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ON ERDŐS CHAINS IN THE PLANE

  • Passant, Jonathan
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.5
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    • pp.1279-1300
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    • 2021
  • Let P be a finite point set in ℝ2 with the set of distance n-chains defined as ∆n(P) = {(|p1 - p2|, |p2 - p3|, …, |pn - pn+1|) : pi ∈ P}. We show that for 2 ⩽ n = O|P|(1) we have ${\mid}{\Delta}_n(P){\mid}{\gtrsim}{\frac{{\mid}P{\mid}^n}{{\log}^{\frac{13}{2}(n-1)}{\mid}P{\mid}}}$. Our argument uses the energy construction of Elekes and a general version of Rudnev's rich-line bound implicit in [28], which allows one to iterate efficiently on intersecting nested subsets of Guth-Katz lines. Let G is a simple connected graph on m = O(1) vertices with m ⩾ 2. Define the graph-distance set ∆G(P) as ∆G(P) = {(|pi - pj|){i,j}∈E(G) : pi, pj ∈ P}. Combining with results of Guth and Katz [17] and Rudnev [28] with the above, if G has a Hamiltonian path we have ${\mid}{\Delta}_G(P){\mid}{\gtrsim}{\frac{{\mid}P{\mid}^{m-1}}{\text{polylog}{\mid}P{\mid}}}$.

An Analytic Study on factors Affecting the School Nurse's Activities in Daegu City and Kyungpook Province (대구.경북지역 일부 양호교사의 업무수행에 미치는 요인분석)

  • Gwak, Oh-Gae
    • Research in Community and Public Health Nursing
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    • v.1 no.1
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    • pp.503-517
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    • 1989
  • This study is to analyze factors affecting the school nurse's activities. The survey was undertaken during Sept. 1-Nov. 30, 1986. The subjects were 137 school nurses from elementary, junior-high, and senior-high schools in Daegu City and Kyungppk Province. The results are as follows: 1. Correlational findings between school nurse's self-confidence and their general characteristics 1) Program Planning & Evaluation: Health Experinece(r=-0.1803, p<0.05) Salary Step(r=-0.1741, p<0.05) 2) Clinic Management: Salary STep(r=-0.2580, p<0.01) 3) Health Education: Salary Step(r=-0.1929, p<0.05) 4) Management of School Environment: Salary Step(r=-0.2501, p<.05) 5) Health Care Services: Health Experience(r=0.1901, p<0.05) Salary Step(r=-0.2424, p<0.05) 2. The degrees of school nurse's self-confidence(high: 4 point, low: 1 point) 1) Clinic Management: 2.92 2) Health Education: 2.86. 3) Program Planning & Evaluation: 2.74 4) Health Care Services: 2.73 5) Management of School Environment: 2.67 6) Operating of School Health Organization: 2.42 3. Significances to self-confidence on school nurse's activities 1) Program Planning as Evaluation: Expending Times for Health Care Services (r=-0.2262, p<0.05) Expending Times for Health Education (r=0.2943, p<0.05) Size of Clinic(r=0.2163, p<0.05) Location of Clinic(t=2.43, gH0.047) Use of Clinic(t=2.06, p<0.007) 2) Clinic Management: Location of Clinic (t=3.36, p<0.010) 3) Health Education: Purchase of Medicine(r=-0.1736, p<0.05) No, of Classes (r=-0.1794, p<0.05) (4) Management of School Environment: School Health Budget(r=0.1731, p<0.05) Home Message(r=0.1805, p<0.05) Location of Clinic(t=4.46, p<0.0001) 5) Operating of School Health Organization: School Health Budget(r=0.1878, p<0.05) Use of Clinic(t:1.90, p<0.018) 6) Health Care Services: School Health Budget(r=1.90, p<0.018) Expending Times for Health Education(r=0.2577, p<0.05) Size of Clinic(r=0.4336, p<0.001) Location of Clinic(t:5.10, p<0.001)

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Association Analysis of Polymorphisms on Dystrobrevin Binding Protein 1(DTNBP1) Gene with Schizophrenia in the Korean Population (한국인에서 Dystrobrevin Binding Protein 1(DTNBP1) 유전자의 다형성과 정신분열병의 연합에 대한 고찰)

