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ON THE γ-TH HYPER-KLOOSTERMAN SUMS AND A PROBLEM OF D. H. LEHMER

  • Tianping, Zhang;Xifeng, Xue
    • Journal of the Korean Mathematical Society
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    • v.46 no.4
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    • pp.733-746
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    • 2009
  • For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.

Comparison of Pepper Anthracnose Pathogens from Korea and China

  • Shin, Hyun-Joo;Chen, Zhu-Jun;Hwang, Jae-Moon;Lee, Soon-Gu
    • The Plant Pathology Journal
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    • v.15 no.6
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    • pp.323-329
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    • 1999
  • Anthracnose of pepper casued by Colletotrichum spphas been a great problems for pepper production in Korea and China. Especially Colletotrichum gloeosporioides was found predominantly over cultivation areas during infection periods and caused severe rots on bath unripe and ripe fruits that resulted in major yield losses. In this study, comparison of Colletrichum spp.isolated from Korea and China in morphology and pathgenicity, and RAPD-PCR analysis were conducted. Based on morphological characteristics, the pathogen isolates, K1 and C1, K2 and C2, and K3 and C3 were identified as Colletotrichum gloeosporioides (G) type, C. gloeosporioides (R) type and C. coccodes, respectively. in pathogenicity test, K1 and C1, and K2 and C2 were found to attack mainly fruits and to be the most virulent among isolates. K3 and C3 were strongly virulent to leaves and seedling. Pathogenicity between Korean and Chinese isolates. K3 and C3 were strongly virulent to leaves and seedling. Pathogenicity between Korean and Chinese isolates did not show any difference. Results of the RAPD-PCR analyses indicate the varying levels of molecular diversity within and between Colletotrichum spp.of Korea and China. The similarities between K1 and C1, K2 and C2, and K3 and C3 were 85.71%, 71.43% and 50.0% respectively.

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HOMOGENEOUS $C^*$-ALGEBRAS OVER A SPHERE

  • Park, Chun-Gil
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.859-869
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    • 1997
  • It is shown that for $A_{k, m}$ a k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1$ such that no non-trivial matrix algebra can be factored out of $A_{k, m}$ and $A_{k, m} \otimes M_l(C)$ has a non-trivial bundle structure for any positive integer l, we construct an $A_{k, m^-} C(S^{2n - 1} \times S^1) \otimes M_k(C)$-equivalence bimodule to show that every k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1)$. Moreover, we prove that the tensor product of the k-homogeneous $C^*$-algebra $A_{k, m}$ with a UHF-algebra of type $p^\infty$ has the tribial bundle structure if and only if the set of prime factors of k is a subset of the set of prime factors of pp.

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Articulatory Attributes in Korean Nonassimilating Contexts

