• 대한수학회지
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• 제8권1호
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.

• 대한수학회보
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• 제37권4호
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• pp.729-741
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• 2000

In this paper, we study in Banach spaces the existence of fixed points of asymptotically regular mapping T satisfying: for each x, y in the domain and for n=1, 2,…, $$\parallelT^nx-T^ny\parallel\leq$\leq$a_n\parallelx-y\parallel+b_n (\parallelx-T^nx\parallel+\parallely-T^ny\parallely)$$ where $a_n,\; b_n,\; C_n$ are nonnegative constants satisfying certain conditions. We also establish some fixed point theorems for these mappings in a Hibert space, in L(sup)p spaces, in Hardy space H(sup)p, and in Soboleve space $H^{k,p} for 1<\rho<\infty \; and \; k\geq0$. We extend results from papers [10], [11], and others.

• Structural Engineering and Mechanics
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• 제13권6호
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• pp.671-694
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• 2002

This paper presents theoretical investigation on the cross correlation between torsional vibration ($u_{\theta}$) and translation vibration ($u_x$) of asymmetrical structure under white noise excitation. The formula reveals that the cross correlation coefficient (${\rho}$) is a function of uncoupled frequency ratio (${\Omega}={\omega}_{\theta}/{\omega}_x$), eccentricity, and damping ratio (${\xi}$). Simulations involving acceleration records from fifteen different earthquakes show correlation coefficients results similar to the theoretical correlation coefficients. The uncoupled frequency ratio is the dominating parameter to ${\rho}$; generally, ${\rho}$ is positive for ${\omega}_{\theta}/{\omega}_x$ > 1.0, negative for ${\omega}_{\theta}/{\omega}_x$ < 1.0, and close to zero for ${\omega}_{\theta}/{\omega}_x$ = 1.0. When the eccentricity or damping ratio increases, ${\rho}$ increases moderately for small ${\Omega}$ (< 1.0) only. The relation among $u_x$, $u_{\theta}$ and corner displacement are best presented by ${\rho}$; a simple way to hand-calculate the theoretical dynamic corner displacements from $u_x$, $u_{\theta}$ and ${\rho}$ is proposed as an alternative to dynamic analysis.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2002년도 하계학술대회 논문집 Vol.3 No.2
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• pp.764-768
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• 2002

Characteristics of ohmic Co/Si/Co contacts to n-type 4H-SiC are investigated systematically. The ohmic contacts were formed by annealing Co/Si/Co sputtered sequentially. The annealings were performed at $800^{\circ}C$ using RTP in vacuum ambient and $Ar:H_2$(9:1) ambient, respectively. The specific contact resistivity$(\rho_c)$, sheet resistance$(R_s)$, contact resistance$(R_c)$, transfer length$(L_T)$ were calculated from resistance$(R_T)$ versus contact spacing(d) measurements obtained from TLM(transmission line method) structure. While the resulting measurement values of sample annealed at vacuum ambient were $\rho_c=1.0{\tiimes}10^{-5}{\Omega}cm^2$, $R_c=20{\Omega}$ and $L_T$ = 6.0 those of sample annealed at $Ar:H_2$(9:1) ambient were $\rho_c=4.0{\tiimes}10^{-6}{\Omega}cm^2$, $R_c=4.0{\Omega}$ and $L_T$ = 2.0. The physical properties of contacts were examined using XRD and AES. The results showed that cobalt silicide was formed on SiC and Co was migrated into SiC.

• Bulletin of the Korean Chemical Society
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• 제24권1호
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• pp.91-94
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• 2003

Kinetic studies of the reaction of O-methyl-S-phenylthiocarbonates with benzylamines in methanol at 45.0 ℃ have been carried out. The reaction proceeds by a stepwise mechanism in which the rate-determining step is the breakdown of the zwitterionic tetrahedral intermediate, $T^{\pm}$, with a hydrogen-bonded four-center type transition state (TS). These mechanistic conclusions are drawn based on (ⅰ) the large magnitude of ${\rho}_X\;and\;{\rho}_Z$, (ⅱ) the normal kinetic isotope effects $(k_H/k_D\;>\;1.0)$ involving deuterated benzylamine nucleophiles, (ⅲ) the positive sign of ${\rho}_{XZ}$ and the larger magnitude of ${\rho}_{XZ}$ than that for normal $S_N2$ processes, and lastly (ⅳ) adherence to the reactivity-selectivity principle (RSP) in all cases.