  • Moon, Hyun-Il;Lee, Yeon Jung;Park, Byung-Lae;Shin, Hyung Doo;Choi, Ihn-Geun;Han, Sun Ho;Woo, Sung-Il
    • Korean Journal of Biological Psychiatry
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    • v.16 no.3
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    • pp.149-158
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    • 2009
  • Objectives : This study was designed to investigate the association of schizophrenia and P1320, P1325, P1635, P1655, P1763 and SNP A polymorphisms on dystrobrevin binding protein 1(DTNBP1) gene in Korean patients. Methods : We analyzed P1320, P1325, P1635, P1655, P1763 and SNP A polymorphisms on DTNBP1 gene from their DNAs extracted from their blood in 388 Korean schizophrenic patients (male 198, female 190) and 372 control subjects(male 247, female 125). We compared the differences of genotype and allele distributions of the six polymorphisms on DTNBP1 gene between the Korean schizophrenic patient group and the normal control group. Results : There were no statistically significant differences of genotype and allele distributions of the P1320, P1325, P1635, P1655, P1763 and SNP A polymorphisms on DTNBP1 gene between the schizophrenic patient group and the normal control group. Conclusion : The results of this study suggest that P1320, P1325, P1635, P1655, P1763 and SNP A polymorphism on DTNBP1 gene do not have influence on the risk of the schizophnenic in the Korean population.

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Experimental Evaluation of the Effect of the Mixing Design Factors of the Cementitious Composite for 3D Printer on the Printing Quality (3D 프린터용 시멘트 복합체의 배합요인에 따른 출력 품질의 실험적 평가)

  • Seo, Ji-Seok;Kim, Yun-Yong
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.26 no.1
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    • pp.89-96
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    • 2022
  • In this paper, to evaluate the output quality of the cementitious composite mixture for printing with the ME method for construction 3D printer, visual inspection of the output appearance and the dimensional error rate, compressive strength and flexural strength of the output were measured. As a result of the test, the mixing design with excellent output appearance was P1-2, P1-4, P2-5, P2-6, and the mixing design with good output appearance was P0-1, P1-1, P1-3, P1-6, P1-7 and P2-4. Of these mixing designs, P0-1 and P2-6 had the lowest dimensional error rates As a result of evaluating the compressive strength and flexural strength of the various mixing designs, the Mixing design with excellent output designs showed good mechnical properties. However, mixing designs with excellent mechanical properties does not necessarily have excellent output quality. Therefore, in order to accurately evaluate the output quality, it is judged that visual inspection and dimensional error rate inspection should be performed first, and then the mechanical characteristics should be reviewed.

Zinc Porphyrin-Cored Dendrimers; Axial Coordination of Pyridine and Photoinduced Electron Transfer to Methyl Viologen

  • Park, Ji-Eun;Choi, Dae-Ock;Shin, Eun-Ju
    • Bulletin of the Korean Chemical Society
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    • v.32 no.12
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    • pp.4247-4252
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    • 2011
  • The porphyrin-incorporated arylether dendrimers ZnP-D1 and ZnP-D4 were investigated to discover the influence of dendritic environments for the axial ligation of pyridine and photoinduced electron transfer by methyl viologen. Absorption and fluorescence spectra of ZnP, ZnP-D1, and ZnP-D4 were measured in dichloromethane with the addition of pyridine or methyl viologen dichloride. Axial ligation of pyridine was confirmed by red-shifted absorption spectrum. The complex formation constants $K_f$ (Table 1) for axial coordination of pyridine on ZnP, ZnP-D1, and ZnP-D4 were estimated to be $4.4{\times}10^3\;M^{-1}$, $3.3{\times}10^3\;M^{-1}$, and $1.7{\times}10^3\;M^{-1}$, respectively. The photoinduced electron transfer to methyl viologen dichloride was confirmed by fluorescence quenching. Stern-Volmer constants Ksv for ZnP, ZnP-D1, and ZnP-D4 were calculated to be $2.6{\times}10^3$, $2.5{\times}10^3$, and $2.1{\times}10^3$, respectively. ZnP-D4 surrounded by 4 aryl ether dendrons shows the smallest $K_f$ and Ksv values, with comparison to ZnP and ZnP-D1.

