• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.649-658
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• 2019

In this paper, we prove some congruences involving the generalized Catalan numbers and harmonic numbers modulo $p^2$, one of which is $$\sum\limits_{k=1}^{p-1}k^2B_{p,k}B_{p,k-d}{\equiv}4(-1)^d\{{\frac{1}{3}}d(2d^2+1)(4pH_d-1)-p\({\frac{26}{9}}d^3+{\frac{4}{3}}d^2+{\frac{7}{9}}d+{\frac{1}{2}}\)\}\;(mod\;p^2)$$, where a prime number p > 3 and $1{\leq}d{\leq}p$.

• Korean Journal of Pharmacognosy
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• v.30 no.2
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• pp.168-172
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• 1999

Five compounds were isolated from the roots of Polygala tenuifolia (Polygalaceae). On the basis of spectroscopic evidences, the structures of these compounds were characterized as ${\alpha}-D-(6-O-sinapoyl)-glucopyranosyl(1{\rightarrow}2')-{\beta}-D-(3'-O-sinapoyl)-fructofuranoside$ (P3), ${\alpha}$-D-{6-O-(p-methoxybenzoyl)}-glucopyranosyl-$(1{\rightarrow}2')$-${\beta}$-D-{3'-O-(3',4',5'-trimethoxycinnamoyl)}-fructofuranoside(P4), ${\alpha}$-D-{6-O-(p-hydroxybenzoyl)}-glucopyranosyl-$(1{\rightarrow}2')$-${\beta}$-D-{3'-O-(3',4',5'-trimethoxycinnamoyl)}-fructofuranoside(P5), ${\alpha}-D-glucopyranosyl-(1{\rightarrow}2')-{\beta}-D-(1'-O-sinapoyl)-fructofuranoside$(P6), $1,5-anhydro-D-glucitol$(P7) respectively. ${\alpha}$-D-{6-O-(p-Methoxybenzoyl)}-glucopyranosyl-$(1{\rightarrow}2')$-${\beta}$-D-{3'-O-(3',4',5'-trimethoxycinnamoyl)}-fructofuranoside(P4) and ${\alpha}-D-glucopyranosyl-(1{\rightarrow}2')-{\beta}-D-(1'-O-sinapoyl)-fructofuranoside$(P6) were isolated for the first time from the genus of Polygala. 1,5-Anhydro-D-glucitol(P7) was isolated without hydrolysis for the first time from the root of Polygala tenuifolia.

• Journal of the Korean Chemical Society
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• v.28 no.1
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• pp.14-19
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• 1984

The stability difference of metmyoglobin in $H_2O$ and $D_2O$ at pH 5.7 and pH 7.0 toward pressure denaturation is studied. Metmyoglobin is denatured in $D_2O$ at smaller pressure than in $H_2O$. The stability difference in $H_2O$ and $D_2O$ is more pronounced at pH 5.7 than at pH 7. The main reasons for the stability difference in $H_2O$ and $D_2O$are the difference in positive charge due to $H^+$and $D^+$ binding to the protein in $H_2O$ and $D_2O$, and the structural change that accompany deuteration.

• Journal of Plant Biology
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• v.19 no.3
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• pp.85-91
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• 1976

A comparison betwen the productivity of Pinus rigida which is native in the Eastern United States, and P. rigitaeda which is F1 hybrid between P. rigida and P. taeda, has been established. For each tree the diameter at breast height (D) and the height of tree (H) were measured in three years. The standard sample trees were down and then weighed each organ. From obtained data the allometric relation between $D_2H$ and dry weight of the trunk (Ws), the branches (Wb) and the leaves (Wl) of P. rigida were approxmated by $$Ws=0.0592 (D^2H)^{0.837}$$ $$Wb=0.0065 (D^2H)^{0.989}$$ $$Wl=0.0447(D^2H)^{0.690}$$ and those of P. rigitaeda were approximated by $$Ws=0.0522 (D^2H)^{0.843}$$ $$Wb=0.0037 (D^2H)^{1.117}$$ $$Wl=0.0207 (D^2H)^{0.856}$$ From the above, the standing crops of above ground of P. rigida were estimated to be as much as 16.93-34.35 ton dry matter per ha, and those of P. rigitaeda were 20.45-45.55 ton per ha. Annual net production was appraised at 8.07-9.35 ton/ha.yr in P. rigida and at 11.59-13.41 ton/ha.yr in P. rigitaeda (1.0:1.4). It is assumed that high productivity of P. rigitaeda stand compared with P. rigida resulted from an increase of the leaf amount with age. Photosynthetic ability under the saturated light of the current and theold leaves of P. rigida were respectively 2.62 and 0.66mg CO2/g. d. wt..hr and those of P. rigitaeda were 1.17 and 0.96mg CO2/g.d. wt.hr. Respiration of the current and the old leaves at $25^{\circ}C$ were 1.00 and 0.90 mg CO2/g. d. wt..hr. in P. rigida and 0.90 and 0.45mg CO2/g.d.wt.hr in P. rigitaeda. It is assumed that photosynthetic longevity of P. rigitaeda leaves was vigorously maintained longer than that of P. rigida.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• Korean Journal of Soil Science and Fertilizer
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• v.36 no.1
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• pp.41-49
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• 2003

