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DIVISOR FUNCTIONS AND WEIERSTRASS FUNCTIONS ARISING FROM q-SERIES

  • Kim, Dae-Yeoul;Kim, Min-Soo
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.693-704
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    • 2012
  • We consider Weierstrass functions and divisor functions arising from $q$-series. Using these we can obtain new identities for divisor functions. Farkas [3] provided a relation between the sums of divisors satisfying congruence conditions and the sums of numbers of divisors satisfying congruence conditions. In the proof he took logarithmic derivative to theta functions and used the heat equation. In this note, however, we obtain a similar result by differentiating further. For any $n{\geq}1$, we have $$k{\cdot}{\tau}_{2;k,l}(n)=2n{\cdot}E_{\frac{k-l}{2}}(n;k)+l{\cdot}{\tau}_{1;k,l}(n)+2k{\cdot}{\sum_{j=1}^{n-1}}E_{\frac{k-1}{2}(j;k){\tau}_{1;k,l}(n-j)$$. Finally, we shall give a table for $E_1(N;3)$, ${\sigma}(N)$, ${\tau}_{1;3,1}(N)$ and ${\tau}_{2;3,1}(N)$ ($1{\leq}N{\leq}50$) and state simulation results for them.

The Water Quality and the Phytoplankton Communities in the Dong River of Kangwon Province, Korea (강원도 동강의 수질과 식물플랑크톤군집)

  • Lee, Jin-Hwan
    • ALGAE
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    • v.19 no.3
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    • pp.217-226
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    • 2004
  • The present study is to examine the water quality and to analyze the plank tonic and benthic phytoplankton communities at 6 stations in the Dong River and its tributary streams of Kangwon Province from November, 2001 to March, 2002. During the studies, water temperature ranged from 3.5 to 12.8℃; pH, 6.5-7.9; DO, 9.29-11.36 mg·l^(-1); BOD_5, 0.20-2.38 mg·l^(-1); TN, 1.2842-3.1871 mg·l^(-1); TP, 0.0052-0.0576 mg·l^(-1); and SS, 0.85-9.62 mg·l^(-1). The standard of water quality according to the Korean Environmental Preservation Law showed the first class except St. 6 through the survey. Six taxa of plank tonic phytoplankton identified were poor flora in November, 2001. The representative species frequently observed were the diatoms Achnanthes lanceolata, Achnanthes minutissima, Cymbella minuta, Cymbella parva, Diatoma vulgare, Fragilaria construens, Gomphonema pervulum, Navicula cryptocephala, Nitzschia palea., Scenedesmus sp. of green algae and Stephanodiscus hantzschii. Monthly dominant species of phytoplankton were Achnanthes lanceolata and A. minutissima in both February and March, 2002, but the blue-green algae, Oscillatoria sp. and the diatom, Stephan discus hantzschii were predominant at some stations in March. Phytoplankton standing crops ranged from 9.84 ${\times}$ 10$^3$ to 3.56 ${\times}$ 10$^4$ cell·l$^{-1}$ in November and 1.68-2.99 ${\times}$ 10$^5$ cell·l$^{-1}$ in February, while it changed 4.52-8.01 ${\times}$ 10$^5$ cell·l$^{-1}$ at St. 1, 2, 3 and 1.03-1.71 ${\times}$ 10$^6$ cell·l$^{-1}$ at St. 4, 5, 6 in March. Benthic phytoplankton communities was composed of 38 taxa in November, 31 taxa in February and 23 taxa in March. It showed a contrary tendency to planktonic phytoplankton diversity. Benthic diatoms which were more than 25% of the total populations were Cymbella turgida, Diatoma vulgare, Cocconeis placentula, Navicula cryptocephala var. intermedia in November; Achnanthe lanceolata, Cocconeis placentula, Achnanthes minutissima in February; and Achnanthes lanceolata and Cyclotella meneghiniana in March.

