• Journal of the Korean Mathematical Society
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• v.8 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1441-1462
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• 2018

In this paper, we investigate the fractional p&q-Kirchhoff type system $$\{M_1([u]^p_{s,p})(-{\Delta})^s_pu+V_1(x){\mid}u{\mid}^{p-2}u\\{\hfill{10}}={\ell}k^{-1}F_u(x,\;u,\;v)+{\lambda}{\alpha}(x){\mid}u{\mid}^{m-2}u,\;x{\in}{\Omega}\\M_2([u]^q_{s,q})(-{\Delta})^s_qv+V_2(x){\mid}v{\mid}^{q-2}v\\{\hfill{10}}={\ell}k^{-1}F_v(x,u,v)+{\mu}{\alpha}(x){\mid}v{\mid}^{m-2}v,\;x{\in}{\Omega},\\u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}{\subset}{\mathbb{R}}^N$ is an unbounded domain with smooth boundary ${\partial}{\Omega}$, and $0<s<1<p{\leq}q$ and sq < N, ${\lambda},{\mu}>0$, $1<m{\leq}k<p^*_s$, ${\ell}{\in}R$, while $[u]^t_{s,t}$ denotes the Gagliardo semi-norm given in (1.2) below. $V_1(x)$, $V_2(x)$, $a(x):{\mathbb{R}}^N{\rightarrow}(0,\;{\infty})$ are three positive weights, $M_1$, $M_2$ are continuous and positive functions in ${\mathbb{R}}^+$. Using variational methods, we prove existence of infinitely many high-energy solutions for the above system.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.1
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• pp.35-42
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• 2001

The primitive polynomial on GF(q) is used in the area of the scrambler, the error correcting code and decode, the random generator and the cipher, etc. The algorithm that generates efficiently the primitive polynomial on GF(q) was proposed by A.D. Porto. The algorithm is a method that generates the sequence of the primitive polynomial by repeating to find another primitive polynomial with a known primitive polynomial. In this paper, we propose the algorithm that is improved in the A.D. Porto algorithm. The running rime of the A.D. Porto a1gorithm is O($\textrm{km}^2$), the running time of the improved algorithm is 0(m(m+k)). Here, k is gcd(k, $q^m$-1). When we find the primitive polynomial with m odor, it is efficient that we use the improved algorithm in the condition k, m>>1.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.789-804
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• 2010

We here investigate an existence and uniqueness of the nontrivial, nonnegative solution of a nonlinear ordinary differential equation: $$[\mid(w^m)]'\mid^{p-2}(w^m)']'\;+\;{\beta}rw'\;+\;{\alpha}w\;+\;(w^q)'\;=\;0$$ satisfying a specific decay rate: $lim_{r\rightarrow\infty}\;r^{\alpha/\beta}w(r)$ = 0 with $\alpha$ := (p - 1)/[pd-(m+1)(p-1)] and $\beta$:= [q-m(p-1)]/[pd-(m+1)(p-1)]. Here m(p-1) > 1 and m(p - 1) < q < (m+1)(p-1). Such a solution arises naturally when we study a very singular solution for a doubly degenerate equation with nonlinear convection: $$u_t\;=\;[\mid(u^m)_x\mid^{p-2}(u^m)_x]_x\;+\;(u^q)x$$ defined on the half line.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2006.06a
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• pp.317-318
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• 2006

일반적인 CMOS공정으로는 높은 주파수 대역에서 높은 Q factor를 갖는 인덕터를 구현하는데 어렵고 이에 반해 RF ICs는 갈수록 high Q 를 가지는 인덕터가 요구되고 있다. 이를 LTCC 기판 위에 인덕터를 구현했을 때 높은 주파수 대역에서 성능을 알아보기 위해 모의 실험하였다. 인덕터를 설계하는데 있어서 인덕터 코일의 폭, 코일의 두께와 간격이 인덕터의 성능을 결정짓는다는 것을 고려하였고, MEMS 공정을 이용하여 high Q를 갖는 인덕터를 설계하였다. 인덕터의 전체 크기는 $330{\mu}m\;{\times}\;330{\mu}m$에서 선폭은 $30{\mu}m$, 선간의 간격은 $20{\mu}m$로 기판위에 $80{\mu}m$ 높이로 인덕터를 띄어서 설계하였고, 그리고 이를 LTCC 기판위에 high Q 의 인덕터 구현을 위해 simulation 한 결과가 Q값이 50 정도의 크기를 나타냈다.

