• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.773-793
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• 2001

The explicit expressions for the 2n+1 primitive idempotents in R/sub pⁿ/ = F[x]/< x/sup pⁿ/ -1>, where F is the field of prime power order q and the multiplicative order of q modulo pⁿ is ø(pⁿ)/2(n≥1 and p is an odd prime), are obtained. An algorithm for computing the generating polynomials of the minimal QR cyclic codes of length pⁿ, generated by these primitive idempotents, is given and hence some bounds on the minimum distance of some QR codes of prime length over GF(q)(q=2, 3, ...) are obtained.

• Journal of the Korean Chemical Society
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• v.22 no.5
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• pp.317-319
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• 1978

The change of the electron densities of polydentate amine ligands in the reaction of protonation are discussed on the basis of the calculation by Two Center Huckel method. From results, such as ${\Delta}E_{\sigma}$, $q_N,\;q_H$ , and observed pKb, it is concluded that the stabilities of polydentate amine ligands are in the order of trien > en > gly > dien.

• Journal of the Korean Institute of Landscape Architecture
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• v.20 no.1
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• pp.80-94
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• 1992

To inspect the changing of the forest soil and plants community structrure by air plooutand & acid rain during from September to November in 1990, the smapling sites were selected in the Piwon, Namsan and Kwangnung forest. In sites, plots were set up in Q. aliena forest at Piwon, Quercus mongolica and Pinus densiflora forest at Namsan and Q. mongolica and Pinus densiflora forest at Kwangnung. To obtain the individual number of trees, number of species, importance values and species diversity, using the Curtis & McIntosh methods. The results are following that; 1) In Pinus densiflora community, it was almost dominated by Q. spp. in the canopy layer and P. densiflora and Carpinus laxiflora through the subtree to shrub layer at Kwangnung. It wassaid that C. laxiflora is the climax species in moddle temperature zone. On the contrary, in Namsan forest, there is no appearance thesamplings of P. densiflora & C. laxiflora, but Styrax japonica and Stephanandra incisa that are acid-tolerance species are dominant ones. On the other hand, in Q. spp. community, Q. spp. and C. laxiflora are dominant ones. On the other hand, in Q. spp. community, Q. spp. and C. laxiflora are dominant species through all layer, and in addition C. cordata somewhat appear at Kwangnung. But at Namsan and Piwon forest, Q. mongolica & Q. aliena that were dominant species in canopy layer disappeared in the subtreeand shrub layer, and C. laxiflora and Corunus cordata absolutely disappeared. It were similarly dominated by Robinia pseudo-acacia, Styrax japonica, Sorbus alnifolia, Acer pseudo-sieboldianum, Rhododendrn mucronulatum and so on at Namsn and Piwon forest. In the light of these facts, it found out that disclimax was similar between Namsan and Piwon forest. 2) Species diversity and maximum species diversity were decreased in Kwangnumg, Namsan, Piwon in order. It was xpected that vegetational community was affected by environmental pollutant. 3) As the vegetational community structure analyses, using DCA technique among the ordination, ecological successional series are stopped to Q. spp. from P. densiflora at Namsan and Piwon, but that of Kwangnung is on the way that P. densiflora, Q. alena, C. laxiflora. It was obvi ously different from Namsan and Piwon. 4) In Q. spp. & P. densiflora community, the number of woody plants inNamsan & Piwon is much less than that of Kwangnung through all Layer. Especially, Piwon shown very severe difference. Through all community, the number of individuals of Piwon and Namsan are less than that of Kwangnung. Specially, that of the shrub layer is obvious. 5) In the growth rate of trees, it found out that all sites showed the growth decline phenomena. Especially, since in 1975, there have been the micro disclimax phenomena in Q. community of Kwangnung. 6) In the Q. community, soil acidity of Namsan & Piwon measured 4.57, 4.40 respectively. It was very strong acidity and far lower than that of Kwangnung. Also the content amount of Mg++ in Namsan & Piwon forest were still lower than Kwangnung.