Enfluence of Herbal Extract on Lactic Acid Bacteria Growth and Cryoprotectants (생약 추출물이 유산균의 생육 및 동결건조 보호제로서의 효과)

  • Choi Jong-Bum;Shin Yong-Woo;Paek Nam-Soo;Kim Young-Man
    • The Korean Journal of Food And Nutrition
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    • v.17 no.3
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    • pp.286-293
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    • 2004
  • Extract of Eleutherococcus senticosus, Lycium chinensis, Angelica acutiloba and Schizandra chinensis were investigated to determine whether its addition may inflict on growth of lactic acid bacteria, freeze dry and cell viability during the storage. In cultivation with herbal extract, all strains tested did not demonstrate a significant reduction in their cell population, particularly Lactobacillus. acidophilus, L. bulgaricus, L. paracasei. But Schizandra chinensis extract inhibited growth of several strains. Immediately after freeze-drying using the skim milk 10%(w/v), sucrose 5%(w/v) with herbal extract 2.5%(v/v), the percentage viability was about 81.7%, 63.8%, 73.2%, 78.1 % in L. acidophilus, L. bulgaricus, L. paracasei, L. casei respectively. The protective effect of herbal extract to cell damage from freeze-drying was weak in comparison with control. During accelerated storage of freeze-dried lactic acid bacteria, those survival rate decrease rapidly, reaching 8 -18% in one month. But addition of Eleutherococcus senticosus extract in freeze dry of L. acidophilus showed a positive activity in storage.

Comparison of Blood Metal Concentration in Ohjeok-san(Wuji-san) Treated Rats - Dose-Response Relationship and Mechanism - (오적산을 투여한 흰쥐의 혈액중 금속농도 비교에 관한 연구 - 용량-반응관계와 기전을 중심으로 -)

  • 이정렬;이선동
    • The Journal of Korean Medicine
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    • v.23 no.1
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    • pp.67-82
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    • 2002
  • Objectives: In recent years, extensive focus has been laid on adulteration of herbal medicine with heavy metals. This may be mainly due to soil contamination by environmental pollution. The objective of this study is to identify the contents of various heavy metals in the blood from Ohjeok-san (Wuji-san) Decoction (OD) treated-rats. Methods: For this study, 13 kinds of metals including essential and heavy metals, i.e. A1, As, Cd, Co, Cr, Cu, Fe, Hg, Mn, Ni, Pb, Se and Zn were analyzed by a slight modification of EP A methods and the following results are obtained. Results: 1. There was no significant difference between the OD-treated groups and control group in liver, kidney, bone, brain and weight, especially no significant difference at the 5th and 10th days in weight and the amount of food intake. 2. The amount of each metal analyzed in the blood were as follows; A1: 2.3~3.07 mg/l, As: 2.90~3.66 mg/l, Cd: 0~0.001 mg/l, Co: 0~0.01 mg/l, Cr: 0.40~043 mg/l, Cu: 0.93~1.88 mg/l, Fe: 414.35~464.46 mg/l, Hg: 0.01 mg/l, Mn: 0.10~0.17 mg/l, Ni: 0.01 mg/l, Pb: 0.03~012 mg/l, Se: 0.73 mg/l, Zn: 3.41~4.13 mg/l by groups, respectively. In control and experimental group, Experimental I and other experimental II, III, IV, and V groups, there were no significant differences. 3. The amount of non-toxic metals (A1, Co, Cu, Fe, Mn, Se, Zn) were $64.1{\pm}7.71{\;}mg/l$ in the control group and 60.70~67.58 mg/l in the experimental groups I, II, III, IV and V. The amount of Toxic metals (As, Cd, Cr, Ag, Pb) were $0.68{\pm}0.21{\;}mg/l$ in the control group and 0.57 ~ 0.66mg/l in the experimental groups. The total amount of metals were 32.35 mg/l in the control group and 30.48~34.12 mg/l in the test groups I, II, III, IV and V, respectively. Conclusions: There was no significant difference of metal concentration in the blood from the OD-treated-rats compared to those of the control group even if higher dosage (1~8 times the dosage for a person) of OD was administered. This may be mainly due to a decoction treatment which contains only supernatants filtered from the herb-mass after boiling. This indicates the legal limitation for metal concentration in herbal medicine must be applied according to different treatment methods of herbal medicine.