  • Son, Minjung
    • Phonetics and Speech Sciences
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    • v.5 no.1
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    • pp.109-121
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    • 2013
  • This study examined several kinematic properties of the primary articulator (the tongue dorsum) and the supplementary articulator (the jaw) in the articulation of the voiceless velar stop (/k/) within nonassimilating contexts. We examined in particular the spatiotemporal properties (constriction duration and constriction maxima) from the constriction onset to the constriction offset by analyzing a velar (/k/) followed by the coronal fricative (/s/), the coronal stop (/t/), and the labial (/p/) in across-word boundary conditions (/k#s/, /k#t/, and /k#p/). Along with these measurements, we investigated intergestural temporal coordination between C1 and C2 and the jaw articulator in relation to its coordination with the articulation of consonant sequences. The articulatory movement data was collected by means of electromagnetic midsagittal articulometry (EMMA). Four native speakers of Seoul Korean participated in the laboratory experiment. The results showed several characteristics. First, a velar (/k/) in C1 was not categorically reduced. Constriction duration and constriction degree of the velar (/k/) were similar within nonassimilating contexts (/k#s/=/k#t/=/k#p/). This might mean that spatiotemporal attributes during constriction duration were stable and consistent across different contexts, which might be subsequently associated with the nontarget status of the velar in place assimilation. Second, the gestural overlap could be represented as the order of /k#s/ (less) < /k#p/ (intermediate) < /k#t/ (more) as we measured the onset-to-onset lag (a longer lag indicated shorter gestural overlap.). This indicates a gestural overlap within nonassimilating contexts may not be constrained by any of the several constraints including the perceptual recoverability constraint (e.g., more overlap in Front-to-Back sequences compared to the reverse order (Back-to-Front) since perceptual cues in C1 can be recovered anytime during C2 articulation), the low-level speech motor constraint (e.g., more overlap in lingual-nonlingual sequences as compared to the lingual-lingual sequences), or phonological contexts effects (e.g., similarity in gestural overlap within nonassimilating contexts). As one possible account for more overlap in /k#t/ sequences as compared to /k#p/, we suspect speakers' knowledge may be receptive to extreme encroachment on C1 by the gestural overlap of the coronal in C2 since it does not obscure the perceptual cue of C1 as much as the labial in C2. Third, actual jaw position during C2 was higher in coronals (/s/, /t/) than in the labial (/p/). However, within the coronals, there was no manner-dependent jaw height difference in C2 (/s/=/t/). Vertical jaw position of C1 and C2 was seen as inter-dependent as higher jaw position in C1 was closely associated with C2. Lastly, a greater gap in jaw height was associated with longer intergestural timing (e.g., less overlap), but was confined to the cluster type (/kp/) with the lingual-nonlingual sequence. This study showed that Korean jaw articulation was independent from coordinating primary articulators in gestural overlap in some cluster types (/k#s/, /k#t/) while not in others (e.g., /k#p/). Overall, the results coherently indicate the velar stop (/k/) in C1 was robust in articulation, which may have subsequently contributed to the nontarget status of the velar (/k/) in place assimilation processes.

Detection of Hydrocarbons to Determine Post-Irradiation of Dry Soup Base Ingredients in Instant Noodle (라면 건조 스프 재료의 방사선 조사 검지를 위한 Hydrocarbon류 검출)

  • Hwang, Keum-Taek;Park, Jun-Young
    • Korean Journal of Food Science and Technology
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    • v.30 no.5
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    • pp.1018-1023
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    • 1998
  • Hydrocarbons in dry soup base and its ingredients in instant noodle were analyzed to determine whether the analysis of hydrocarbons is a potential method to detect post-irradiation of the soup base. Soup base ingredients were irradiated individually, irradiated before mixing, or mixed after irradiation. Lipids were extracted with hexane and hydrocarbons were separated from the lipids through Florisil column. The hydrocarbons were analyzed with GC. Hydrocarbons C17:2, C16:3, C17:1, and C16:2 were detected in palm oil, red pepper powder, and sesame seeds irradiated at 10 kGy, but not in unirradiated ones. C17:2, C16:3, C17:1, and C16:2 were not detected in the soup base mixture of unirradiated ingredients. The four hydrocarbons were detected in the soup base mixture using irradiated palm oil or sesame seeds. In the mixture using irradiated red pepper powder, C17:2 and C16:3 were detected. When the soup mixture was irradiated after mixing unirradiated ingredients, C17:2, C17:1, and C16:2 were detected in the sample irradiated at 1 kGy, and C17:2, C16:3, C17:1, and C16:2 were in large amounts at 5 and 10 kGy.

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Altered Vascular Calcium Regulation in Hypertension

