongolica-Q.aliena-Q.accutissima community, Robinia pseudoacaia-Q.accutissima-Poplus${\times}$albaglandulosa community and R.pseudoacacia community. The successional trends of tree species seems to be from P.densiflora, P.rigida, Sorbus alniflora to Q.mongolica, Q.aliena and from P.${\times}$albaglandulosa, R.pseudoacacia, through Q.accutissima, to Q. mongolica, Q.aliena. The species diversity of plant community was high in natual plant community but was low in artificial planting community respectively. Number of species, number of species individuals, indices of species diversity was lowered and soil hardness was increased by the user's trampling, undercutting work and planting P.koraiensis after thinning. In the basis of study results, we proposed the management plan for the urban forest.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.6
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• pp.221-228
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• 2013

It is impossible directly to find a prime number p,q of a large semiprime n = pq using Trial Division method. So the most of the factorization algorithms use the indirection method which finds a prime number of p = GCD(a-b, n), q=GCD(a+b, n); get with a congruence of squares of $a^2{\equiv}b^2$ (mod n). It is just known the fact which the area that selects p and q about n=pq is between $10{\cdots}00$ < p < $\sqrt{n}$ and $\sqrt{n}$ < q < $99{\cdots}9$ based on $\sqrt{n}$ in the range, [$10{\cdots}01$, $99{\cdots}9$] of $l(p)=l(q)=l(\sqrt{n})=0.5l(n)$. This paper proposes the method that reduces the range of p using information obtained from n. The proposed method uses the method that sets to $p_{min}=n_{LR}$, $q_{min}=n_{RL}$; divide into $n=n_{LR}+n_{RL}$, $l(n_{LR})=l(n_{RL})=l(\sqrt{n})$. The proposed method is more effective from minimum 17.79% to maxmimum 90.17% than the method that reduces using $\sqrt{n}$ information.