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Workload Characteristics-based L1 Data Cache Switching-off Mechanism for GPUs

  • Do, Thuan Cong;Kim, Gwang Bok;Kim, Cheol Hong
    • Journal of the Korea Society of Computer and Information
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    • v.23 no.10
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    • pp.1-9
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    • 2018
  • Modern graphics processing units (GPUs) have become one of the most attractive platforms in exploiting high thread level parallelism with the support of new programming tools such as CUDA and OpenCL. Recent GPUs has applied cache hierarchy to support irregular memory access patterns; however, L1 data cache (L1D) exhibits poor efficiency in the GPU. This paper shows that the L1D does not always positively affect the applications in terms of performance and energy efficiency for the GPU. The performance of the GPU is even harmed by using the L1D for lots of applications. Our proposed technique exploits the characteristics of the currently-executed applications to predict the performance impact of the L1D on the GPU and then decides whether to continuously use the cache for the application or not. Our experimental results show that the proposed technique improves the GPU performance by 9.4% and saves up to 52.1% of the power consumption in the L1D.

Noise Exposure Level Measurements for Different Job Categories on Ships (선박의 담당업무에 따른 소음노출레벨 측정에 관한 연구)

  • Im, Myeong-Hwan;Choe, Sang-Bom
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.27 no.6
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    • pp.875-882
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    • 2021
  • To minimize occupational noise induced hearing loss, it is recommended that workers should not be exposed to noise levels exceeding 85 dBA for over 8 h. In the present study, noise exposure levels were measured for seven workers based on their tasks on a training ship. The A-weighted noise exposure level (Lex,24h) was measured by taking into account the A-weighted equivalent continuous sound level (LAeq,i), duration (h) and noise contribution (Lex,24h,i) from the workers' locations. Results are thus obtained for different job categories as follows: officer group Lex,24h=56.1 dB, navigation crew Lex,24h=58.9 dB, navigation cadet Lex,24h=62.0 dB, ship's cook Lex,24h=64.3 dB, engine cadet Lex,24h=91.1 dB, engineer Lex,24h=91.1 dB, and engine crew Lex,24h=95.1 dB. It was determined that the engineers, engine crews, and engine cadets in charge of machinery must wear hearing protection devices. By wearing hearing protection devices when working in highly noisy engine rooms, it is estimated that the noise expose levels could be reduced by the following amounts: engineer Lex,24h=23.1 dB, engine Crew Lex,24h=24.4 dB, and engine cadet Lex,24h=21.5 dB. Moreover, if the no. 2 lecture room and mess room bottom plates in the cadets accommodations were improved to the 64 mm A-60-class floating plates, then further reductions are possible as follows: navigation cadet Lex,24h=4.3 dB and engine cadet Lex,24h=1.8 dB.

Study on Myocardial Protective Effect of L-arginine (L-Arginine의 흰쥐 적출심근보호 효과에 관한 연구)

  • 이인성;이헌재
    • Journal of Chest Surgery
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    • v.29 no.10
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    • pp.1076-1080
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    • 1996
  • The results about the myocardial protection of recta of the nitric oxide precursor L-arginine upon reperrusion injury after ischemia are diverse. These diversities may be model dependent. Experiments were designed and performed to investigate myocardial protection effects according to the concentration of L-arginine. The Isolated rat hearts were subjected in a 30 minutes oi normothermic ischemia and reperfused for 30 minutes with reperfusate containing 0, 1, 2, 3, 4 moil L-arginine. After 30 minutes of reperfusion, group with 1 and 2 mM/L L-arginine showed a trend of better recovery in left ventricular systolic function(left ventricular developed pressure, positive maximum dpfdt), diastolic function(negative maximum dpfdt) and coronary flow compared to control group(reperfusate no L-arginine). Recovery was impaired with a higher concentration, and at 4 moil L-arginine r covery was worse than control(p (0, 05). These results suggest that optimal concentration of L-arginine Is Important or the recovery of myocardial and endothelial function after ischemia and reperfusion.

