• 대한수학회보
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• 제52권1호
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• pp.35-43
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• 2015

Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

• ALGAE
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• 제19권4호
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• pp.303-309
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• 2004

The laboratory culture study of Porphyra seriata Kjellman from Korea was conducted at different conditions of temperatures (5, 10, 15, 20, 25 and 30${^{\circ}C}$), photon flux densities (10, 20, 40 and 80 $\mu$mol $^{-2}s^{-1}$) and photoperiods (14L: 10D and 10L:14D). Conchocelis filaments grew fast at 15-20${^{\circ}C}$ and 20-80 $\mu$mol $^{-2}s^{-1}$ under both photoperiods. Concho sporangial branches were produced at 5-25${^{\circ}C}$, and abundant when the conchocelis filaments were cultured at higher temperatures of 20-25${^{\circ}C}$ under both photoperiods. Foliose thalli grew well at 15-20${^{\circ}C}$ under 10L:14D and at 20${^{\circ}C}$ under 14L:10D. At 30${^{\circ}C}$, the foliose thallus failed to survive. No archespores were observed at any culture conditions. Spermatangia and zygotosporangia were formed in squarish patches at the upper marginal portion of mature thalli. Anatomical examination revealed that the mature spermatangia were 64 (a/4, b/2, c/8) and 128 (a/4, b/4, c/8), and that of zygotosporangium was 16 (a/2, b/2, c/4) according to the Hus' formula.

• 대한화학회지
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• 제34권6호
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• pp.517-526
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• 1990

D-glucitol hexaacetate 와 xylitol pentaacetate의 결정구조를 단결정 X-선 회절법으로 연구하였다. D-glucitol hexaacetate 는 공간군 P2$_1$, 단위세포 상수는 a = 10.275 (2), b = 8.363 (1), c = 12.560 (5) $\AA$, $\beta$= 95.97 $(2)^{\circ}$; Z = 2이고, xylitol pentaacetate는 공간군이 P2$_1$/C이고, a = 18.126 (1), b = 11.422 (2), c = 8.649 (1) $\AA$, $\beta$ = 95.03 $(1)^{\circ}$이며 Z = 4이다. 회절세기는 diffractomerer로 얻었고, 분자구조는 직접법으로 밝혔으며, 최소자승법으로 정밀화하였다. 두 분자에 결쳐 결합의 평균길이는 C($sp^3)-C(sp^3$)가 1.514 (10), C($sp^3)-O: 1.444 (6),\; C(sp^2)-O: 1.347 (9),\; C(sp^2)=O: 1.197 (6),\; C(sp^2)-C(sp^3): 1.479(9){\AA}$이고, 평균 결합각도는 C($sp^3)-C(sp^3)-C(sp^3): 114.6 (17),\; O-C(sp^3)-C(sp^3): 109.4 (23),\; C(sp^2)-O-C(sp^3): 117.4 (6),\; O=C(sp^2)-O: 122.6 (6),\; C(sp^3)-C(sp^2)-O: 111.8 (7), C(sp^3)-C(sp^2)=O: 125.5 (4)${\circ}$이다. 두 분자내의 탄소 사슬들은 extended zigzag chain으로 되어 있어 D-glucitol과 xylitol 분자들의 conformation과는 다르다. Acetate group들의 각 원자들은 모두 한 평편상에 놓여있다.

• Advances in Traditional Medicine
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• 제10권4호
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• pp.319-321
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• 2010

Plant saponins are widely distributed amongst plants and have a wide range of biological properties. Icosahydropicenic acid, $C_{51}H_{80}O_{19}$ ((4S,6bS)-8a-((4,5-dihydroxy-6-methyl-3-((3R)-3,4,5-trihydroxy-6-methyl-tetrahydro-2H-pyran-2-yloxy)-tetrahydro-2H-pyran-2-yloxy)carbonyl)-2-hydroxy-4, 6a, 6b, 11, 14b-pentamethyl-11-(2-methylprop-1-enyl)-3-(3,4,5-trihydroxy-6-(hydroxymethyl) - tetrahydro-2Hpyran-2-yloxy)-1, 2, 3, 4, 4a, 5, 6, 6a, 6b, 7, 8, 8a, 9, 10, 11, 12, 12a, 14, 14a, 14b-icosahydropicene-4-carboxylic acid), a new saponin was first time isolated from the roots of Clerodendrum Serratum (L) Moon (Verbenaceae). The structure elucidation of the compound was carried out by $^1H$ NMR and DART-MS studies.

