• 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 $b_{\upsilon}$.

• Journal of the Korean Wood Science and Technology
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• v.31 no.6
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• pp.31-39
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• 2003

The enzymatic isolation of residual lignins obtained from spruce and beech pulps (obtained by sulfite, kraft, ASAM and soda/AQ/MeOH pulping processes) and their characterization was described in previous publications. Here, the residual lignins have been submitted to potassium permanganate oxidation (KMnO₄ degradation), and 9 aromatic carboxylic acids (3 of them are dimeric) were identified after methylation with diazomethane by GC/MS. The analytical challenge during qantification by the internal standard methods was the partly high protein content of the samples, which resulted in elevated anisic acid yields in the degradation mixture of sulfite residual lignins. The results are compared with the KMnO₄ degradation of the corresponding MWLs and discussed in terms of S/G ratios and degrees of condensation. The latter was calculated as a quotient between the aromatic carboxylic acids derived from condensed and non-condensed lignin structures. Typical degradation patterns for the various processes have been observed. Among other parameter, the relative compositions between iso-hemipinic acid (which is for condensation in pos. 5 of the aromatic ring) and meta-hemipinic acid and 3,4,5-trimethoxyphthalic acid (both are for condensation in pos. 6 of the aromatic ring) was found to be process specific. Kraft and soda/AQ/MeOH residual lignins yielded higher amounts of iso-hemipinic acid. In contrast, the relative yields of meta-hemipinic acid and 3,4,5-trimethoxyphthalic acid (the latter in beech lignins) are higher in sulfite and particularly in ASAM residual lignin. In case of beech residual lignins the amount of acids originated from non-condensed syringyl type lignin units was surprisingly high. The condensation degree of residual lignins was shown to be generally higher than that of MWLs. This was especially true for the G units. ASAM residual lignin exhibited very high S/G ratios and degrees of polymerization. Causality between condensation degree and total yield of degradation products was demonstrated.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.875-883
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• 2012

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.

• Journal of Biomedical Engineering Research
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• v.25 no.5
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• pp.343-349
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• 2004

Electroglottograph(EGG) is a signal recorded from the vocal cord vibration by measuring electrical impedance across the vocal folds through the neck skin. The purpose of this study was to develop EGG system and to evaluate possibility for the application on speech analysis and laryngeal disease diagnosis. EGG system was composed of two pairs of ring electrodes, tuned amplifier, phase sensitive detector, low pass filter, and auto-gain controller. It was designed to extract electric impedance after detecting by amplitude modulation method with 2.7MHz carrier signal. Extracted signals were transmitted through line-in of PC sound card, sampled and quantized. Closed Quotient(CQ), Speed Quotient(SQ), Speed Index(SI), fundamental frequency of vocal cord vibration(F0), pitch variability of vocal fold vibration (Jitter), and peak-to-peak amplitude variability of vocal fold vibration(Shimmer) were analyzed as EGG parameters. Experimental results were as follows: the faster vocal fold vibration, the higher values in CQ parameter and the lower values in SQ and SI parameters. EGG and speech signals had the same fundamental frequency. CQ, SQ, and SI were significantly different between normal subjects and patients with laryngeal cancer. These results suggest that it is possible to implement portable EGG system to monitor the function of vocal cord and to test functional changes of the glottis.

• 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 for History of Mathematics
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• v.21 no.4
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• pp.1-10
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• 2008

In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.

• The KIPS Transactions:PartD
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• v.10D no.6
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• pp.1059-1066
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• 2003

In this paper, the magnetic sensing system is designed and implemented for the safe security in internet commerce system. When the payment is required inthe internet commerce system, the magnetic sensing system will get the information from a credit card without keyboard input and then encrypt and transmit the information to server. The credit card sensing system, which is proposed in this paper, is safe from keyboard hacking because it encrypts card information immediately in its internal chip and sends the information to host system. For the protection of information, the magnetic sensing system is basically based on a synchronous stream cipher cryptosystem which is related to a group of matrices. The size of matrices and the bits of keys for the best performances are determined for various cases. It is shown that for credit card payments. matrices of size 2 have good performance even at most 128bits keys with the consideration of inverse matrices. For authentication of general-purpose data, the magnetic sensing system needs more than 1.5KB data and in this case, the optimum size of matrices is 2 or 3 at more 256bits keys with consideration of inverse matrices.