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Radon Concentration in Groundwater of Korea (전국 규모로 본 국내 지하수의 라돈 함량)

  • Cho, Byong-Wook
    • The Journal of Engineering Geology
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    • v.28 no.4
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    • pp.661-672
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    • 2018
  • Radon concentration was measured in a total of 5,453 groundwater samples from wells across Korea. The radon concentrations showed the values ranging from 0.1 Bq/L to 7,218.7 Bq/L, with a median of 48.8 Bq/L which is lower than those of other countries having similar geological conditions. The distribution of radon concentrations was lognormal. The median value is high in the granite areas (63.5-105.1 Bq/L) while it is low in the sedimentary rocks and Cheju volcanic area (16.0-20.3 Bq/L). When grouping the groundwater with well depth, the median radon value is high in weathering and/or upper bedrock zone (61.4 Bq/L) while it is low in alluvium and/or weathering zone (28.5 Bq/L). About 17.7% of the total samples exceeded 148 Bq/L of USEPA guideline value. The exceeding radon ratio more than 148 Bq/L in groundwater is highest in Jurassic granite area, however, the exceeding radon rates more than 300 Bq/L and 500 Bq/L are highest in CGRA area.

WEAKTYPE $L^1(R^n)$-ESTIMATE FOR CRETAIN MAXIMAL OPERATORS

  • Kim, Yong-Cheol
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1029-1036
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    • 1997
  • Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

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Control of Phytoplankton Bloom using Apple Snail(Pomacea canaliculata: Ampullariidae) (왕우렁이를 이용한 식물플랑크톤 대발생 제어)

  • Lee, Min Hyuk;Kim, Min Ji;Kim, Yong Jae
    • Korean Journal of Environmental Biology
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    • v.33 no.1
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    • pp.83-91
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    • 2015
  • This study is measured the change of chlorophyll-${\alpha}$ concentration and phytoplankton density, the grazing rates (GR) and pseudofaeces production (PFP), by grazing of freshwater apple snail, Pomacea canaliculata, to investigated that the snails are able to control of phytoplankton bloom. The experiments are performed to evaluate the GR and PFP at different conditions such as incubation time (0, 2, 4, 6, 8, 10 and 12 hr), shell height (1.0 to 4.0 cm, n=108), snail density (1, 1.5, 2.5, 3.5 and 5 indiv. $L^{-1}$) and food concentration (200, 400, 600, 800 and $1000{\mu}g$ $L^{-1}$). Regarding feeding time, the highest GR (2.5 L. $gAFDW^{-1}h^{-1}$) and PFP (15.3 mg $AFDW^{-1}$) showed at 4 hr after snail stocking, respectively. The snail, smaller than 1.5 cm in body size, showed the highest of GRs (2.54 L. $gAFDW^{-1}h^{-1}$) for the initial period (2 hr of stocking), compared to those greater than 1.5 cm, which showed a stable FR, higher than 0.099 L. $gAFDW^{-1}h^{-1}$. Upon snail density effect, the density of 5 indiv. $L^{-1}$ induced the most effective inhibition on phytoplankton biomass with the highest PFP. On the food concentration, the highest GR (0.54 L. $gAFDW^{-1}h^{-1}$) and PFP (8.5 mg $gAFDW^{-1}$) were induced at the level of $600{\mu}g$ $L^{-1}$, respectively. We checked that it is possible to control of phytoplankton bloom by the grazing of apple snail as well as Reeve. However, it required a through research for the remove of pseudofaeces and 2nd problem by the decomposition of the organic materals.