• Journal of Life Science
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• v.24 no.10
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• pp.1092-1101
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• 2014

In this study, the distribution patterns of Quercus mongolica and Q. serrata in Korea were investigated, and the possibility of introgressive hybridization and gene flow between Q. mongolica and Q. serrata in Mt. Seorak was inferred by flavonoid analyses. The most critical factor in the vertical and horizontal distribution patterns of Q. mongolica and Q. serrata was the temperature, in accordance with latitude and altitude. The species showed a zonal distribution, with a Q. mongolica zone in the upper area and a Q. serrata zone in the lower area. In Mt. Seorak, Central Korea, the range of the vertical distribution of Q. mongolica was generally above an altitude of 100 m, whereas that of Q. serrata was an altitude of 0-400 m (-500) and rarely above an altitude of 500 m. However, in Mt. Jiri, Southern Korea, Q. serrata was found up to an altitude of 1,000~1,200 m, whereas the frequency of Q. mongolica was reduced at lower elevations and the species was rare below an altitude of 300 m, although pure stands were found on higher mountain slopes above an altitude of 1,200 m. The altitudinal distribution of the two species overlapped, where the two species occurred together. The leaf flavonoid constituents of thirty-four individuals of Q. mongolica and Q. serrata in Mt. Seorak and Mt. Jiri, Korea were examined. Twenty-four flavonoid compounds were isolated and identified. These were glycosylated derivatives of flavonols kaempferol, quercetin, isorhamnetin, myricetin. Five compounds among the flavonoid compounds were acylated. Kaempferol 3-O-glucoside, quercetin 3-O-glucoside, quercetin 3-O-galactoside, and its acylated compounds were major constituents and present in all individuals. Quercus mongolica is distinguished from Q. serrata by the presence of quercetin 3-O-arabinosylglucoside, a high concentration of three acylated compounds (kaempferol 3-O-glucoside, quercetin 3-O-glucoside, and quercetin 3-O-galactoside), and a relatively low concentration or lack of rhamnosyl flavonol compounds. Intraspecific variations, however, were found in the flavonoid profiles of Q. mongolica and Q. serrata, and the flavonoid profiles of individuals belonging to the two species in a hybrid zone (sympatric zone) tended to be similar, qualitatively and quantitatively. These findings strongly suggest that gene exchange or gene flow occurs through introgressive hybridization between Q. mongolica and Q. serrata in Mt. Seorak.

• Korean Journal of Ecology and Environment
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• v.53 no.4
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• pp.427-435
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• 2020

The most important thing to successfully restore an oak forest is finding suitable climatic conditions and topographic factors for the oak species to be introduced. In this study, in order to find suitable environmental conditions for the five dominant oak trees on the Korean Peninsula, we carried out analysing the information on the location of forest vegetation on the Korean Peninsula. The range of annual mean temperature of the five oak trees was narrow in the order of Q. mongolica (7.7~14.3℃), Q. variabilis (9.2~13.8℃), Q. acutissima (10.5~14.3℃), Q. serrata (11.4~13.7℃), Q. aliena (11.0~12.9℃). The range of annual precipitation of oaks was narrow in order of Q. mongolica (1072.7~1780.9 mm), Q. variablis (1066.6~1554.9 mm), Q. acustissima (1036.5~1504.8 mm), Q. serrata (1062.6~1504.7 mm). The range of altitude was in order of Q. mongolica (147~1388m), Q. serrata (93~950m), Q. variabilis(90~913m), Q. acustissima (60~516m), Q. aliena (55~465 m). The range of slope was in the order of Q. mongolica (8~56°), Q. variabilis(5~52°), Q. serrata (11~45°), Q. aliena (15~38°), Q. acustissima (16~37°). These results are considered to be very useful in the case of ecological restoration using deciduous oak trees on the Korean Peninsula.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.79-90
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• 2005

In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.545-558
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• 2017

In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered m-right ideals, ordered (p, q)-lateral ideals and ordered n-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered (m,(p, q), n)-quasi ideals are examined. We also characterize these notions in terms of minimal ordered (m,(p, q), n)-quasi-ideals in ordered ternary semigroups. Moreover, m-right simple, (p, q)-lateral simple, n-left simple, and (m,(p, q), n)-quasi simple ordered ternary semigroups are defined and some properties of them are studied.