• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1001-1017
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• 2023

Let R be a commutative graded ring with nonzero identity and n a positive integer. Our principal aim in this paper is to introduce and study the notions of graded n-irreducible and strongly graded n-irreducible ideals which are generalizations of n-irreducible and strongly n-irreducible ideals to the context of graded rings, respectively. A proper graded ideal I of R is called graded n-irreducible (respectively, strongly graded n-irreducible) if for each graded ideals I₁, . . . , I_n+1 of R, I = I₁ ∩ · · · ∩ I_n+1 (respectively, I₁ ∩ · · · ∩ I_n+1 ⊆ I ) implies that there are n of the I_i 's whose intersection is I (respectively, whose intersection is in I). In order to give a graded study to this notions, we give the graded version of several other results, some of them are well known. Finally, as a special result, we give an example of a graded n-irreducible ideal which is not an n-irreducible ideal and an example of a graded ideal which is graded n-irreducible, but not graded (n - 1)-irreducible.

• YAKHAK HOEJI
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• v.35 no.4
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• pp.288-294
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• 1991

A new fluorescent derivatizing reagent was developed to be used in HPLC for the trace determination of primary and secondary amines. This new reagent, 1-(N,N-dimethylamino)pyrene-6-sulfonyl chloride, was synthesized by the chlorination of sodium 1-(N,N-dimethylamino)pyrene-6-sulfonate which was obtained from 1-(N,N-dimethylamino)pyrene after sulfonation. Ephedrine and norephedrine were derivatized quantitatively by this reagent. The optimum conditions for the derivatization such as pH, reagent concentration, reaction time and reaction temperature ware examined. The structures of derivatives were identified by IR, $^{1}$H-NMR and MS methods. The fluorescence properties and the stability of the derivatives were examined. The derivatives were separated on silica column with an isocratic elution using the mixture of n-hexane and ethylacetate and monitored by fluorescene detector. Linear calibration curves were obtained and detection limits in a 10 $\mu$l injection volume were 5 picomole for ephedrine and norephedrine.

• Journal of the Korean Ceramic Society
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• v.32 no.7
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• pp.809-816
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• 1995

Ti1-xAlxN films were successfully deposited on high speed steel and silicon wafer by plasma-assisted chemical vapor deposition using a TiCl4/AlCl3/N2/Ar/H2 gas mixture. Plasma process enabled N2 gas to nitride AlCl3, which is not possible in sense of thermodynamics. XPS analyses revealed that the deposited layer contained Al-N bond as well as Ti-N bond. Ti1-xAlxN films were polycrystalline and had single phase, B1-NaCl structure of TiN. Interplanar distance, d200, of (200) crystal plane of Ti1-xAlxN was, however, decreased with Al content, x. Al incorporation into TiN caused the grain size to be finer and changed strong (200) preferred orientation of TiN to random oriented microstructure. Those microstructural changes with Al addition resulted in the increase of micro-hardness of Ti1-xAlxN film up to 2800Kg/$\textrm{mm}^2$ compared with 1400Kg/$\textrm{mm}^2$ of TiN.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.35-48
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• 2023

Let 𝔼 be a CAT(0) space and K be a nonempty closed convex subset of 𝔼. Let T : K → 𝓟(K) be a multimap such that F(T) ≠ ∅ and ℙ_T(x) = {y ∈ Tx : d(x, y) = d(x, Tx)}. Define sequence {x_n} by x_n+1 = (1 - α)𝜈_n⊕αw_n, y_n = (1 - β)u_n⊕βw_n, z_n = (1-γ)x_n⊕γu_n where α, β, γ ∈ [0; 1]; u_n ∈ ℙ_T (x_n); 𝜈_n ∈ ℙ_T (y_n) and w_n ∈ ℙ_T (z_n). (1) If ℙ_T is quasi-nonexpansive, then it is proved that {x_n} converges strongly to a fixed point of T. (2) If a multimap T satisfies Condition(I) and ℙ_T is quasi-nonexpansive, then {x_n} converges strongly to a fixed point of T. (3) Finally, we establish a weak convergence result. Our results extend and unify some of the related results in the literature.

