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Complete Moment Convergence of Moving Average Processes Generated by Negatively Associated Sequences

  • Ko, Mi-Hwa
    • 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.

Comparison of Water Quality Between Private and Simple-Piped Drinking Water Supply in Rural Community (농촌지역 개인소유 음용수와 간이상수도의 수질에 대한 비교 연구)

  • 이진헌;이인숙
    • Journal of Environmental Health Sciences
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    • v.20 no.1
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    • pp.54-61
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    • 1994
  • This study was carried out to investigate the degree of contamination in private-drinking water supply (PDWS) and simple-piped water supply (SPWS), and to compare of water quality between them for 3 years from 1990 to 1992. The results of the study were as follows: 1. Private-drinking water supply (PDWS) (1) Field-Site (ㄱ) The items which were very significantly over the criteria (p<0.01), were temp., pH, NO-N, standard plate count (S.P.C.) and Coliform. (ㄴ) No. of households which were over the criteria, were 11.2~51.7% in temp., pH, NH$_3$-N and NO$_2$-N, and 83.1~93.3% in NO-N, S.P.C. and Coliform. (2) Moutain-Site (ㄱ) The items which were over the criteria, were NO$_2$-N (p<0.05), S.P.C. (p<0.01) and Coliform (p<0.01). (ㄴ) No. of households which were over the criteria, were 33.6 ~ 75.6% in NO$_2$-N, S.P.C. and Coliform. (3) No. of households which were fit to the criteria of all items, were 9.0% in field-site and 14.1% in mountain-site. 2. Simple-piped water supply (SPWS) (1) The items which were very significantly over the critera (p<0.01), were standard plate count (S.P.C.) and Coliform. (2) The water qualities of adjacent and remote samples were better than those of source samples. (3) Residual chloride was not detected in any sample. In conclusion, rural community requires to be continually performed the policy of safety drinking water supply, and to be devised an epoch-making counterplan for the level-up of simple-piped water supply (SPWS), espically on the method of disinfection.

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Effect of Duration Treated on Reproductive Performance in Holstein Cows Treated with Progesterone with and without Estradiol (인공수정 후 외인성 Progesterone과 Estradiol 병용 및 Progesterone 단독 투여 기간이 젖소의 번식 성적에 미치는 영향)

  • Baek, K.S.;Lee, W.S.;Park, S.B.;Park, S.J.;Kim, H.S.;Lee, H.J.;Ki, K.S.;Kang, S.J.;Ahn, B.S.
    • Journal of Embryo Transfer
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    • v.22 no.3
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    • pp.195-198
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    • 2007
  • This study was carried out to investigate the effects of hormones treated (progesterone, and combination of progesterone and estradiol) on the reproductive performance of dairy cattle. The intravaginal CIDR was inserted in the vagina of cow on day 14 (P-7, PE-7), 16 (P-5, PE-5) and 18 (P-3, PE-3) post-insemination to stimulate progesterone secretion with (PE) and without estradiol(P). The CIDR was removed on 7 (P-7, PE-7), 5 (P-5, PE-5) and 3 (P-3, PE-3) days after. The cows for control group were not treated with CIDR or hormones. Conception rate, the duration needed for conception after AI and the number of AI services needed for conception were measured. Conception rate in control, CIDR without estradiol (P-7, P-5 and P-3) and CIDR treated (PE-7, PE-5 and PE-3) cows were 15.8%, 40.0%, 31.5%, 28.6%, 62.5%, 50.0% and 0%, respectively. The days needed for conception after AI in control, P-7, P-5, p-3, PE-7, PE-5 and PE-3 were 64.9, 63.0, 59.1, 8.0, 0.0, 18.9 and 83.3 days, respectively. The days needed for conception in cows treated with CIDR (PE-7) has shown longer than control and PE-3 (p<0.05). The number of AI services needed for conception in control, CIDR (PE-7, PE-5 and PE-3) and CIDR without estradiol treated cows (P-7, P-5 and P-3) were 27, 2.3, 1.9, 1.3, 1.0, 1.7 and 2.8 times, respectively. The number of AI services needed for conception have shown significantly lower in PE-7 compared to control and PE-3.

