• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.457-466
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• 2004

Let{$X_{ni}$\mid$\;1\;{\leq}\;i\;{\leq}\;k_n,\;n\;{\geq}\;1$} be an array of rowwise negatively associated random variables such that $P$\mid$X_{ni}$\mid$\;>\;x)\;=\;O(1)P($\mid$X$\mid$\;>\;x)$ for all $x\;{\geq}\;0,\;and\; \{k_n\}\;and\;\{r_n\}$ be two sequences such that $r_n\;{\geq}\;b_1n^r,\;k_n\;{\leq}\;b_2n^k$ for some $b_1,\;b_2,\;r,\;k\;>\;0$. Then it is shown that $\frac{1}{r_n}\;max_1$\mid${\Sigma_{i=1}}^j\;X_{ni}$\mid$\;{\rightarrow}\;0$ completely convergence and the strong convergence for weighted sums of N A arrays is also considered.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.427-436
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• 2005

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and v be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple v-ideals $m=P_0\;{\supset}\;P_1\;{\supset}\;{\cdotS}\;{\supset}\;P_t=P$ and all the other v-ideals are uniquely factored into a product of those simple ones. It then was also shown by Lipman that the predecessor of the smallest simple v-ideal P is either simple (P is free) or the product of two simple v-ideals (P is satellite), that the sequence of v-ideals between the maximal ideal and the smallest simple v-ideal P is saturated, and that the v-value of the maximal ideal is the m-adic order of P. Let m = (x, y) and denote the v-value difference |v(x) - v(y)| by $n_v$. In this paper, if the m-adic order of P is 2, we show that $O(P_i)\;=\;1\;for\;1\;{\leq}\;i\; {\leq}\;{\lceil}\;{\frac{b+1}{2}}{\rceil}\;and\;O(P_i)\;=2\;for\;{\lceil}\;\frac{b+3}{2}\rceil\;{\leq}\;i\;\leq\;t,\;where\;b=n_v$. We also show that $n_w\;=\;n_v$ when w is the prime divisor associated to a simple v-ideal $Q\;{\supset}\;P$ of order 2 and that w(R) = v(R) as well.

• Journal of the Korean Academy of Clinical Electrophysiology
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• v.6 no.1
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• pp.17-30
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• 2008

This study was investigated the effects of pain and functional recovery when low frequency electrical stimulation and aquatic exercise applied to sciatic nerve injured rats. The rats were assigned into four groups; Group I(n=20, control group), Group II(n=20, low frequency electrical stimulation group), Group III(n=20, aquatic exercise group), Group (n=20, applied low frequency electrical stimulation and aquaatic exercise group). Each IV group measured hot plate examination, sciatic nerve functional index(SFI), c-fos.. In hot plate examination, group II, IV showed effect than group Iat 14 days after injured(p<0.01) and group III, Ⅳ showed effect than group I at 21, 28 days after in-jured(p<0.01, p<0.001). In SFI, group II, III, IV showed effect II, III, IV than group I and group IV showed effect than group II at 14, 21 days after injured(p<0.001). group II, III, IV showed effect than group I at 28 days after injured(II = p<0.01, III and IV = p<0.001). Effects of pain and function recovery when low frequency electrical stimulation and aqua-exercise applied to sciatic nerve injured rats, group Ⅳ were most effected to sciatic nerve injured rats. As well as group II and III were effected to sciatic nerve injured rats.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.3
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• pp.111-117
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• 2014

In this paper I propose a simple optimal solution seeking algorithm to a stable marriage problem. The proposed algorithm firstly constructs an $n{\times}n$ matrix of the sum of each gender's preference of the other gender $p_{ij}$. It then selects the minimum sum preference $_{min}p_{ij}$ in the constructed matrix and deletes its corresponding row i and column j. This process is repeated until $i=0{\cap}j=0$, after which the algorithm compares initially or last chosen $_{min}p_{ij}$ its alternatives to finally determine one that yields the maximum marginal increase in preference. When applied to 7 stable marriage problems, the proposed algorithm has improved on initial solutions of existing algorithms.

• East Asian mathematical journal
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• v.31 no.1
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• pp.103-107
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• 2015

We use some known contiguous function relations for $_2F_1$ to show how simply the following three recurrence relations for Jacobi polynomials $P_n^{({\alpha},{\beta)}(x)$: (i) $({\alpha}+{\beta}+n)P_n^{({\alpha},{\beta})}(x)=({\beta}+n)P_n^{({\alpha},{\beta}-1)}(x)+({\alpha}+n)P_n^{({\alpha}-1,{\beta})}(x);$ (ii) $2P_n^{({\alpha},{\beta})}(x)=(1+x)P_n^{({\alpha},{\beta}+1)}(x)+(1-x)P_n^{({\alpha}+1,{\beta})}(x);$ (iii) $P_{n-1}^{({\alpha},{\beta})}(x)=P_n^{({\alpha},{\beta}-1)}(x)+P_n^{({\alpha}-1,{\beta})}(x)$ can be established.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.4
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• pp.302-312
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• 2001