  • Kim, Won-Jae;Lee, Jong-Un;Park, Yong-Hyun;Nam, Sang-Chae
    • The Korean Journal of Physiology and Pharmacology
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    • v.1 no.5
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    • pp.529-535
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    • 1997
  • The present study was aimed at investigating whether the vascular calcium regulation is altered in hypertension. Two-kidney, one clip (2K1C) and deoxycorticosterone acetate (DOCA)-salt hypertension were made in rats, and their thoracic aortae were taken 4 weeks later. The isometric contractile response and calcium uptake of the endothelium-denuded aortic preparations were determined. Caffeine ($0.1{\sim}35\;mmol/L$) induced a greater contraction in 2K1C and DOCA-salt hypertension than in normotensive control. When the vascular calcium store was functionally-depleted by a repeated exposure to caffeine, it took longer to reload the store and to resume the initial contraction force in response to caffeine in both 2K1C and DOCA-salt hypertension. The vascular $^{45}Ca$ uptake following the functional depletion of the cellular store was also greater in both models of hypertension than in control. Ryanodine, calcium channel activator of the sarcoplasmic reticulum, attenuated the restoration of caffeine-induced vascular contraction, which was not affected by either 2K1C or DOCA-salt hypertension. Nifedipine, an L-type $Ca^{2+}$ channel blocker, attenuated the restoration of caffeine-induced contraction, which was not affected by DOCA-salt hypertension, but was more pronounced in 2K1C hypertension. Nifedipine also diminished the vascular $^{45}Ca$ uptake, which was not affected by DOCA-salt hypertension, but was more pronounced in 2K1C hypertension. Ouabain, a $Na^+,\;K^+-ATPase$ inhibitor, increased the caffeine-induced contraction by a similar magnitude in control and 2K1C hypertension, which was, however, markedly attenuated in DOCA-salt hypertension. Ouabain enhanced the vascular $^{45}Ca$ uptake, the degree of which was not affected by 2K1C hypertension, but was markedly attenuated in DOCA-salt hypertension compared with that in control. Cyclopiazonic acid, a selective inhibitor of $Ca^{2+}-ATPase$ of the sarcoplasmic reticulum, attenuated the restoration of caffeine-induced contraction, which was not affected by 2K1C hypertension, but was more marked in DOCA-salt hypertension. These results suggest that the increased vascular calcium storage may be attributed to an enhanced calcium influx in 2K1C hypertension, and to an impaired $Na^+-K^+$ pump activity of the cell membrane and subsequently increased calcium pump activity of the cellular store in DOCA-salt hypertension.

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Calcium silicate의 생성반응에 미치는 $\SO_3$의 영향

  • 박병철
    • Cement
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    • pp.41-54
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    • 1983
  • Calcium Silicate의 생성 및 분해에 미치는 $K_2SO_4$$MgSO_4$의 영향을 비교 검토하였으며 Calcium Silicate의 생성을 최대로 하는 $SO_3$, MgO와 $K_2O$의 최적비를 반응표면분석기법으로 조사하였다. $K_2SO_4$의 혼합비 증감에 따라 $C_3S$의 생성촉진에 미치는 영향은 없었다. $C_3S$의 조합원료에 $CaSO_4$를 4.0wt$\%$이상 첨가시 $CaSO_4$$C_2S$주위에 Sulphate reaction rim을 형성함으로써 $C_2S$와 CaO의 반응을 방해해 $C_3S$의 생성을 억제하였으나 적당량의 MgO가 첨가되면 $CaSO_4$가 4.0wt$/%$이상이라도 $C_3S$의 생성은 억제되지 않았다. $C_3S$의 생성을 최대로 하기 위한 $SO_3$, MgO와 $K_2O$의 최적비를 반응표면분석기법을 이용하여 다음과 같은 결론을 얻었다. 1. $K_2SO_4$$K_2O$에 비해 소결에 미치는 영향이 적으므로 크링카에 고용되고 남은 $K_2O$는 전량 $K_2SO_4$로 전환시켜야한다. 2. $SO_3$$K_2O$의 최적비율은 1.5이다. 3. $CaSO_4$와 MgO의 최적비율을 유지하기 위해서는 $CaSO_4$중의 wt$\%SO_3$=0.7의 수준으로 Sulphate의 함량을 조절하여야 한다. 4. $SO_3$와 결합하고 남은 $K_2O$가 0wt$\%$인 경우는 $K_2SO_4$=2.3wt$\%$, MgO=1.5wt$\%$일때 $C_3S$의 생성이 최대로 된다. 5. $SO_3$와 결합하고 남은 $K_2O$가 2.0wt$\%$인 경우는 $K_2$$SO_4$=4.5wt$\%$, MgO=3.0wt$\%$일때 $C_3S$의 생성이 최대로 된다.

