• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.405-434
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• 2005

We establish appropriate $L^p$ estimates for a class of maximal operators $S_{\Omega}^{(\gamma)}$ on the product space $R^n\;\times\;R^m\;when\;\Omega$ lacks regularity and $1\;\le\;\gamma\;\le\;2.\;Also,\;when\;\gamma\;=\;2$, we prove the $L^p\;(2\;{\le}\;P\;<\;\infty)\;boundedness\;of\;S_{\Omega}^{(\gamma)}\;whenever\;\Omega$ is a function in a certain block space $B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ (for some q > 1). Moreover, we show that the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is nearly optimal in the sense that the operator $S_{\Omega}^{(2)}$ may fail to be bounded on $L^2$ if the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is replaced by the weaker conditions $\Omega\;{\in}\;B_q^{(0,\varepsilon)}(S^{n-1}\;\times\;S^{m-1})\;for\;any\;-1\;<\;\varepsilon\;<\;0.$

• Polymer(Korea)
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• v.36 no.4
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• pp.427-433
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• 2012

A series of poly(imide-aramid-sulfone)s with alternatingly introduced imide/aramid groups were prepared by reacting divinyl sulfone (DVS) and $N^1,N^4$-bis(4-(vinylsulfonyl)phenyl)terephthalamide (2) with pyromellitic diimide. Three model compounds, N-[2-(p-aminophnenylsulfonyl)ethyl]phthalimide (3), 2,2'-(2,2'-sulfonylbis(ethane-2,1-diyl))diisoindoline-1,3-dione (4), and N,N-bis(4-(2-(1,3-dioxoisoindolin-2-yl)ethylsulfonyl)phenyl)terephthalamide (5), resembling polymers were prepared with good yields by reacting p-aminophenyl vinyl sulfone, DVS, and 2 with phthalimide. Condensation polymerization was carried out by Michael-type addition reaction of the difunctional phthalimide group with the DVS group in the presence of tetrabutylammonium hydroxide (TBAH), resulting in poly(imide-aramid-sulfone)s 6-12 with moderate molecular weights and good yields. They were highly soluble in polar solvents such as N,N-dimethylformamide, dimethylsulfoxide, N-methylpyrrolidinone and tetrahydrofuran. The ratios of DVS/2 were 1/0, 3/1, 2/1, 1/1, 1/2, 1/3, and 0/1. Molecular weight and physical properties such as solubility, viscosity, and thermal properties of the polymers were examined.

• Journal of Sericultural and Entomological Science
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• v.45 no.1
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• pp.6-9
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• 2003

This experiment was done to know developmental characteristics of Sericin jam. Incubation periods were 10 day 2 hr, and 10 day 1 hr. 11 day 1 hr for Nd-s jam, N $d^{H}$ jam, and Baegok jam, respectively. Hatching rates were 83.9, 83.3 and 96.0% for Nd-s jam, N $d^{H}$ jam, and Baegok jam. Larval periods were, 20 days 1 hr for Nd-s jam, 20 days 5 hrs for N $d^{H}$ jam, and 22 days 12 hrs for Baegok jam. Death rate of larvae was highest in N $d^{H}$ iam, followed by Nd-s jam and Baegok jam. Pupation rate was highest in Baegok Jam followed by Nd-s jam and that of N $d^{H}$ jam was the lowest among the three. Cocoon weight was 1.39, 1.08, and 2.01 g for Nd-s jam, N $d^{H}$ jam, and Baegok jam, respectively. Shell weight were 13, 3, and 48 cg for Nd-s jam, N $d^{H}$ jam, and Baegok jam. Cocoon shell ratios were 9.0% for Nd-s jam, 2.8% for N $d^{H}$ jam and 23.9% for Baegok jam. Cocoon sizes were 30.6${\times}$15.8 mm for Nd-s jam, 24.7${\times}$14.9 mm for N $d^{H}$ jam and 35.8 ${\times}$ 20.5 mm(1${\times}$w) for Baegok jam.w) for Baegok jam.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.25-43
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• 2005

Let F be a finite field of prime power order q(odd) and the multiplicative order of q modulo $2^{n}\;(n>1)\;be\; {\phi}(2^{n})/2$. If n > 3, then q is odd number(prime or prime power) of the form $8m{\pm}3$. If q = 8m - 3, then the ring $R_{2^n} = F[x]/ < x^{2^n}-1 >$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length $2^{n}$ generated by these idempotents are completely described. If q = 8m + 3 then the expressions for the 2n - 1 primitive idempotents of $R_{2^n}$ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n-1 idempotents are also obtained. The case n = 2,3 is dealt separately.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.19-25
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• 2017

This paper deals with integer factorization of two prime p,q of SHA-256 secure hash value n for Bit coin mining. This paper proposes an algorithm that greatly reduces the execution time of Pollard's rho integer factorization algorithm. Rho(${\rho}$) algorithm computes $x_i=x^2_{i-1}+1(mod\;n)$ and $y_i=[(y^2_{i-1}+1)^2+1](mod\;n)$ for intial values $(x_0,y_0)=(2,2)$ to find the factor 1 < $gcd({\mid}x_i-y_i{\mid},n)$ < n. It however fails to factorize some particular composite numbers. The algorithm proposed in this paper applies multiple initial values $(x_0,y_0)=(2^k,2^k)$ and ($2^k,2$), $2{\leq}k{\leq}10$ to the existing Pollard's Rho algorithm. As a results, the proposed algorithm achieves both the factorization of all the composite numbers and the reduction of the execution time of Pollard's Rho by 67.94%.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.

