• 대한수학회지
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• 제55권6호
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• pp.1469-1483
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• 2018

We study a subclass of p-ary functions in n variables, denoted by ${\mathcal{A}}_n$, which is a collection of p-ary functions in n variables satisfying a certain condition on the exponents of its monomial terms. Firstly, we completely classify all p-ary (n - 1)-plateaued functions in n variables by proving that every (n - 1)-plateaued function should be contained in ${\mathcal{A}}_n$. Secondly, we prove that if f is a p-ary r-plateaued function contained in ${\mathcal{A}}_n$ with deg f > $1+{\frac{n-r}{4}}(p-1)$, then the highest degree term of f is only a single term. Furthermore, we prove that there is no p-ary r-plateaued function in ${\mathcal{A}}_n$ with maximum degree $(p-1){\frac{n-4}{2}}+1$. As application, we partially classify all (n - 2)-plateaued functions in ${\mathcal{A}}_n$ when p = 3, 5, and 7, and p-ary bent functions in ${\mathcal{A}}_2$ are completely classified for the cases p = 3 and 5.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.229-234
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• 2005

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $x_{n+l} =\alpha+\frac{x_{n-1}^{p}}{x_{n}^{p}},\;\; n = 0, 1, ...$ is investigated, where all the coefficients are nonnegative real numbers.

• 대한수학회보
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• 제49권3호
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• pp.465-479
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• 2012

For $0<p{\leq}{\infty}$ and a convex body $K$ in $\mathbb{R}^n$, Lutwak, Yang and Zhang defined the concept of dual $L_p$-centroid body ${\Gamma}_{-p}K$ and $L_p$-John ellipsoid $E_pK$. In this paper, we prove the following two results: (i) For any origin-symmetric convex body $K$, there exist an ellipsoid $E$ and a parallelotope $P$ such that for $1{\leq}p{\leq}2$ and $0<q{\leq}{\infty}$, $E_qE{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$; For $2{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, $2^{-1}{\omega_n}^{\frac{1}{n}}E_qE{\subseteq}{\Gamma}_{-p}K{\subseteq}{2\omega_n}^{-\frac{1}{n}}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$. (ii) For any convex body $K$ whose John point is at the origin, there exists a simplex $T$ such that for $1{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, ${\alpha}n(nc_{n-2,p})^{-\frac{1}{p}}E_qT{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qT$ and $V(K)=V(T)$.

• 호남수학학술지
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• 제16권1호
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• pp.119-135
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• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• 한국통신학회논문지
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• 제33권9C호
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• pp.669-675
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• 2008

홀수인 소수 p와 n=4k, 그리고 $d=((p^2k+1)/2)^2$에 대해서, 주기가 $p^n-1$인 p-진 m-수열 s(t)에 대해서 $(p^{2k}+1)/2$개의 서로 다른 decimated 수열들 s(dt+1), $0{\leq}l<(p^{2k}+1)/2$가 존재한다. 이 논문에서는 s(t)와 s(dt+l), $0{\leq}l<(p^{2k}+1)/2$ 사이의 상호상관 값이 $\{-1,-1{\pm}\sqrt{p^n},-1+2\sqrt{p^n}\}$과 같음을 보이고, 상호 상관 값의 분포를 유도하였다.

• 대한화학회지
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• 제37권6호
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• pp.618-625
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• 1993

25$^{\circ}C$의 50%(v/v) 메탄올-물의 혼합용액 속에서 pH 변화에 따른 X-치환된 N-(benzoyl)-C-(N-methylanilino)imidoylchloride(s)들의 가수분해 반응속도상수를 측정하여 반응속도식, 치환기효과, 용매효과, 염효과, 열역학적 활성화 파라미터 및 가수분해반응 생성물 분석 등의 결과로부터 pH 3.0~10.0까지의 사이에서는 azocarbonium ion 중간체를 지나는 $S_N$1형 반응, pH 3.0 이하의 pH 10.0 이상의 pH에서는 사면체 중간체를 지나는 친핵성 첨가-제거반응(A$d_{N-E}$)이 일어남을 제안하였다.