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The Vasodilating Mechanism of Atrial Natriuretic Peptide in 2-kidney 1 Clip Renovascular Hypertensive Rats (2-kidney 1 clip 신혈관성 고혈압흰쥐에서의 심방이뇨??????타이드의 혈관이완작용의 기전)

  • Jung, Jin-Young;Ahn, Young-Chul;Kim, Hun-Sik;Koh, Gou-Young;Ahn, Hee-Yul;Kim, Myung-Suk
    • The Korean Journal of Pharmacology
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    • v.32 no.1
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    • pp.51-56
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    • 1996
  • The objectives of this study is to find out mechanism of vasodilating effects of ANP in 2K-1C renovascular hypertensive rat aorta and to compare with those of normotensive rat aorta. In 2K-1C renovascular hypertensive rat, average arterial blood pressure and plasma renin activity were higher than in normotensive rat. In 2K-1C renovascular hypertensive rat aorta, NE sensitivity was more increased and maximal contraction of aorta by NE was higher than those of normotensive rat aorta. ANP inhibited NE-induced contraction in both 2K-1C renovascular hypertensive and normotensive rat aorta, concentration-dependently. However, ANP was less effective for relaxing NE-induced contraction in 2K-1C renovascular hypertensive rat aorta than in normotensive rat aorta. ANP inhibited $^{45}Ca^{2+}$ uptake induced by NE in both 2K-1C renovascular hypertensive and normotensive rat aorta. From these results. inhibition of $Ca^{2+}$ influx may be one of the vasodilating mechanism of ANP in 2K-1C renovascular hypertensive rat aorta. Although the potency of ANP in relaxing NE-induced contractions was attenuated, the efficacy of ANP was not changed in 2K-1C renovascular hypertensive rat aorta compared with that of ANP in normotensive rat aorta. Abbreviations: ANP, Atrial natriuretic peptide; 2K-1C, 2-kidney 1 clip; NE, norepinephrine; SHR, Spontaneously hypertensive rat; DOC, Deoxycorticosterone; EDTA, Ethylenediaminetetra-acetic acid; PSS, Physiological salt solution; TRIS, tris(hydroxymethyl) aminomethane

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Interactions between Hydrodenitrogenation of Pyridine and Hydrodeoxygenation of m-Cresol over sulfided CoMo/γ-Al2O3 Catalyst (황화 CoMo/γ-Al2O3 촉매상에서 수첨탈질반응과 수첨탈산소 반응의 상호작용)

  • Kim, Hak-Soo;Park, Hea-Kyung;Kim, Kyung-Lim
    • Applied Chemistry for Engineering
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    • v.2 no.2
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    • pp.108-118
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    • 1991
  • Interactions between pyridine hydrodenitrogenation (HDN) and m-cresol hydrodeoxygenation(HDO), and the kinetic analysis were studied over sulfided $CoMo/{\gamma}-Al_2O_3$ catalyst at the range of temperatures between 473 K and 723 K, the total pressures between $10{\times}10^5Pa$ and $50{\times}10^5Pa$, and the contact times between 0.0125 g-cat. hr/ml-feed and 0.03g-cat. hr/ml-feed. HDN of pyridine and HDO of m-cresol were inhibited by each other and the inhibition effect of HDO by pyridine is higher than that of HDN by m-cresol. But reactivity of m-cresol is higher than that of pyridine. The rate equations of pyridine and m-cresol were given to be ${\gamma}_{HDN}=k_{HDN}{\cdot}K_pC_p/(1+K_cC_c+K_pC_p)$ and ${\gamma}_{HDO}=k_{HDO}{\cdot}K_cC_c/(1+K_cC_c+K_pC_p)$ in terms of Langmuir-Hinshellwood-Hougen-Watson model. At each temperature, reaction rate constants and adsorption equilibrium constants were determined and activation energies of pyridine HDN and m-cresol HDO are 13.83kcal/mol, respectively and the heat of adsorption are -6.458 and -5.045kcal/mol, respectively.

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