• Journal of the Korean Chemical Society
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• v.54 no.3
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• pp.287-290
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• 2010

In the present work we described oxidative cyclisation of peracetylated lactosyl carbamides with N-phenyl-S-chloro isothiocarbamoyl chloride and structural elucidation of novel peracetylated N-Lactosyl-1,2,4-Thiadiazolidin-3-one hydrochlorides. Antimicrobial activities of the title compounds were determined against bacteria S. aureus, E. coli, P. Vulgaris, P. Aeruginosa and fungi A. Niger, Penicillium.

• Journal of Animal Environmental Science
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• v.18 no.3
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• pp.145-150
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• 2012

This study was conducted to measure methane ($CH_4$) and nitrous oxide ($N_2O$) emissions from the 6 month old litter stockpile used for korean native cattle (Hanwoo) from August 3, 2007 to October 4, 2007. Daily mean $CH_4$ emissions was peaked to 273.013 ${\mu}g\;m^{-2}\;s^{-1}$ (SE : ${\pm}1.047{\mu}g\;m^{-2}\;s^{-1}$) on first day and then gradually decreased to 2.309 ${\mu}g\;m^{-2}\;s^{-1}$ (SE : ${\pm}0.061{\mu}g\;m^{-2}\;s^{-1}$) at the end of this experiment. Daily mean $N_2O$ emissions was as little as 0.269 ${\mu}g\;m^{-2}\;s^{-1}$ (SE : ${\pm}0.018{\mu}g\;m^{-2}\;s^{-1}$) on first day, but exponentially increased up to 3.569 ${\mu}g\;m^{-2}\;s^{-1}$ (SE : ${\pm}0.454{\mu}g\;m^{-2}\;s^{-1}$) on 43rd day and then slowly decreased to 1.888 ${\mu}g\;m^{-2}\;s^{-1}$ (SE : ${\pm}0.012{\mu}g\;m^{-2}\;s^{-1}$) at the end of this experiment. Carbon dioxide equivalent ($CO_2$-eq), calculated by global warming potentials of $CH_4$ or $N_2O$, of $CH_4$ on first day occupied approximately 99% of sum of $CO_2$-eq of $CH_4$ and $N_2O$. Methane emissions decreased and $N_2O$ emissions increased so that $CO_2$-eq ratio of $CH_4$ to $N_2O$ was 50:50 on 34th day. The effect of $N_2O$ on the ratio was increase thereafter. The ratio of daily mean $CH_4$ and $N_2O$ emissions to daily error of the mean was calculated to find daily fluctuation of $CH_4$ and $N_2O$ emissions. The ratio of $CH_4$ was less than 1.0% till 11th day but increased to 10.9% on 57th day. The ratio of $N_2O$ (0.4%~51.0%) was higher than that of $CH_4$, showing high in early stage and then gradually decrease, which was different from the pattern of $CH_4$. The ratio of daily mean emissions to daily error of the mean was little in case of active $CH_4$ or $N_2O$ generation period, which would be caused by the temporal and spatial heterogeneity of composting process. Hence more air supply on early stage to decrease $CH_4$ generation and proper turning to reduce spatial heterogeneity are needed to mitigate greenhouse gas emissions.

• Bulletin of the Korean Chemical Society
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• v.23 no.1
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• pp.123-131
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• 2002

Solvolyses rate constant of 1- and 2- naphthoyl chlorides (1 and 2) are reported for aqueous binary mixtures with methanol, ethanol, fluorinated alcohol, acetonitrile and dioxane. Kinetic solvent isotope effects (KISE) in methanol and product selectivities (S) of 2-naphthoyl chloride (2) in alcohol-water are also reported. Dispersions in Grunwald-Winstein correlations $(r{\leq}0.901)$ are discussed by multiple regression analysis incorporating ionizing power $(Y_{Cl})$ scale and rate-rate profiles. Major causes for these phenomena are investigated as an aromatic ring solvation effects, in conjunction with weakly nucleophilic solvation effects ($S_N2$ character), for solvolyses of 1 and for solvolyses of 2, as dual reaction channels, described as $S_N1$-$S_N2$ and $S_AN$-$S_N2$ processes. Distinct border lines between the two pathways are derived from solvolyses rates of 2 in 18 solvent using the results of $log(k/k_o)=mY_{Cl}+lN_T+hI$ plot with values of 1.13 for m, 0.37 for l and 0.15 for h value in 5 aqueous fluorinated alcohol mixtures. Using rate-product correlation, the validity of a third order model based on a general base catalyzed by solvent and contribution from these rate constants, $k_{aa},\;k_{aw}$ and $k_{aw}$, are investigated for $S_AN$-$S_N2$ solvolyses of 2 favored in more rich alcohol media and gradual addition of water to alcohol solvent shows a great shift away from stoichiometric solvation to predominantly medium effects. Rate-rate correlation between solvolyses of 2 and trimethyl acetylchloride (5) with alkyl group in the 29 aqueous solvent mixtures shows appreciable linearity (slope = 0.84, r = 0.987), caused by the same pathway ($S_N1$-$S_N2$ process), even if this correlation coincides with appreciable dispersion (different solvation effect).

• Journal of the Korean Vacuum Society
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• v.6 no.4
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• pp.314-320
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• 1997

A chemical reaction and electronic structure change at the interface between copper and titanium nitride were investigated by XPS. A thin Cu layer was deposited on a TiN substrate oxidized by exposure to air at room temperature. We observed the Ti(2p), O(1s), N(1s), Cu(2p) core-level, and Cu LMM Auger line spectra. With increasing of the thickness of Cu layer, these spectra do not show any changes in the line shape as well as in peak position. In addition, the valence band spectra in XPS do not show any changes, which indicates that Cu does not react with Ti, N, and O. This inreactivity of Cu might cause a poor adhesion between Cu and TiN.