• 대한수학회지
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• 제43권2호
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• The Korean Journal of Ecology
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• 제21권3호
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• pp.269-276
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• 1998

The study of the Rana plancyi, was done during the calling period at a pond in Osong, Chungbuk, Korea from May to the middle of August of 1996 and 1997. Five basic types of call-A, B, C, D, E, - were identified in Rana plancyi according to the structure of call types. The structure of A type call has only one pulse, B type call has two pulses and C, D type call has one separated pulse which is called introductory call and pulse group as follow it. On the other hand, E type call has 3-6 separate pulses. The interval between introductory call and pulse group is $0.73{\pm}0.29$ s(n=159) in C type call and $0.60{\pm}0.21$ s (n=48) in D type call. The number of pulses in the pulse group is $30.08{\pm}8.69$ in C type call and $15.78{\pm}2.40$ in D type call. An increase in water temperature induces a decrease in C and D type call duration (C type call r= -0.4153, p<0.001, D type call r=-0.7064, p<0.001). In case of C and D type call, the interval between introductory call and pulse group influenced more call duration than pulse group duration. We regarded A, B type call as a territorial call and C, D type call as a mating call and we recognized that E type call has the function of threat or alarm.

• 대한치과교정학회지
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• 제21권1호
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• pp.171-183
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• 1991

This investigation was designed to categorize Angle's class II malocclusion groups through analyzing horizontal and vertical components of craniofacial skeleton in Angle's class II malocclusion. The material selected for this study consisted in standard lateral cephalogram of two hundred and twenteen children, eighty eight boys and one hundred twenty four girls, aged 6 through 18 years, having Angle's class II malocclusion. On the basis of findings of this study, the following results were obtained. 1. In horizontal skeletal classifications, 16 groups were classified according to FMN-A-B, SE-FMN-A, Ba-SE-Me, Ba-Se/Ra P. The sequences that have relatively high frequency are as follows: a) Horizontal Group 16 b) Horizontal Group 12 c) Horizontal Group 13 d) Horizontal Group 9 & 15 2. In vertical skeletal classification, 8 groups were classified according to the PMV/PP, PMV/Occ. P. PMV/Mn. P. The sequences that relatively high frequency are as follows; a) Vertical Group A b) Vertical Group D c) Vertical Group C d) Vertical Group H 3. In vertical and horizontal skeletal classifications, the sequence that relatively high frequency are as follows; a) Group13-A b) Group16-A & 9-A c) Group12-A & 15-A d) Group16-C

• 대한소아치과학회지
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• 제8권1호
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• pp.89-102
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• 1981

1147 preschool children aged from 3 to 6 living in some farm villages in Kyungki-do were surveyed on dmf and distribution of dental caries in primary dentition. The results were as follows: 1. dmf rate ... 92.76 % boy ... 94.52 % girl ... 90.5.5 % 2. dmf t rate ... 37.07 % dmf t index ... 7.09 3. dmf s rate ... 13.74 % dmf s index ... 13.14 % 4. df t index ... 6.94 5. Each percentage of d, m & f per dmf teeth d rate ... 89.96 % m rate ... 7.24 % f rate ... 2.67 % 6. Most frequent site of dental caries in each tooth $\underline{A}$ mesial $\overline{A}$ distal $\underline{B}$ mesial $\overline{B}$ distal $\underline{C}$ distal $\overline{C}$ distal $\underline{D}$ disto-occlusal $\overline{D}$ disto-occlusal $\underline{E}$ linguo-occlusal $\overline{E}$ occlusal 7. Order of caries susceptibility $\overline{E}$ $\underline{E}$ $\overline{D}$ $\underline{D}$ $\underline{A}$ $\underline{B}$ $\overline{C}$ $\underline{C}$ $\overline{B}$ $\overline{A}$ 8. All the values in caries criteria showed a marked increae from those of 1968.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(II)
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• pp.947-949
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• 1987

This paper describes the design of echo cancslling method(ECM) for transmission with full-duplex which ie transmitted on "2B+D"(144kbps)data through two-wire loop plants. The design objective is 40dB attenuation with a signal-to-noise ratio of $10{\sim}20dB$. Since the transhybrid loos can be as low as $6{\sim}10dB$, the required attenuation of the echo signal is on the order of $50{\sim}55dB$. The used algorithms based on the sign algorithm, and have been improved by using adoptive reference voltage level algorithm.

• 대한화학회지
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• 제39권9호
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• pp.734-740
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• 1995

Xanthomonas palargonii 5S rRNA의 일차구조 및 이차구조를 결정하고 에틸니트로소 우레아, Pb2+, 황산 이메틸 , 피로탄산 이에틸 들의 화학 탐침과 몇 가지 효소 탐침을 사용하여 고차원 구조를 분석하였다. 에틸니트로소 우레아는 삼차 상호작용에 관련되는 포스포디에스테르 결합을 조사하는데 사용되었다. Mg2+이 있을 때 에틸니트로소 우레아에 의한 변형에 대해서 저항성이 있는 자리는 불안정한 d 나선의 Nucleotides G72, A73, G75, A78, G98, G100, A101 들, c고리의 C36, C37, C39, C41들, 그리고 C 줄기의 A29, G33 들이다.이러한 결과와 Pb2+에 의한 가수분해 반응과 화학 탐침과 효소 탐침을 사용하여 얻은 결과들을 종합해 봄으로써 5S 의 b-C 구역과 d 나선 구역은 5S rRNA의 삼차 상호작용에서 돌쩌귀의 구실을 할 것으로 추정할 수 있었다.