• 충청수학회지
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• 제23권2호
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• pp.231-236
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• 2010

Using the properties of the concave function, we show that the Hausdorff dimension of the product $C_{\frac{a+b}{2},\frac{a+b}{2}}{\times}C_{\frac{a+b}{2},\frac{a+b}{2}}$ of the same symmetric Cantor sets is greater than that of the product $C_{a,b}{\times}C_{a,b}$ of the same anti-symmetric Cantor sets. Further, for $1/e^2$ < a, b < 1/2, we also show that the dimension of the product $C_{a,a}{\times}C_{b,b}$ of the different symmetric Cantor sets is greater than that of the product $C_{\frac{a+b}{2},\frac{a+b}{2}}{\times}C_{\frac{a+b}{2},\frac{a+b}{2}}$ of the same symmetric Cantor sets using the concavity. Finally we give a concrete example showing that the latter argument does not hold for all 0 < a, b < 1/2.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2009년도 제40회 하계학술대회
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• pp.1252_1253
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• 2009

The composites were fabricated by adding 0, 15, 20, 25[vol.%] Zirconium Diboride(hereafter, $ZrB_2$) powders as a second phase to Silicon Carbide(hereafter, SiC) matrix. The physical, mechanical and electrical properties of electroconductive SiC ceramic composites by spark plasma sintering(hereafter, SPS) were examined. Reactions between $\beta$-SiC and $ZrB_2$ were not observed in the XRD analysis The relative density of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ composites are 90.97[%], 74.62[%], 77.99[%] and 72.61[%] respectively. The XRD phase analysis of the electroconductive SiC ceramic composites reveals high of SiC and $ZrB_2$ and low of ZrO2 phase. The electrical resistivity of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ composites are $4.57{\times}10^{-1}$, $2.13{\times}10^{-1}$, $1.53{\times}10^{-1}$ and $6.37{\times}10^{-2}[{\Omega}{\cdot}cm]$ at room temperature, respectively. The electrical resistivity of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ are Negative Temperature Coefficient Resistance(hereafter, NTCR) in temperature ranges from 25[$^{\circ}C$] to 100[$^{\circ}C$]. It is convinced that SiC+20[vol.%]$ZrB_2$ composite by SPS can be applied for heater above 1000[$^{\circ}C$].

• 한국고분자학회:학술대회논문집
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• 한국고분자학회 2006년도 IUPAC International Symposium on Advanced Polymers for Emerging Technologies
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• pp.224-225
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• 2006

The Ethylene polymerization behavior of a series of polymethylene bridged dinuclear CGC $[Zr({\eta}^{5}:{\eta}^{1}-C_{9}H_{5}SiMe_{2}NCMe_{3})Me_{2}]_{2}[(CH_{2})_{n}]\;[_{n}=6(1),\;9(2),\;12(3)]$ in the cocatalytic activation with $Ph_{3}C^{+}B^{-}(C_{6}F_{5})_{4}\;(B_{1})\;or\;Ph_{3}C^{+}(C_{6}F_{5})_{3}B^{-}C_{6}F_{4}B^{-}(C_{6}F_{5})_{3}Ph_{3}C^{+}\;(B_{2})\;or\;B(C_{6}F_{5})_{3}\;(B_{3})$ were investigated to study the nuclearity effects as well as the counteranion effects. The ethylene polymerization and ethylene/1-hexene copolymerization were conducted at $30^{\circ}C$ It was found that both in ethylene polymerization and ethylene/1-hexene copolymerization, activities increased in the order of 1 < 2 < 3, which indicates the presence of longer bridge between two active sites contributes more efficiently to facilitate the polymerization activity.

• 한국토양비료학회지
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• 제34권5호
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• pp.311-315
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• 2001

토양검정의 적중율을 높이기 위하여 농업과학기술원에서 실시한 10개의 pot시험 결과를 Bray등이 개정한 Mitscherlich-Baule-Spillman식(A)에 넣어 토양질소와 시비질소의 이용계수 $C_2$와 $C_1$을 계산하고, 적정 수량을 생산하는데 소요되는 시비량(x) 산출식(B)을 유도하였다. log(Ymax-Y) = logYmax-$C_1x-C_2b$ (A) Ymax : 최고수량, Y: 무비구 또는 일정량의 시비구 수량 b: 토양의 $NO_3{^-}-N(mg\;kg^{-1})$, x:시비량 log(0.05))=$-C_1x-C_2b$ =-C_1x-C_2b (B) 실제 시비량에 대한 식 B로 계산되는 비료 소요량과 는 유의한 정의 상관 관계를 보였다. 식 A와 B의 $C_1$과 $C_2$값에 관한 정밀한 연구는 토양검정의 실용성을 높일 수 있다.

• Applied Biological Chemistry
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• 제43권1호
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• pp.39-45
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• 2000