As the data transfer rate between chips gets higher, both crosstalk and SSN (Simultaneous Switching Noise) deteriorate seriously the performance of a system. The proposed interface scheme uses P-CTR and N-CTR(Positive/Negative Constant Transition Rate) which encodes data at both falling and rising edges, where the transition directions of N-CTR and P-CTR are opposite. And the proposed bus system places two P-CTR drivers and two N-CTR drivers alternatively. In the proposed P/N-CTR interface scheme, the signals of neighboring interconnection lines at both sides of a bus will not switch simultaneously in the same direction, which leads to reduction in the maximum crosstalk and SSN compared to conventional interfaces. For verification of noise reduction of the proposed interface scheme, the scheme is applied to several kinds of bit-wide buses with various interconnection structures, and HSPICE simulation was performed with 0.35 ${\mu}{\textrm}{m}$ SPICE parameters. The simulation results show that in the 32-bit or less wide bus, the maximum SSN and crosstalk are reduced to at least 26.78% and 50%, respectively in comparison with the conventional interface scheme.

• Korean Journal of Optics and Photonics
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• v.8 no.6
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• pp.500-505
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• 1997

Experimental amorphous photodiode is fabricated on CMOS IC using a-Si:H p-i-n structure. Amorphous photodiode is scuccessfully integrated on CMOS IC using amorphous Si produced by PECVD system. The PECVD system can deposit a-Si:H at low temperature so that photodiode can be integrated with CMOS IC structure without any process incompatibility. The fabricated amorphous photodiode has a breakdown voltage of below -20 V, a leakage current of about 1 $\mu\textrm{A}$, and turn-on voltage of 0.6~0.8 V. It is demonstrated that the photocurrent of optical signal can be turned on and off by a small voltage and the fabricated amorphous p-i-n photodiode can be used as an optical switch.

• The Journal of Natural Sciences
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• v.9 no.1
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• pp.57-60
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• 1997

Let {$X_{ni}$,1$\leq$i$\leq$,n$\geq$1} be an array of rowwise independent B-valued random variables which is uniformly bounded by a random various X satisfying $E|X|^{2p}<\infty$ for some p$\geq$1. Let {$a_{ni}$,1$\leq$i$\leq$,n$\geq$1} be an array of constants. Under some auxiliary conditions on {$a_{ni}$}, it is shown that $sum_{i=1}^n a_{ni}X_{ni}\rightarrow0$ in probability if and only if $sum_{i=1}^n a_{ni}X_{ni}$ converges completely ot 0.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.511-528
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• 2008

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and $\upsilon$ be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple $\upsilon$-ideals $m\;=\;P_0\;{\supset}\;P_1\;{\supset}\;{\cdots}\;{\supset}\;P_t\;=\;P$ and all the other $\upsilon$-ideals are uniquely factored into a product of those simple ones [17]. Lipman further showed that the predecessor of the smallest simple $\upsilon$-ideal P is either simple or the product of two simple $\upsilon$-ideals. The simple integrally closed ideal P is said to be free for the former and satellite for the later. In this paper we describe the sequence of simple $\upsilon$-ideals when P is satellite of order 3 in terms of the invariant $b_{\upsilon}\;=\;|\upsilon(x)\;-\;\upsilon(y)|$, where $\upsilon$ is the prime divisor associated to P and m = (x, y). Denote $b_{\upsilon}$ by b and let b = 3k + 1 for k = 0, 1, 2. Let $n_i$ be the number of nonmaximal simple $\upsilon$-ideals of order i for i = 1, 2, 3. We show that the numbers $n_{\upsilon}$ = ($n_1$, $n_2$, $n_3$) = (${\lceil}\frac{b+1}{3}{\rceil}$, 1, 1) and that the rank of P is ${\lceil}\frac{b+7}{3}{\rceil}$ = k + 3. We then describe all the $\upsilon$-ideals from m to P as products of those simple $\upsilon$-ideals. In particular, we find the conductor ideal and the $\upsilon$-predecessor of the given ideal P in cases of b = 1, 2 and for b = 3k + 1, 3k + 2, 3k for $k\;{\geq}\;1$. We also find the value semigroup $\upsilon(R)$ of a satellite simple valuation ideal P of order 3 in terms of $b_{\upsilon}$.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.19-25
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• 2017

This paper deals with integer factorization of two prime p,q of SHA-256 secure hash value n for Bit coin mining. This paper proposes an algorithm that greatly reduces the execution time of Pollard's rho integer factorization algorithm. Rho(${\rho}$) algorithm computes $x_i=x^2_{i-1}+1(mod\;n)$ and $y_i=[(y^2_{i-1}+1)^2+1](mod\;n)$ for intial values $(x_0,y_0)=(2,2)$ to find the factor 1 < $gcd({\mid}x_i-y_i{\mid},n)$ < n. It however fails to factorize some particular composite numbers. The algorithm proposed in this paper applies multiple initial values $(x_0,y_0)=(2^k,2^k)$ and ($2^k,2$), $2{\leq}k{\leq}10$ to the existing Pollard's Rho algorithm. As a results, the proposed algorithm achieves both the factorization of all the composite numbers and the reduction of the execution time of Pollard's Rho by 67.94%.