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STRUCTURE OF THE ZEROS OF q-BERNOULLI POLYNOMIALS

  • RYOO C. S.
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.49-58
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    • 2005
  • In this paper we observe the structure of the roots of q-Bernoulli polynomials, ${\beta}_n(w,h{\mid}q)$, using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots of ${\beta}_n(w,h{\mid}q)$ for $-{\frac{1}{5}},-{\frac{1}{2}}$. Finally, we give a table for numbers of real and complex zeros of ${\beta}_n(w,h{\mid}q)$.

Distribution characteristics of geothermal anomalies related with direction of faults and lineaments (지열분포와 단층 및 선구조 방향성과의 상호연관성)

  • Baek, Seung-Gyun;Kim, Hyoung-Chan;Lee, Cheol-Woo;Park, Jeong-Min
    • 한국신재생에너지학회:학술대회논문집
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    • 2009.06a
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    • pp.608-610
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    • 2009
  • 지열 분포에 관련된 지질구조의 특성을 파악하기 위하여 지온경사, 지열류량 자료와 인접한 선구조의 방향성에 대한 상관성 분석을 실시하였다. GIS를 이용하여 지열정보데이터베이스에서 발췌한 209개 지온경사 자료와 218개 지열류량 자료에 대하여 전국 광역단열도로부터 가장 인접한 선구조를 추출하고 10도 간격의 방향별 지온경사 및 지열류량 자료 빈도 및 평균값을 그래프에 도시하였다. 인접 선구조의 방향별 지온경사 평균은 $N30^{\circ}{\sim}40^{\circ}W$, $N10^{\circ}{\sim}20^{\circ}E$ 방향에서 $58.9^{\circ}C/km$, $54.9^{\circ}C/km$로 가장 높았고, 인접 선구조의 방향별 지열류량 평균은 $N80^{\circ}{\sim}90^{\circ}W$, $N50^{\circ}{\sim}60^{\circ}W$ 방향에서 98.71 $mW/m^2$, $98.70mW/m^2$로 가장 높았다. 각 선구조 상의 좌표들을 이용하여 지열류량 분포도에서 지열류량 값을 추출한 결과 $N10^{\circ}W{\sim}N40^{\circ}E$, $N60^{\circ}{\sim}70^{\circ}W$, $N50^{\circ}{\sim}60^{\circ}E$ 방향의 지열류량 높은 것으로 나타났다. 결과적으로 지온경사와 지열류량 자료에 대한 인접 선구조의 방향은 북북동, 북서, 서북서 방향이 우세한 것으로 나타났다. 이는 우리나라 조구조 운동과 관련한 단층, 절리 등의 단열구조의 우세 방향과 잘 일치하는 것으로 해석된다.

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Synthesis, Characterization, and Catalytic Properties of Gp 6 Metal Complexes of 1-N,N-dimethylaminomethyl-$1^{\prime}$,2-bis(diphenylphosphino)ferrocene (FcNPP). X-ray Crystal Structure of W$(CO)_4({\eta}^2-FcNPP(O)-P,N)$

  • Kim, Tae-Jeong;Kim, Yong-Hoon;Kim, Eun-Jin;Oh, Sang-Ho;Kim, Hong-Seok;Jeong, Jong-Hwa
    • Bulletin of the Korean Chemical Society
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    • v.15 no.5
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    • pp.379-386
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    • 1994
  • Reactions of 1',2-bis(diphenylphosphino)-l-(N,N-dimethylaminomethyl)ferrocene (FcNPP) with $M(CO)_6$ (M=Cr, Mo, W) in the presence of TMNO (Trimethylamine oxide) in a stoichiometric ratio of 1 : 1.5 : 3.5 produced a series of Gp 6 metal carbonyl derivatives with a variety of coordination modes: M(CO)$_4({\eta}^2$-FcNPP-P,P) (M=Cr, Mo, W), $M(CO)_5({\eta}^1-FcNPP-P) (M=Mo, W)\;,\; M_2(CO)_9({\eta}^1\;,\;{\eta}^2-FcNPP-P,P,N) (M=Cr, Mo)\;,\;M_2(CO)_{10}({\eta}^1\;,\;{\eta}^1-FcNPP-P,P) (M=Cr, Mo, W)\;, and\;W(CO)_4({\eta}^2-FcNPP(O)-P,N)$. All these complexes were characterized by microanalytical and spectroscopic techniques. In one case, the structure of W(CO)$_4({\eta}^2$-FcNPP(O)-P,N) was determined by X-ray crystallography. Crystals are monocinic, space group P$2_{1/C}$, with a=10.147(2), b=19.902(3), c=19.821(4) ${\AA},\;{\beta}=96.88(2)^{\circ},\;V=3974(l){\AA}^3$, Z=4, and $D_{calc}=1.64 g cm^{-3}$. The geometry around the central tungsten metal is a distorted octahedron, with the nitrogen and phosphorus atoms being cis to each other. Some of these complexes exhibited catalytic activities in the allylic oxidation and epoxidation of cholesterly acetate. Other oxidation products were also formed with the different chemical yields and product distribution depending upon the ligand and the central metal.