• Journal of the Korean Geographical Society
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• v.30 no.1
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• pp.68-92
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• 1995

Recentry the structure of the retail trade have been chanaed with its environmantal changes. Some studies may be necessary on the changing process of environment and fundamental structure analyses of the retail trade. This study analyzes the location of retail trades, inhabitants' behavior in retail tredes and their desirable utilization scheme of them in Kwangju-si. Some study methods, contents and coming-out results are as follows: 1. Retail trades can be classified into independent stores, chain-stores (supermarket, voluntary chain and frenchiise system and convenience store), department stores, cooperative associations, traditional, markets mail-order marketing, automatic vending and others by service levels, selling-items, prices, managements, methods of retailing and store or nonstore type. 2. In Kwangju, the environment of retail trades is related to the consumers of population structure: chanes in consumers pattern, trends toward agings and nuclear family, increase of leisur: time and female advances to society. Rapid structural shift in retail trade has also been occurred due to these social changes. Traditionl and premodern markets until 1970s altere to supermarkets or department stores in 1980s, and various types, large enterprises and foreign capitals came into being in 1990s. 3. The locational characteristics of retail trades are resulted from the spatial analysis of the total population distribution, and from the calculation of segregation index in the light of potential demand. The densely-populated areas occurs in newly-built apartment housing complex which is distributed with a ring-shaped pattern around the old urban core. The numbers and rates of the aged over sixty in Kwangsan-gu and the circumference area of Mt.Moodeung, are larger and higher where rural elements are remarkable. A relation between population distribution and retail trade are analysed by the index of population per shop. The index of the population number per shop is lower in urban center, as a whole, being more convenient for consumers. In newly-formed apartment complex areas, on the other, the index more than 1,000 per shop, meeting not the demands for consumers. Because both the younger and the aged are numerous in these areas, the retail trade pattern pertinent to both are needed. Urban fringes including Kwangsan-gu and the vicinity of Mt.Moodeung have some problems owing to the most of population number per shop (more than 1, 500) and the most extensive as well. 4. The regional characteristic of retail trade is analyzed through the location quotient of shops by locational patterns and centerality index. Chungkum-dong is the highest-order central place in CBD. It is the core of retail trades, which has higher-ordered specialty store including three big department stores, supermarkets and large stores. Taegum-dong, Chungsu-dong, Taeui-dong, and Numun-dong that are neiahbored to Chungkum-dong fall on the second group. They have a central commercial section where large chain stores, specialty shopping streets, narrow-line retailing shops (furniture, amusement service, and gallary), supermarkets and daily markets are located. The third group is formed on the axis of state roads linking to Naju-kun, Changseong-kun, Tamyang-kun, Hwasun-kun and forme-Songjeong-eup. It is related to newly, rising apartment housing complex along a trunk road, and characterized by markets and specialty stores. The fourth group has neibourhood-shopping centers including older residential area and Songjeong-eup area with independent stores and supermarkets as main retailing functions. The last group contains inner residential area and outer part of a city including Songjeong-eup. Outer part of miscellaneous shops being occasionally found is rural rather than urban (Fig. 7). 5. The residents' behaviors using retail trade are analyzed by factors of goods and facilities. Department stores are very high level in preference for higher-order shopping-goods such as clothes for full dress in view of both diversity and quality of goods(28.9%). But they have severe traffic congestions, and high competitions for market ranges caused by their sma . 64.0% of respondents make combined purpose trips together with banking and shopping. 6. For more efficiency of retail-trading, it is necessary to induce spatial distribution policy with regard to opportunity frequency of goods selection by central place, frontier regions and age groups. Also we must consider to analyze competition among different types of retail trade and analyze the consumption behaviors of working females and younger-aged groups, in aspects of time and space. Service improvement and the rationalization of management should be accomplished in such as cooperative location (situation) must be under consideration in relations to other functions such as finance, leisure & sports, and culture centers. Various service systems such as installment, credit card and peremium ticket, new used by enterprises, must also be carried service improvement. The rationalization and professionalization in for the commercial goods are bsically requested.