A Linkage Study of Chromosome 5 D5S39(p105-153Ra), D5S76(p105-599Ha), and $D_2$, $D_3$ Receptor Gene($DRD_2$, $DRD_3$) in Schizophrenics in Korean Pedigree (한국인 정신분열병 가계의 염색체 5번 D5S39(p105-153Ra), D5S76(p105-599Ha) 및 도파민 $D_2$, $D_3$ 수용체 유전자좌간의 연관관계 연구)

  • Oh, Kang-Seob;Kim, Young-Tae;Lee, Min-Soo
    • Korean Journal of Biological Psychiatry
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    • v.1 no.1
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    • pp.67-78
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    • 1994
  • The author examined the relationship of two markers, D5S39(p105-153Ra), D5S76(p105-599Ha) of chromosome 5 and $D_2$, $D_3$ receptor genes in a Korean schizophrenic pedigree using polymerase chain reaction(PCR). The results were as follows : 1) On D5S39 locus, 5 different alleles(224/226 bp : 4 cases, 218/226 bp : 3 cases, 222/226 bp : 3 cases, 218/230 bp : 1 case, 222/224 bp : 1 case) were produced. 2) On D5S76 locus, 5 different alleles(102/112 bp : 4 cases, 94/112 bp : 3 cases, 108/112 bp 3 cases, 94/94 bp : 1 case, 102/108 bp 1 case) were produced. 3) On $D_2$ receptor gene, 3 different alleles($A_1A_2$ : 8 cases, $A_1A_1$ : 2 cases, $A_2A_2$ : cases) were produced. 4) On $D_3$ receptor gene, 2 different alleles(1/2 : 7 cases, 1/1 : 5 cases) were produced. The author had not find any specific alleles on all four loci in all pedigree nor any specific alleles in the schizophrenic patients. Though the author has not found absolute relationship between the four loci and the onset of schizophrenia, there still remains the possibilities if the more detailed and elaborated pedigree studies are done.

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Genetic Variants of Serum Proteins and Enzymes in Holstein-Friesian Cattle (홀스타인종 유우의 혈청단백질 및 효소의 유전적 변이체)

  • Sang, Byung Chan;Ryoo, Seung Heui;Seo, Kil Woong;Lee, Chang Soo
    • Korean Journal of Agricultural Science
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    • v.22 no.2
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    • pp.163-169
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    • 1995
  • This study was carried out to examine the genetic constitution of serum proteins and enzymes in Holstein Friesian cattle population. The genetic variants of post-transferrin-2(pTf-2), transferrin(Tf), post-albumin(pAlb), ceruloplasmin(Cp) and amylase-I(Am-I) were analyzed by using PAGE(polyacrylamide gel electrophoresis) and STAGE(starch gel electrophoresis). In serum proteins, the pTf-2 locus were observed to be controlled by codominant alleles designated F and S, and the distribution of genotypes were 76.34, 14.50 and 9.10% for pTf-2 FF, FS and SS types, respectively. The gene frequencies of the pTf-2 F and S allele were 0.836 and 0.164. The Tf locus were found to be controlled by four alleles, Tf A, D1, D2 and E at a single locus, and the distribution of genotypes were 6.11, 32.06, 19.08, 1.53, 10.69, 18.32, 9.92 and 2.29% for Tf AA, AD1, AD2, AE, D1D1, D1D2, D2D2 and D2E type, respectively. The gene frequencies of the Tf A, D1, D2 and E wee 0.321, 0.359, 0.298 and 0.019. The pAlb locus were identified to be genetically controlled by two alleles, pAlb F and S allele, and the distribution of genotypes were 32.06, 29.77 and 38.17% for pAlb FF, FS and SS types, respectively. The gene frequencies of the pAlb F and S allele were 0.461 and 0.531. The Alb locus were observed to be controlled by Alb A and B allele, and the gene frequencies of these were 0.996 and 0.004. In serum enzymes, the Cp locus were found to be controlled by F and S allele, and the distribution of genotypes were 46.57, 27.48 and 25.95% for Cp FF, FS and SS types, respectively. The gene frequencies of F and S allele were 0.603 and 0.394. The Am-I locus were observed to be controlled by Am-I B and C allele, and the distribution of genotypes were 39.69, 21.73 and 38.93% for Am-I BB, BC and CC types, the gene frequencies of Am-I B and C were 0.503 and 0.497, respectively.

