• Journal of the Korean Mathematical Society
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• v.55 no.6
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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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• v.18 no.1_2
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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.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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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 $V(K)=V(T)$.

• Honam Mathematical Journal
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• v.16 no.1
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.9C
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• pp.669-675
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• 2008

For an odd prime p, n=4k and $d=((p^2k+1)/2)^2$, there are $(p^{2k}+1)/2$ distinct decimated sequences, s(dt+1), $0{\leq}l<(p^{2k}+1)/2$, of a p-ary m-sequence, s(t) of period $p^n-1$. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l) takes the values in $\{-1,-1{\pm}\sqrt{p^n},-1+2\sqrt{p^n}\}$ and their, cross-correlation distribution is also derived.

• Journal of the Korean Chemical Society
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• v.37 no.6
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• pp.618-625
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• 1993

Rate constants of hydrolysis of N-(benzoyl)-C-(N-methylanilino)imidoylchlorides were determined by UV spectrophotometry in 50% (v/v) aqueous methanol at 25$^{\circ}C$. On the basis of rate equation, substituent effect, solvent effect, salt effect, thermodynamic parameters and hydrolysis product analysis, it may be concluded that the hydrolysis of N-(benzoyl)-C-(N-methylanilino)imidoylchlorides proceed through $S_N$1 mechanism via azocarbonium ion intermediate in the range of from pH 3.0 to pH 10.0, while above pH 10.0 and below pH 3.0 the hydrolysis proceeds through nucleophilic addition-elimination (A$d_{N-E}$) mechanism.

• Korean Journal of Environmental Biology
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• v.31 no.4
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• pp.383-392
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• 2013

The objective of this study was to determine the effects of N:P ratio on primary productivity measured as chlorophyll-a (CHL) using the approach of In Situ Nutrient Enrichment Bioassays (NEBs) in Daechung Reservoir. The effects of NEBs on the N:P mass ratios were compared with the field data obtained from monthly-chemical monitoring during 2009~2012. The short-term NEBs showed that the response of primary productivity in the phosphorus spiked treatments (5, 15, 20 and 30 N:P ratios) were greater than the responses in the control (C) and nitrogen spiked treatment (N:P ratio=150, $T_{VI}$). The response in the nitrogen treatment (N:P ratio=150, $T_{VI}$) was less compared to control and all five treatments ($T_I{\sim}T_{VI}$). The outcomes of the NEBs suggest that phosphorus limited the phytoplankton growth and nitrogen addition inhibited the algal growth. In the analysis of nutrients and CHL from the ambient epilimnetic water in Daechung Reservoir, minimum N:P ratios resulted in maximum concentrations of CHL. Overall, our results suggest that the N:P ratio was the key factor in regulating the phytoplankton growth in NEB experiments.

• Journal of Ginseng Research
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• v.20 no.3
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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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• v.17 no.2
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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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• v.46 no.2
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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 $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.