Effects of Carbide and Matrix Structures on Abrasion Wear Resistance of Multi-Component White Cast Iron (다합금계 백주철의 탄화물 및 기지조직이 내마모성에 미치는 영향)

  • Ryu, Seong-Geun
    • Korean Journal of Materials Research
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    • v.7 no.4
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    • pp.310-316
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    • 1997
  • The effects of carbide and matrix structures on the abrasion wear resistance of multi-component white cast irons with 3.0 mass%C have been studied in this paper. Four different heats were poured in order to obtain the specimens with different combinations of the carbide structures: a basic iron(3.0 mass%C-5.0 mass%Cr-5.0 mass%V-5.0 mass% Mo-12.5mass%W)for M$_{6}$C and M$_{7}$C$_{3}$ carbides, and a Cr free iron(3.0 mass%C-5.0 mass%V-2.5mass%Mo-12.5 mass%W) for MC and M6C carbides. A conventional high Cr free free iron(3.0 mass%C-5.0 mass%V-2.5 mass%Mo-12.5 mass%W) for MC and M6C carbides. A conventional high Cr white cast iron was also poured to compare its wear resistance with those of the multi-component white cast irons. In the as-cast condition, the range of abrasive wear rate(Rw=mg/min) was from 4.15 to 5.98 . The lowest Rw, which means the highest wear resistance, was obtained in the basic iron with nodular MC, lamellar M$_{2}$C and cellular M$_{7}$C$_{3}$ carbides. On the other hand, the Rw of the high Cr white cast iron ranked between the basic iron and the Mo and W free iron. In each alloy, the Rw of air hardened or tempered specimen was lower than that of the as-cast one because of the change of matrix structures by the heat treatments. The Rw of the hear treated speci-mens increased in the order Mo and W free iron, basic iron, Cr free iron, high Cr iron, and V free iron.n.n.n.

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Effect of Cooling Water Capacity on the Engine Performance for Small Diesel Engine (냉각수(冷却水) 용량(容量)이 소형(小型) 디젤기관(機關)의 성능(性能)에 미치는 영향(影響))

  • Myung, Byung Soo;Kim, Soung Rai
    • Korean Journal of Agricultural Science
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    • v.13 no.2
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    • pp.265-278
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    • 1986
  • This study was attempted to improve the thermal efficiency of 6 kW water-cooled diesel engine on power tiller. The engine performance tests were conducted to find out the effect of cooling water capacity of 2700cc, 2800cc, 2900cc, 3000cc, 3100cc on power, brake specific fuel consumption (BSFC), torque, temperature of cooling water and lubricating oil and friction losses of the engine with D. C. dynamometer. The results obtained in the study are summarized as follows: 1. The performance of the engine tested was adequated to Korea Industrial Standard but actual economy power was 10% higher than the labeled rated power of the engine. The BSFC of the engine tested 297.8g/kW-h which is belong a little higher level than hreign products. The temperature of cooling water was $101^{\circ}C$ which is higher than SAE standard ($88^{\circ}C$) 2. The friction losses of engine tested was 3.656 kW at 2200 rpm of rated rpm (piston speed 6.97m/sec) and is higher than those of foreign products. 3. When the cooling water capacity was increased from 2700cc to 3100cc the power output of the engine was increased from 6.7 kW to 7.13 kW at the rate of 6.4% and also the torque of the engine was increased from 28.85 N.m to 30.76 N.m at the rate of 6.39%. 4. When the cooling water capacity was increased from 2700cc to 3100cc, the BSFC was decreased 6.9g/kW-h from 310.9g/kW-h to 304.1g/kW-h, and after one half hour operation with full load, the temperature of cooling water was decreased $13^{\circ}C$ from $101^{\circ}C$ to $88^{\circ}C$ and also the temperature of lubricant oil was decreased $6.4^{\circ}C$ from $76.7^{\circ}C$ to $70.4^{\circ}C$. 5. The mechanical efficiency was increased from 70.08% to 71.08% when the cooling water capacity was increased from 2700cc to 3100cc.

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Distributional Characteristics of Fault Segments in Cretaceous and Tertiary Rocks from Southeastern Gyeongsang Basin (경상분지 남동부 일대의 백악기 및 제3기 암류에서 발달하는 단층분절의 분포특성)