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Effects of Planting Soil on the Soil Moisture and the Growth of Vitex rotundifolia for Green Roof (옥상녹화 식재지반이 토양수분과 순비기나무의 생육에 미치는 영향)

  • Park, Jun-Suk;Park, Je-Hea;Ju, Jin-Hee;Yoon, Yong-Han
    • Journal of the Korean Institute of Landscape Architecture
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    • v.38 no.3
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    • pp.98-106
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    • 2010
  • This study focuses on the appropriate planting soil for Vitex rotundifolia by planting soil. Different soil depth levels were achieved at 15cm and 25cm in the green roof module system that was created with woody materials for a $500{\times}500{\times}300mm$ area. The soil mixture ratio was $S_{10}$, $L_{10}$, $S_7L_3$, $S_5L_5$, $P_7P_1L_2$, $P_6P_2L_2$, $P_5P_3L_2$ and $P_4P_4L_2$. This study was carried out over five months between April and September, 2006. The amount of soil moisture tends to decrease according to the planting soil. For the experimental items $S_{10}$, $S_7L_3$ and $S_5L_5$, the amount of soil moisture tends to decrease rapidly. However, for the experimental items $P_7P_1L_2$, $P_6P_2L_2$, $P_5P_3L_2$ and $P_4P_4L_2$, conditions containing perlite and peat moss, the amount of moisture tends to decrease more gradually. As a result, the use of soil-improving amending for the afforestation planting of roofs with a low level of management is need. After experimenting with the ratio of soil mixture for Vitex rotundifolia, the planting soil for experimental item $P_6P_2L_2$, $P_5P_3L_2$ and $P_4P_4L_2$ appeared excellent. For experimental item $S_{10}$, the growth of Vitex rotundifolia seemed to be weaker than that of others, because of the low levels of moisture and organic matter in the soil. For experimental item $L_{10}$, there appeared to be a low level of growth, even when the levels of moisture and organic matter were high. This may have occurred because of the low level of soil pH and the excessive amount of exchangeable cation. At the depth of 25cm, the growth of Vitex rotundifolia is vigorous overall. For experimental item at 15cm, Vitex rotundifolia was able to survive for 14 days without any rainfall and Vitex rotundifolia was better in amended soil, $P_6P_2L_2$, $P_5P_3L_2$ and $P_4P_4L_2$, than natural soil, SL.

Comparison of occurrence rate of the epileptiform discharge between awake EEG and sleep EEG in childhood epilepsy (소아청소년 간질 환자에서 수면 뇌파와 각성 뇌파의 간질파 발현율의 비교)

  • Jung, Yu Jin;Kwon, Kyoung Ah;Nam, Sang Ook
    • Clinical and Experimental Pediatrics
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    • v.51 no.8
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    • pp.861-867
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    • 2008
  • Purpose : We carried out this study to determine if there is any difference in the occurrence rate of the epileptiform discharge between awake EEG and sleep EEG and if there are any factors influencing on the occurrence rate of EEG. Methods : This study included 178 epileptic children who had visited neurology clinic of the department of pediatrics, Pusan National University Hospital from July 2005 to July 2006. The medical and EEG records of these children who had had both awake EEG and sleep EEG were reviewed. We analysed the occurrence rate of the epileptiform discharge between awake EEG and sleep EEG. We investigated the related clinical factors which included sex, seizure types, underlying causes, age at first seizure, antiepileptic drug (AED) medication, age at recording, and background activity. Results : Among 178 epileptic children, 91 patients (51.1%) showed epileptiform discharge in awake or sleep states, 10 patients (11.0%) abnormal only in awake, 40 patients (44.0%) abnormal only in sleep, 41 patients (45.0%) abnormal in both awake EEG and sleep EEG. The occurrence rate of sleep EEG was 81 of 178 patients (45.5%) which was more than that of the awake EEG (28.7%) (P<0.001). The occurrence rate of sleep EEG is more than that of the awake EEG regardless of sex and underlying causes. But there is no significant difference from awake EEG and sleep EEG in finding the epileptiform discharge in the patient with generalized seizure, younger than 5 years old at first seizure, younger than 10 years old at recording, no antiepileptic medication, and abnormal background activity. Conclusion : The sleep EEG is thought to be more helpful in the diagnosis of childhood epilepsy.