• Journal of the Korean Chemical Society
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• v.19 no.2
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• pp.134-141
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• 1975

DL-1-aminoethylphosphonic acid(1-AEP) and DL-1-aminopropylphosphonic acid(1-APP) were synthesized from the propionic acid and butyric acid respectively using the modified cutius degradation. The following unreported derivatives containing peptide linkage were synthesized: N-phthalylglycyl-1-AEP, N-phthalyl-dl-alanyl-1-AEP, N-phthalyl-dl-phenylalanyl-1-AEP, N-phthalylglycyl-1-APP, N-tosylglycyl-1-AEP and N-tosyl-dl-alanyl-1-AEP These compounds were characterized and identified by means of elemental analysis, potentiometric titration, infrared spectroscopy and ninhydrin test.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.457-466
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• 2004

Let{$X_{ni}$\mid$\;1\;{\leq}\;i\;{\leq}\;k_n,\;n\;{\geq}\;1$} be an array of rowwise negatively associated random variables such that $P$\mid$X_{ni}$\mid$\;>\;x)\;=\;O(1)P($\mid$X$\mid$\;>\;x)$ for all $x\;{\geq}\;0,\;and\; \{k_n\}\;and\;\{r_n\}$ be two sequences such that $r_n\;{\geq}\;b_1n^r,\;k_n\;{\leq}\;b_2n^k$ for some $b_1,\;b_2,\;r,\;k\;>\;0$. Then it is shown that $\frac{1}{r_n}\;max_1$\mid${\Sigma_{i=1}}^j\;X_{ni}$\mid$\;{\rightarrow}\;0$ completely convergence and the strong convergence for weighted sums of N A arrays is also considered.

• Archives of Pharmacal Research
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• v.20 no.1
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• pp.53-57
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• 1997

For the purpose of defining the effects of the N-substituted alkyl groups on the anticonvulsant activities of N-Cbz-.alpha.-aminosuccinimides, various (R)- and (S)-N-alkyl substituted N-Cbz-.alpha.-aminosuccinimides (1 and 2) were prepared from the corresponding (R)- and (S)-N-Cbz-aspartic acid by using known reaction and were evaluated the anticonvulsant activies in the MES and PTZ tests, including their neurotoxicities. The most active compound in the MES test was (R)N-Cbz-.alpha.-amino-N-methylsuccinimide (1b) $(ED_{50}=52.5 mg/kg, Pl=3.2)$. And in case of the PTZ test, (R)-N-Cbz-.alpha.-amino-N-ethylsuccinimide (1c) was the most active compound $(ED_{50}/=32.5mg/kg, Pl=3.1)$. The order of anticonvulsant activities of these compounds against the MES test, as judged from the ED_50values for the R series (1), was N-methyl > N-isobutyl > non-substituted > N-ethyl, N-allyl > N-benzyl compound; for the S series (2) N-methyl > N-altyl > non-substituted > N-isobutyl > N-ethyl > N-benzyl compound. The anticonvulsant activities in the PTZ tests of these compounds exhibited somewhat different pattern ; for the R series (1) Nethyl > N-methyl > N-isobutyl> non-substituted > N-allyl > N-benzyl compound in order of decreasing activity; for S series (2) N-ethyl > N-allyl, non-substituted > N-isobutyl > N-methyl > N-benzyl compound in order of decreasing activity.

• Journal of Astronomy and Space Sciences
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• v.9 no.1
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• pp.11-29
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• 1992

In 1963, Toomre built up classes of mass models for the highly flattened galaxies which have free parameters n, $a_n$ and $C_n$. In order to keep the universal dimension, we adopt parameters $b_n({C_n}^2={a_n}^{2n}+^2{b_n}^2/(n-1)!)$ insteal of $C_n$. Series of the normalized Toomre's mass models (G = $V_{max}$ =$R_{max}$ = 1, n = 1 to 7) are derived and the normalized parameters $a_n$ and $b_n$ are determined by the iteration method. Replacing parameters $a_n$ and $b_n$ to ${a_n}^l(=a_nr_{max})$ and ${b_n}^l(=b_n\cdotV_{max}/r_{max})$, we can get the generalization of Toomre's mass model.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.507-513
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• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.501-508
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• 2009

In this paper, we prove that folded hyper-star network FHS(2n,n) is node-symmetric and a bipartite network. We show that FHS(2n,n) can be embedded into odd network On+1 with dilation 2, congestion 1 and Od can be embedded into FHS(2n,n) with dilation 2 and congestion 1. Also, we show that $2n{\time}n$ torus can be embedded into FHS(2n,n) with dilation 2 and congestion 2.