Methane emission was measured in a rice paddy under different water management and organic amendments. Methane emission from planted chambers and unplanted chambers was monitored to evaluate the rice-mediated methane emission. In flooding methane emission from planted chambers with NPK, NPK(+P), was $0.174g\;CH_4\;m^{-2}\;d^{-1}$ while that from unplanted chambers with NPK, NPK(-P), was $0.046g\;CH_4\;m^{-2}\;d^{-1}$ Methane emission from planted chambers with rice straw compost amendment, RSC(+P), was $0.214g\;CH_4\;m^{-2}\;d^{-1}$, while that from unplanted chambers with rice straw compost amendment, RSC(-P), was $0.076g\;CH_4\;m^{-2}\;d^{-1}$. Methane emission from planted chambers with rice straw amendment in Fehruary, RS2(+P), was $0.328g\;CH_4\;m^{-2}\;d^{-1}$, while that from unplanted chambers with rice straw amendment in February, RS2(-P), was $0.1g\;CH_4\;m^{-2}\;d^{-1}$. Methane emission from planted chambers with rice straw amendment in May, RS5(+P), was $0.414g\;CH_4\;m^{-2}\;d^{-1}$, while that from unplanted chamhers with rice straw amendment in May, RS5(-P), was $0.187g\;CH_4\;m^{-2}\;d^{-1}$. In intermittent irrigation methane emission from NPK(+P) was $0.115g\;CH_4\;m^{-2}\;d^{-1}$, while that from NPK(-P) was $0.041g\;CH_4\;m^{-2}\;d^{-1}$. Methane emission from RSC(+P) was $0.137g\;CH_4\;m^{-2}\;d^{-1}$, while that from RSC(-P) was $0.06g\;CH_4\;m^{-2}\;d^{-1}$. Methane emission from RS2(+P) was $0.204g\;CH_4\;m^{-2}\;d^{-1}$, while that from RS2(-P) was $0.09g\;CH_4\;m^{-2}\;d^{-1}$. Methane emission from RS5(+P) was $0.273g\;CH_4\;m^{-2}\;d^{-1}$, while that from RS5(-P) was $0.13g\;CH_4\;m^{-2}\;d^{-1}$. Methane transport via rice plant under flooding for NPK plot, RSC plot, RS2 plot and RS5 plot was 73.6%, 64.5%, 69.5% and 54.8%, respectively, and mean was 65.6%. Methane transport via rice plants under intermittent irrigation for NPK plot, RSC plot, RS2 plot and RS5 plot was 64.3%, 59.2%, 55.9% and 52.4%, respectively, and mean was 58.0%.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.311-329
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• 2010

In this paper we will prove that the groups $D_{p+1}$(2) and $D_{p+1}$(3), where p is an odd prime number, are uniquely determined by their sets of order components. A main consequence of our result is the validity of Thompson's conjecture for the groups $D_{p+1}$(2) and $D_{p+1}$(3).

• The Journal of Korean Academy of Prosthodontics
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• v.35 no.2
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• pp.385-399
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• 1997

The purpose of this experiment was to determine the effects of etching with a Nd : YAG Laser on dentin, or porcelain surface on the bond strength with composite resin. The dentin specimens were devided into the following 4 groups. D1 : No treatment D2 : Etched with 10% phosphoric acid D3 : Laser etchded with 1W, 20PPs D4 : Laser etched with 2W, 20PPS The procelain specimens were devided into the following 4 groups. P1 : diamond roughened P2 : etched with HF acid P3 : Laser etched with 2W, 20PPS P4 : Laser etched with 3W, 20PPS All specimens were veneered with resin. One half of the specimens were stored in $37^{\circ}C$ water for one day and the other half were thermocycled 1000 times at temperature of $5^{\circ}C\;to\;55^{\circ}C$ at 20 seconds intervals. After that, the bonding strength of composite resin to the dentin and porcelain was measured. The surface treated state and fractured state were observed with SEM. The following results were obtained. 1. In the dentin specimens, the bond strength of group D2 was highter than that of groups D1 and D3 in the case of the specimens stored in $37^{\circ}C$ water for one day, there was a statistically significant difference between group D2 and D1, D3 (P<0.05). The bonding strength of the specimens that were thermocycled decreased in the following order : group D2,D4,D3 and then D1. 2. In the porcelain specimens, the bonding strength of groups P1,P2 were higher than that of group P3 in the case of the specimens stored in $37^{\circ}C$ water for one day (P<0.05). The bonding strength of the specimens of being thermocycled decreased in the following order : group P2,P1,P4 and then P3. 3. The groups of high bond strength had a rougher surface and a high level of microporosity with SEM findings.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.

• 한국생물공학회:학술대회논문집
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• 2000.11a
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• pp.749-754
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• 2000

PCR primers were designed based on consensus sequences of dTDP-D-glucose 4,6-dehydratase, one of the enzymes involved in the biosynthesis of deoxysugar. The PCR product (360 bp) was obtained from Thermus caldophilus GK24. Colony hybridization was carried out to the cosmid library constructed from T. caldophilus GK24 genomic DNA by the PCR product DNA fragment. We isolated a cosmid clone (pSMTC-1) that was subcloned to call pKCB series plasmid (BamHI fragments), partially sequenced and analyzed. pKCB80 (4.2 kb-BamHI DNA fragment) of them showed ORFs that was orfA, orfB, orfC and orfD. The orfABCD gene cluster is the deosysugar biosynthetic gene ; orfA (glucose-1-phosphate thymidylytransferase), orfB (dTDP-D-glucose 4,6-dehydratase), orfC (dTDP-4-keto-L-rhamnose reductase) and orfD (dTDP-4-keto-6-deoxy-D-glucose 3,5-epimerase). The gene cluster that was related in biosynthesis of dTDP-L-rhamnose was also identified by computer analysis, and we proposed that the biosynthetic pathway of deoxysugar analyzed from DNA sequencing of pKCB80 is from D-glucose-1-phosphate, dTDP-D-glucose, dTDP-4-keto-6-deoxy-D-glucose via dTDP-4-keto-L-rhamnose to dTDP-L-rhamnose.