본 연구에서는 종합비타민 액제중의 비타민 A, $B_1,\;B_2,\;B_6$, C의 안정성을 규명하기 위하여 경시함량 변화 및 분해속도를 동력학적으로 검토하였다 종합 비타민 액제의 제조에 있어서 지용성 비타민의 가용화를 위하여 계면활성제인 polysorbate 80과 용해보조제인 프로필렌글리콜을 병용하므로써 첨가제의 양을 최소화시킬 수 있었다. 종합 비타민 액제의 안정성 평가를 위한 가속시험에서 heterogenous solution system에서의 반응 기작이 그대로 나타나는 것은 아니겠지만 비타민 A는 zero-order, 비타민 $B_1$과 C는 first-order kinetics에 따르는 분해 양상을 나타내었으며 Arrhenius식을 이용하여 구한 비타민 A, $B_1$, 및 C의 활성화 에너지는 각각 26.27, 21.67 및 23.50 kcal/mol이고 상온$(25^{\circ}C)$에서의 유효기간은 각각 1493, 449 및 639일 이었다. 그리고 비타민 $B_2$ 광퇴색 속도식은 first-order kinetics의 분해양상을 나타내었으나 광희색 반응에 미치는 비타민 $B_2$ 초기농도$(C_0)$ $0.544{\times}10^2{\sim}1.632{\times}10^{-2}M$의 영향을 고려하여 비타민 $B_2$의 광퇴색 반응은 다음과 같은 속도식으로 진행되는 것으로 판명되었다. $-{\frac {dc}{dt}}=K_{c}\;{\frac C{C_0}}$ $K_c\;:\;C_0$에 따르는 상수 비타민 $B_6$의 안정성은 인공광원보다 태양광선에 의한 비타민 $B_6$의 광분해가 촉진되었고 그리고 태양광선에 의한 계절에 따른 분해는 모두 비슷하였다. 한편 용기에 의한 비타민 $B_6$의 광분해는 폴리에틸렌용기>갈색유리병>투명유리병 순으로 안정함을 나타내었다 이상의 실험결과로 종합비타민 액제 설계의 안정성의 기초적 실험에 기여되리라고 사료된다.

• 한국분말재료학회지
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• 제9권5호
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• pp.352-358
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• 2002

The effects of boron or manganese added as $B_4C$, Mn, $TiB_2$, B on TiC-30vo1.%$Ni_3Al$ cermet sintered at 1380 and $1400^{\circ}C$ for 1 hour, were examined in relation with shrinkage, relative density, microstructure, lattice parameter, hardness and fracture toughness ($K_{IC}$). The results are summarized as follows: 1) The highest shrink-age showed about 30.5% in the specimen added B$_4$C and the maximum relative density was about 99% in the specimen added $TiB_2$; 2) The grains of TiC were grown during sintering and made the surrounding structure by adding boron and manganese. The largest grain size showed about $2.8\mutextrm{m}$ in the specimen with boron sintered at $1400^{\circ}C$;3) The lattice parameter of TiC was about $4.325\AA$ and $Ni_3Al$ about $3.592\AA$ by adding other elements; 4) The highest hardness was about $1100kgf/\textrm{mm}^2$ in the specimen with B4C; 5) The fracture toughness ($K_{IC}$) showed about $15MNm^{-3/2}$ in the specimen added $TiB_2$.

• 대한수학회보
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• 제53권2호
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• pp.487-494
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• 2016

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

• 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.

• 전기학회논문지
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• 제58권9호
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• pp.1757-1763
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• 2009

The composites were fabricated by adding 0, 15, 20, 25[vol.%] Zirconium Diboride(hereafter, $ZrB_2$) powders as a second phase to Silicon Carbide(hereafter, SiC) matrix. The physical, mechanical and electrical properties of electroconductive SiC ceramic composites by Spark Plasma Sintering(hereafter, SPS) were examined. Reactions between ${\beta}-SiC$ and $ZrB_2$ were not observed in the XRD analysis. The relative density of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ composites are 90.93[%], 74.62[%], 74.99[%] and 72.61[%], respectively. The XRD phase analysis of the electroconductive SiC ceramic composites reveals high of SiC and $ZrB_2$ and low of $ZrO_2$ phase. The lowest flexural strength, 108.79[MPa], shown in SiC+15[vol.%] $ZrB_2$ composite and the highest - 220.15[MPa] - in SiC+20[vol.%] $ZrB_2$composite at room temperature. The trend of the mechanical properties of the electroconductive SiC ceramic composites moves in accord with that of the relative density. The electrical resistivities of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ composites are 4.57${\times}10^{-1}$, 2.13${\times}10^{-1}$, 1.53${\times}10^{-1}$ and 6.37${\times}10^{-2}$[${\Omega}$ cm] at room temperature, respectively. The electrical resistivity of mono SiC, SiC+15[vol.%]$ZrB_2$. SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ are Negative Temperature Coefficient Resistance(hereafter, NTCR) in temperature ranges from 25[$^{\circ}C$] to 100[$^{\circ}C$]. The declination of V-I characteristics of SiC+20[vol.%]$ZrB_2$ composite is 3.72${\times}10^{-1}$. It is convinced that SiC+20[vol.%]$ZrB_2$ composite by SPS can be applied for heater or electrode above 1000[$^{\circ}C$]

• 한국미생물학회:학술대회논문집
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• 한국미생물학회 2006년도 International Meeting of the Microbiological Society of Korea
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• pp.129-131
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• 2006

Through molecular phylogenetic analysis using the nef gene sequences of HIV-l isolated from Korean registered in the NCBI GenBank together with 41 reference strains and 94 foreign isolates, we verified that most (${\sim}80%$) of Korean isolates belonged to subtype B and 78% of subtype B were clustered together exclusively of foreign isolates, and this cluster was named Korean clade subtype B ($K_cB$). Similarity study suggested that the $K_cB$ cluster was more homogeneous than and clearly distinctive from the non-Korean subtype B ($NK_cB$). Comparison of the consensus amino acid sequences of the $K_cB\;or\;NK_cB$ revealed characteristic $K_cB$ signature amino acid pattern comprised of 13 amino acid residues. The $K_cB$ signature amino acid residues were critical in separating the $K_cB$ ftom the $NK_cB$, since substitution of the $NK_cB$ sequences with $K_cB$ signature amino acids relocated them to the Koran clade, and vice versa. Synonymous and nonsynonymous substitution rate study suggested positive selection event for the $K_cB$.