Anti-corrugation activity of micosporine-like amino acid mixtures from Chlamydomonas sp. (Chlamydomonas sp. 유래 mycosporine-like amino acid 혼합물의 항주름 활성)

  • Suh, Sung-Suk;Seo, Hyo Hyun;Lee, Jeong Hun;Hwang, Jinik;Park, Mirye;Moh, Sang Hyun;Lee, Taek-Kyun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.15 no.8
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    • pp.5393-5399
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    • 2014
  • To examine the effects of a mycosporine-like amino acids (MAAs) mixture from microalgae, Chlamydomonas sp, on the anti-wrinkle activities, the expression levels of genes that are associated with skin aging, including type I procollagen, elastin and involucrin, were analyzed. Asterina 330+palythine (A+P) and shinorine+palythine (S+P) mixtures were purified from Chlamydomonas sp using the following steps: 80% methanolic extraction, column purification, and HPLC analysis. As a result of the MTT assay, A+P and S+P did not induce cellular cytotoxicity with up to 0.1 mg/mL of both MAAs. In addition, the treatment of UV-exposed fibroblasts with A+P (0.05 mg/mL) and S+P (0.01 mg/mL) increased the levels of the PCOLCE mRNAs by 2.7 and 3.6 fold compared to the control group, respectively, The levels of elastin gene expression were elevated 5.59 and 3.1 fold in the A+P and S+P treated (0.01 mg/mL) cells, respectively. In particular, at a concentration of 0.01 mg /mL, the A+P and S+P expression levels of Involucrin mRNAs were increased 3.5 and 2.5 fold in the UV-exposed cells compared to the control, respectively. In conclusion, the MAAs derived from Chlamydomonas sp can be utilized as functional cosmetic materials with anti-wrinkle effects on the skin.

ON MARCINKIEWICZ'S TYPE LAW FOR FUZZY RANDOM SETS

  • Kwon, Joong-Sung;Shim, Hong-Tae
    • Journal of applied mathematics & informatics
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    • v.32 no.1_2
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    • pp.55-60
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    • 2014
  • In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

ON THE EXISTENCE OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR ELLIPTIC SYSTEM WITH MULTIPLE PARAMETERS AND SINGULAR WEIGHTS

  • Rasouli, S.H.
    • Communications of the Korean Mathematical Society
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    • v.27 no.3
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    • pp.557-564
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    • 2012
  • This study concerns the existence of positive solution for the following nonlinear system $$\{-div(|x|^{-ap}|{\nabla}u|^{p-2}{\nabla}u)=|x|^{-(a+1)p+c_1}({\alpha}_1f(v)+{\beta}_1h(u)),x{\in}{\Omega},\\-div(|x|^{-bq}|{\nabla}v|q^{-2}{\nabla}v)=|x|^{-(b+1)q+c_2}({\alpha}_2g(u)+{\beta}_2k(v)),x{\in}{\Omega},\\u=v=0,x{\in}{\partial}{\Omega}$$, where ${\Omega}$ is a bounded smooth domain of $\mathbb{R}^N$ with $0{\in}{\Omega}$, 1 < $p,q$ < N, $0{{\leq}}a<\frac{N-p}{p}$, $0{{\leq}}b<\frac{N-q}{q}$ and $c_1$, $c_2$, ${\alpha}_1$, ${\alpha}_2$, ${\beta}_1$, ${\beta}_2$ are positive parameters. Here $f,g,h,k$ : $[0,{\infty}){\rightarrow}[0,{\infty})$ are nondecresing continuous functions and $$\lim_{s{\rightarrow}{\infty}}\frac{f(Ag(s)^{\frac{1}{q-1}})}{s^{p-1}}=0$$ for every A > 0. We discuss the existence of positive solution when $f,g,h$ and $k$ satisfy certain additional conditions. We use the method of sub-super solutions to establish our results.