• 환경생물
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• 제31권4호
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• pp.383-392
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• 2013

본 연구는 식물성 플랑크톤의 1차 생산력에 대한 N:P ratio의 영향을 분석하기 위해 "영양염 첨가실험(NEBs)"을 실시하였다. 영양염 첨가실험(NEBs)에 의한 N:P Ratio의 영향은 대청호에서 측정된 수질데이터와 비교분석하였다. 단기 영양염 첨가실험 결과, 인 (P)을 첨가한 처리군들 (N:P Ratio=5, 15, 20, 30)에서의 1차 생산력의 반응이 대조군 (Control)과 인(P)을 첨가한 처리군 (N:P Ratio=80, $T_V$), 질소(N)를 첨가한 처리군(N:P Ratio=150, $T_{VI}$)에서보다 높았다. 또한 질소 (N)를 처리한 처리군에서는 대조군과 모든 처리군에서보다 1차 생산력의 반응이 유의하게 작았다. 영양염 첨가실험의 결과, 식물성 플랑크톤의 성장에 인이 제한영양염으로 작용하고 있었으며, 질소첨가 (Spiking N)는 식물성 플랑크톤의 성장을 억제한 것으로 사료된다. 대청호의 영양염 변이 분석 결과, 최소 N:P Ratio에서 엽록소-a의 최대농도가 나타났고, N:P Ratio는 식물성 플랑크톤의 성장에 대한 핵심 조절자로 사료되었다. 본 연구결과를 종합해 볼 때, N:P Ratio가 식물성 플랑크톤의 성장을 조절하는 핵심 인자로 작용 할 것으로 사료된다.

• Journal of Ginseng Research
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• 제20권3호
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• pp.291-298
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• 1996

Free amino acid (FAA) compositions in the central part (pith-xylem : P-X) and the outer part (phloem-cortex : P-C) of root were investigated for P ginseng (P.g), p. quinque-folium (P.q) an, B P nutoginsen (P.n) by an amino acid analyzer. Total free amlno acids content (TFAA) was highest in p.맥 and lowest in p.n. The TFAA of P-Xs were higher than those of P-Cs in these Panax species except p.n. The higher the TFAA in P-X, the higher the ratio of TFAA in P-X to that in P-C. Seven- teen free amino acids and ammonia were identified, and four unknown peaks appeared before the usual amino acids eluted. The total aspartic acid equivalent of these unknown peaks was corresponded to 77% of known TFAA in P-C of p.n, 17% in P. n, and 7% in p.q. The pattern of unknown peaks of p.g was different from p.q and similar to P.n. In all samples six major amino acids and ammonia accounted for 90~95% of TFAA. Arginine was comprised from 29% (P.n) to 43% (P.g) by amole as amino acid and from 50 to 71% by amole as nitrogen (N amole) in TFAA. Ammonia was the second abundant one by amole and the third by Npmole. Histidine was the second by Npmole. Praline was one of major FAA in p.q. Pattern similarity of FAA composition (excluding Arg and Am) by simple correlation was closer between P-C of p.g and P-X of p.q than between both P-Xs and quite different between the P-X of p.g and that of p.n. The pattern similarities of major FAA percent abundance excluding Arg and Am were significant only between P-X and P-C of the same species. Arginine content (amole) had positive correlation (r=0.859, p=0.05) with Arg/Am among species. Ammonia content was higher than arginine in p.n. Tryptophan content was greatest in p.n among species and higher than lysine only in p.n. The ratios of TFAA to N(W/W) were in the range of 3.89~4.14 for TFAA and 3.61~3.92 for TFAA plus ammonia.

• Korean Journal of Mathematics
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• 제17권2호
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• pp.169-179
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• 2009

Let P be a (n, n − 1, j)-poset, which is a partially ordered set of cardinality n with n − 1 maximal elements and $j(1{\leq}j{\leq}n-1)$ minimal elements, and $P^*$ the dual poset of P. In this paper, we obtain two types of incidence codes of nonempty proper subset S of P and $P^*$, respectively, by using Bogart's method [1] (see Theorem 3.3).

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.