• Korean Journal of Mathematics
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• v.19 no.3
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• pp.309-319
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• 2011

We give sufficient conditions that the homogeneous differential equations : for $t{\geq}t_0$(> 0), $$x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+p(t)x(t)=0,\\x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+F(t,x({\phi}(t)))=0$$, are oscillatory where $0{\leq}{\phi}(t)$, 0 < ${\phi}^{\prime}(t)$, $\lim_{t\to{\infty}}{\phi}(t)={\infty}$. and $F(t,u){\cdot}sgn$ $u{\leq}p(t)|u|$. We obtain comparison theorems.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.391-402
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• 2011

We give necessary and sufficient conditions such that the homogeneous differential equations of the type: $$(r(t)x^{\prime}(t))^{\prime}+q(t)x^{\prime}(t)+p(t)x(t)=0$$ are nonoscillatory where $r(t)$ > 0 for $t{\in}I=[{\alpha},{\infty})$, ${\alpha}$ > 0. Under the suitable conditions we show that the above equation is nonoscillatory if and only if for ${\gamma}$ > 0, $$(r(t)x^{\prime}(t))^{\prime}+q(t)x^{\prime}(t)+p(t)x(t-{\gamma})=0$$ is nonoscillatory. We obtain several comparison theorems.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.855-890
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• 1999

Necessary and sufficient conditions on the weight functions u(.) and $\upsilon$(.) are derived in order that the fractional maximal operator $M\alpha,\;0\;\leq\;\alpha\;<\;1$, is bounded from the weighted amalgam space $\ell^s(L^p(\mathbb{R},\upsilon(x)dx)$ into $\ell^r(L^q(\mathbb{R},u(x)dx)$ whenever $1\leq s\leq r<\infty\;and\;1. The boundedness problem for the fractional intergral operator $I_{\alpha},0<\alpha\leq1$, is also studied.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.43-46
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• 2018

It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the Hardy-Littlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from $L^p({\mathbb{R}}^n)$ to $L^q({\mathbb{R}}^n)$ for 1 ${\leq}$ q < p < ${\infty}$.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.195-205
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• 2022

In this paper, we provide various characterizations for the composition operator on Lorentz spaces L(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ to have finite ascent (descent) in terms of its inducing measurable transformation. At the end, in order to demonstrate our outcomes, some examples are given.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.499-513
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• 2011

By using the Riccati transformation technique, we study the oscillation and asymptotic behavior for the third-order nonlinear delay dynamic equations $(c(t)(p(t)x^{\Delta}(t))^{\Delta})^{\Delta}+q(t)f(x({\tau}(t)))=0$ on a time scale T, where c(t), p(t) and q(t) are real-valued positive rd-continuous functions defined on $\mathbb{T}$. We establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Our oscillation results are essentially new. Some examples are considered to illustrate the main results.

• Korean Chemical Engineering Research
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• v.61 no.2
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• pp.273-277
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• 2023

The biosorption of methylene blue (MB) from aqueous solution was investigated using dried Rhodotorula glutinis as the biosorbent. The effects of pH, initial dye concentration, biosorbent dosage, and kinetic studies were determined to obtain valuable information for biosorption. Results indicated that most of the adsorbed MB bound within 30 minutes of contact and the MB adsorption capacity increased from 21.1 to 101.8 mg/g with the initial MB concentration increased from 50 to 300 mg/L. Additionally, the MB adsorption capacity gradually increased from pH 4.0 to 9.0, reaching its peak at an initial pH of 9.0. As the biomass load was increased from 0.25 to 4.0 g/L, the MB removal efficiency increased from 14.1 to 84.5%. The Langmuir model provided the best fit throughout the concentration range, and the maximum adsorption capacity (q_max) and Langmuir constant (b) were determined to be 135.14 mg/g and 0.026 l/mg, respectively. Furthermore, the biosorbent process of R. glutinis was found to follow pseudo-second-order kinetics and the calculated q_eq,cal value showed good agreement with the experimental q_eq value. Overall, the biosorption of MB by R. glutinis can be characterized as a monolayer, single site type phenomenon, and the rate-limiting step was determined to be the chemical reaction between the adsorbent and the adsorbate.