• 대한수학회보
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• 제57권5호
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• pp.1095-1113
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• 2020

In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations $f^nf^{(k)}+Q_{d_*}(z,f)=R(z)e^{{\alpha}(z)}$ and fⁿf^(k) + Q_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z), where $Q_{d_*}(z,f)$ and Q_d(z, f) are differential polynomials in f with small functions as coefficients, of degree d_* (≤ n - 1) and d (≤ n - 2) respectively, R, p₁, p₂ are non-vanishing small functions of f, and α, α₁, α₂ are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.915-923
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• 2022

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

• 한국광과학회:학술대회논문집
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• 한국광과학회 1996년도 학술대회지
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• pp.20-20
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• 1996

• 대한수학회보
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• 제53권4호
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• pp.1185-1196
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• 2016

We show a class of homogeneous polynomials of Fermat-Waring type such that for a polynomial P of this class, if $P(f_1,{\ldots},f_{N+1})=P(g_1,{\ldots},g_{N+1})$, where $f_1,{\ldots},f_{N+1}$; $g_1,{\ldots},g_{N+1}$ are two families of linearly independent entire functions, then $f_i=cg_i$, $i=1,2,{\ldots},N+1$, where c is a root of unity. As a consequence, we prove that if X is a hypersurface defined by a homogeneous polynomial in this class, then X is a unique range set for linearly non-degenerate non-Archimedean holomorphic curves.

• 대한수학회지
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• 제45권5호
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• pp.1483-1503
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• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

• 대한수학회보
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• 제55권5호
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• pp.1529-1561
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• 2018

Let f and g be nonconstant meromorphic (entire, respectively) functions in the complex plane such that f and g are of finite order, let a and b be nonzero complex numbers and let n be a positive integer satisfying $n{\geq}21$ ($n{\geq}12$, respectively). We show that if the difference polynomials $f^n(z)+af(z+{\eta})$ and $g^n(z)+ag(z+{\eta})$ share b CM, and if f and g share 0 and ${\infty}$ CM, where ${\eta}{\neq}0$ is a complex number, then f and g are either equal or at least closely related. The results in this paper are difference analogues of the corresponding results from.

• East Asian mathematical journal
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• 제31권1호
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• pp.103-107
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• 2015

We use some known contiguous function relations for $_2F_1$ to show how simply the following three recurrence relations for Jacobi polynomials $P_n^{({\alpha},{\beta)}(x)$: (i) $({\alpha}+{\beta}+n)P_n^{({\alpha},{\beta})}(x)=({\beta}+n)P_n^{({\alpha},{\beta}-1)}(x)+({\alpha}+n)P_n^{({\alpha}-1,{\beta})}(x);$ (ii) $2P_n^{({\alpha},{\beta})}(x)=(1+x)P_n^{({\alpha},{\beta}+1)}(x)+(1-x)P_n^{({\alpha}+1,{\beta})}(x);$ (iii) $P_{n-1}^{({\alpha},{\beta})}(x)=P_n^{({\alpha},{\beta}-1)}(x)+P_n^{({\alpha}-1,{\beta})}(x)$ can be established.

• 한국식품저장유통학회지
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• 제12권3호
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• pp.275-281
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• 2005

우슬이 민간요법으로 관절염 치료에 우수한 한약재로 알려진 바 우슬 추출물이 cathepsin B 에 대한 저해력을 검토하기 위하여 각종 용매로 우슬 추출물을 순차 분획하고 분획 추출물에 대하여 cathepsin B에 대한 저해활성을 검토하였으며 우슬의 지표물질인 20-hydroxy ecdysone이 추출분획에 검출되는지 TLC 및 HPLC를 이용하여 분석하였으며 우슬의 지표물질이 cathepsin B에 대한 저해활성여부를 확인한바 다음과 같은 결과를 얻었다. 우슬 뿌리에 대해 methanol/water(4:1, v/v) 추출물을 ethyl acetate, chloroform, chloroform/methanol(3:1, v/v), methanol의 각 용매로 분획한 결과, 분획 F4(methanol 분획)에서 수율이 가장 높아 $8.27\%$를 나타내었다. 각 분획별에 따라 cathepsin B에 대한 저해활성을 측정한 결과 F4분획물에서 가장 저해활성이 높았으며 F1분획에서도 높은 저해활성을 나타내었다. F4분획물 중 우슬의 지표물질인 20-hydroxy ecdysone이 검출되었으며 우슬에 함유되어있는 함량은 $0.33\%$이었다. 20-hydroxy ecdysone에 대하여 cathepsin B저해활성을 보기 위하여 cathepsin B저해활성제로 알려진 leupeptin과 활성을 비교해본 결과 기질을 BANA로 사용하였을 경우 leupeptin은 저해율이 $92\%$인데 비하여 20- hydroxy ecdysone은 $88\%$이었으며 F4분획물은 $97\%$를 나타내었고 기질을 CLN으로 사용하였을 경우 leupeptin은 저해율이 $62\%$인데 비하여 20-hydroxy ecdysone은 $36\%$이었으며 F4추출물은 $67\%$를 나타내었다.

• 대한수학회논문집
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• 제33권2호
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• pp.495-505
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• 2018

The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function f(z) that shares a nonzero polynomial a(z) with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_1(z)f^{(1)}(z)+a_2(z)f^{(2)}(z)+{\cdots}+a_n(z)f^{(n)}(z)$, where the coefficients $a_k(z)(k=1,2,{\ldots},n)$ are rational functions and $a_n(z){\not{\equiv}}0$.

• 대한수학회논문집
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• 제20권4호
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.