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.27 no.3
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    • pp.109-120
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    • 2018
  • The distributional characteristics of fault segments in Cretaceous and Tertiary rocks from southeastern Gyeongsang Basin were derived. The 267 sets of fault segments showing linear type were extracted from the curved fault lines delineated on the regional geological map. First, the directional angle(${\theta}$)-length(L) chart for the whole fault segments was made. From the related chart, the general d istribution pattern of fault segments was derived. The distribution curve in the chart was divided into four sections according to its overall shape. NNE, NNW and WNW directions, corresponding to the peaks of the above sections, indicate those of the Yangsan, Ulsan and Gaeum fault systems. The fault segment population show near symmetrical distribution with respect to $N19^{\circ}E$ direction corresponding to the maximum peak. Second, the directional angle-frequency(N), mean length(Lm), total length(Lt) and density(${\rho}$) chart was made. From the related chart, whole domain of the above chart was divided into 19 domains in terms of the phases of the distribution curve. The directions corresponding to the peaks of the above domains suggest the directions of representative stresses acted on rock body. Third, the length-cumulative frequency graphs for the 18 sub-populations were made. From the related chart, the value of exponent(${\lambda}$) increase in the clockwise direction($N10{\sim}20^{\circ}E{\rightarrow}N50{\sim}60^{\circ}E$) and counterclockwise direction ($N10{\sim}20^{\circ}W{\rightarrow}N50{\sim}60^{\circ}W$). On the other hand, the width of distribution of lengths and mean length decrease. The chart for the above sub-populations having mutually different evolution characteristics, reveals a cross section of evolutionary process. Fourth, the general distribution chart for the 18 graphs was made. From the related chart, the above graphs were classified into five groups(A~E) according to the distribution area. The lengths of fault segments increase in order of group E ($N80{\sim}90^{\circ}E{\cdot}N70{\sim}80^{\circ}E{\cdot}N80{\sim}90^{\circ}W{\cdot}N50{\sim}60^{\circ}W{\cdot}N30{\sim}40^{\circ}W{\cdot}N40{\sim}50^{\circ}W$) < D ($N70{\sim}80^{\circ}W{\cdot}N60{\sim}70^{\circ}W{\cdot}N60{\sim}70^{\circ}E{\cdot}N50{\sim}60^{\circ}E{\cdot}N40{\sim}50^{\circ}E{\cdot}N0{\sim}10^{\circ}W$) < C ($N20{\sim}30^{\circ}W{\cdot}N10{\sim}20^{\circ}W$) < B ($N0{\sim}10^{\circ}E{\cdot}N30{\sim}40^{\circ}E$) < A ($N20{\sim}30^{\circ}E{\cdot}N10{\sim}20^{\circ}E$). Especially the forms of graph gradually transition from a uniform distribution to an exponential one. Lastly, the values of the six parameters for fault-segment length were divided into five groups. Among the six parameters, mean length and length of the longest fault segment decrease in the order of group III ($N10^{\circ}W{\sim}N20^{\circ}E$) > IV ($N20{\sim}60^{\circ}E$) > II ($N10{\sim}60^{\circ}W$) > I ($N60{\sim}90^{\circ}W$) > V ($N60{\sim}90^{\circ}E$). Frequency, longest length, total length, mean length and density of fault segments, belonging to group V, show the lowest values. The above order of arrangement among five groups suggests the interrelationship with the relative formation ages of fault segments.

Metal-Dinitrosyl Complexes(III) : Synthesis and Structural Study of Homo-, Hetero-dinuclear Molybdenum and Tungsten Complexes, $[Cl(phen)(NO)_2M({\mu}-pyz)M'(NO)_2(phen)Cl][ClO_4]_2 $(phen = 1,10-phenanthroline, pyz = pyrazine) (금속-디니트로실 착물 (제 3 보) : 몰리브덴과 텅스텐의 호모 및 헤테로 이핵 착물, $[Cl(phen)(NO)_2M({\mu}-pyz)M'(NO)_2(phen)Cl][ClO_4]_2 (phen=1,10-phenanthroline,\;pyz=pyrazine)$의 합성 및 구조에 대한 연구)

  • Sang-Oh Oh;Seong-Jong Mo
    • Journal of the Korean Chemical Society
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    • v.37 no.7
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    • pp.655-661
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    • 1993
  • The neutral monomeric compounds $[Mo(NO)_2Cl_2(phen)]$ and $[W(NO)_2Cl_2(phen)]$ (phen= 1,10-phenanthroline) have been prepared by reactions of polymeric compounds $[{Mo(NO)_2Cl_2}n],\;[{W(NO)_2Cl_2}n]$ with chelate ligands. Additions of one equivalent of silver(I) perchlorate to these cis-dinitrosyl compounds in acetone solution produce $[Mo(NO)_2(phen)(S)Cl][ClO_4]\;and\;[W(NO)_2(phen)(S)Cl][ClO_4]$ (S = acetone). The homo- and hetero-dinuclear complexes, $[Cl(phen)(NO)_2M(pyz)M'(NO)_2(phen)Cl][ClO_4]_2$ (M = Mo, W) and $[Cl(phen)(NO)_2M(pyz)M'(NO)_2(phen)Cl][C1O_4]_2$ (M = Mo, M' = W) have been prepared by these monocationic complexes with pyrazine ligand respectively. These complexes characterized by elemental analysis, $1^H-\;and\;^{13}C-NMR$, infrared, and UV-visible spectroscopy are reported. The spectral data indicate that homo- and hetero-dinuclear complexes were symmetrical structures of $C_{2v}$.

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