• 한국산림과학회지
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• 제84권2호
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• pp.166-177
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• 1995

본 연구의 내용은 임도건설(林道建設) 예정지역(豫定地域)의 흙을 어떻게 토질(土質) 역학적(力學的)으로 실험하여 실제적으로 응용할 수 있는가를 다루는 것이다. 이를 위해 8개 플롯에서 각 플롯 당 2 개씩 총 16개의 토양시료(土壤試料)를 채취하였다. 실험내용은 흙이 흩어지기 전후의 단위중량(單位重量), 함수량(含水量), 액성(液性) 및 소성한계(塑性限界), 다짐도 시험(試驗), 입도시험(粒度試驗) 등이다. 흩어지기(교란(攪亂)) 전후의 전체 단위중량(${\rho}_t$)은 각각 $1.69g/cm^3$과 $1.19g/cm^3$이었으며, 함수량(含水量)은 21.0%와 20.5%였다. 체분석과 비중계(比重計)에 의한 입도시험결과 얻은 균등계수(均等係數) U와 곡율계수(曲率係數) C는 각각 125와 0.42를 보이고 있어 전체적으로 좋은 입도분포는 아니었다. USCS에 의한 토양분류는 SM(실트질 모래 내지 모래실트 혼합토)으로서 성토재료(盛土材料)로서는 좋지 않은 것으로 보인다. 다짐시험결과 자연상태의 단위중량(${\rho}$)과 최적(最適) 단위중량(單位重量)(${\rho}pr$)은 각각 $1.40{\pm}0.065g/cm^3$과 $1.88{\pm}0.049g/cm^3$로 나타났는데, 이것은 ${\rho}pr$에 도달하기 위해 성토시(盛土時) 더 많은 다짐작업과 토량(土量)이 필요함을 의미한다.

• 대한수학회보
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• 제5권1호
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• pp.67-71
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• 1968

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.75-82
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• 2014

In this paper, we consider the periodic boundary value problem with sign changing nonlinearity $$u^{{\prime}{\prime}{\prime}}+{\rho}^3u=f(t,u),\;t{\in}[0,2{\pi}]$$, subject to the boundary value conditions: $$u^{(i)}(0)=u^{(i)}(2{\pi}),\;i=0,1,2$$, where ${\rho}{\in}(o,{\frac{1}{\sqrt{3}}})$ is a positive constant and f(t, u) is a continuous function. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is the nonlinear term f may change sign.

• 천문학논총
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• 제11권1호
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• pp.91-107
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• 1996

We determine analytically the onset of thin-shell formation time of fast wind bubble with power-law energy injection $E_{in}=E_0t^s$, and power-law ambient density structure, ${\rho}_0(r)={\bar{\rho}}(r/{\bar{r}})^{-{\omega}}$. Thin-shell formation time, $t_{sf}$ can be estimated by minimizing the total time elapsed before the complete cooling of shocked gas. For uniform medium (${\omega}=0$) and constant energy injection (s = 1), the onset of shell formation is found to be at $t_{sf}=5.2{\times}10^3yr$, which agrees Quite well with the results of FCT 1D numerical calculation. We solve the line transfer problem with previous result derived by numerical calculation in order to calculate line profile of [OIII] (${\lambda}=5007{\AA}$) forbidden line. In general, radiative outer shell causes the formation of double peaked line profile. Each peak corresponds to approaching and receeding shells with large velocities. Our line profiles show good agreements with observation of expanding shell structure.

• 한국전기전자재료학회논문지
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• 제24권7호
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• pp.559-562
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• 2011

In this study, the effect of $Nb_2O_5$ and sintering time on the positive temperature of coefficient of resistivity (PTCR) behavior of lead free $Ba_{0.99}(Bi_{0.5}Na_{0.5})_{0.01}TiO_3$ (BBNT) ceramics were investigated in order to fabricate a PTC thermistor with high $T_c$ temperature more than $140^{\circ}C$. In particular, BBNT ceramic doped with 0.1mol% $Nb_2O_5$ and sintered at $1350^{\circ}C$ for 4 h has significantly increased Curie temperature ($T_c$) of about $200^{\circ}C$, showed good PTCR behavior of room-temperature resistivity ($\rho_{rt}$) of $40{\Omega}{\cdot}cm$, a high $\rho_{max}/\rho_{min}$ ratio of $43.78{\times}10^3$ and a large resistivity temperature factor (${\alpha}$) of 16.1%/$^{\circ}C$. With increasing addition of $Nb_2O_5$ content, the $\rho_{rt}$ decreased to a minimum value of $40\;{\Omega}cm$ at 0.1mol% $Nb_2O_5$ and the $\rho_{rt}$ increased for x value over 0.1 mol%.