SOLVABILITY FOR SOME DIRICHLET PROBLEM WITH P-LAPACIAN

  • Kim, Yong-In
    • The Pure and Applied Mathematics
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    • v.17 no.3
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    • pp.257-268
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    • 2010
  • We investigate the existence of the following Dirichlet boundary value problem $({\mid}u'\mid^{p-2}u')'\;+\;(p\;-\;1)[\alpha{\mid}u^+\mid^{p-2}u^+\;-\;\beta{\mid}u^-\mid^{p-2}u^-]$ = (p - 1)h(t), u(0) = u(T) = 0, where p > 1, $\alpha$ > 0, $\beta$ > 0 and ${\alpha}^{-\frac{1}{p}}\;+\;{\beta}^{-\frac{1}{p}}\;=\;2$, $T\;=\;{\pi}_p/{\alpha}^{\frac{1}{p}}$, ${\pi}_p\;=\; \frac{2{\pi}}{p\;sin(\pi/p)}$ and $h\;{\in}\;L^{\infty}$(0,T). The results of this paper generalize some early results obtained in [8] and [9]. Moreover, the method used in this paper is elementary and new.

POTENT INHIBITION OF HUMAN CYTOCHROME P450 1 ENZYMES BY DIMETHOXYPHENYL VINYL THIOPHENE

  • Lee, Sang-Kwang;Kim, Sang-Hee;Kim, Mie-Young;Chun, Young-Jin
    • Proceedings of the PSK Conference
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    • 2002.10a
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    • pp.312.3-313
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    • 2002
  • Recently we have reported that various hydroxystilbenes show strong inhibition of human P450 1 activity. A series of synthetic trans-stilbene derivatives were prepared and their inhibitory potentials were evaluated with the bacterial membrane of recombinant human P450 1A1, 1A2 or 1B1 coexpressed with human NADPH-P450 reductase to find new candidates for cancer chemoprevention, Of the compounds tested. SY-021 (3.5-dimethoxyphenyl vinyl thiophene) exhibited a potent inhibition of human P450 181 with an IC$_{50}$ value of 2 nM. SY-021 also showed the inhibitrion of P450 1A1 with IC$_{50}$ value of 61 nM and P450 1A2 with IC$_{50}$ value of 11 nM. SY-021 showed 31-fold selectivity for P450 1B1 over P450 1A1 and 6-fold selectivity for P450 1B1 over 1A2. We have further investigated the inhibition kinetics of P450 1A1. 1A2 and 1B1 by SY-021. The modes of inhibition by SY-021were non-compeitive for all three P450 1 enzymes. Effect of preincubation with NADPH on inhibition of P450 1B1 by SY-021 was determined. These results suggest that SY-021 is one of the mostj potent inhibitor of human P450 1 enzymes and may be considered as a good candidate for a cancer chemopreventive agent in human

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A MEAN VALUE FUNCTION AND ITS COMPUTATIONAL FORMULA RELATED TO D. H. LEHMER'S PROBLEM

  • Wang, Tingting
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.487-494
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    • 2016
  • Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

8-RANKS OF CLASS GROUPS OF IMAGINARY QUADRATIC NUMBER FIELDS AND THEIR DENSITIES

  • Jung, Hwan-Yup;Yue, Qin
    • Journal of the Korean Mathematical Society
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    • v.48 no.6
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    • pp.1249-1268
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    • 2011
  • For imaginary quadratic number fields F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1{\ldots}p_{t-1}})$, where ${\varepsilon}{\in}${-1,-2} and distinct primes $p_i{\equiv}1$ mod 4, we give condition of 8-ranks of class groups C(F) of F equal to 1 or 2 provided that 4-ranks of C(F) are at most equal to 2. Especially for F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1p_2)$, we compute densities of 8-ranks of C(F) equal to 1 or 2 in all such imaginary quadratic fields F. The results are stated in terms of congruence relation of $p_i$ modulo $2^n$, the quartic residue symbol $(\frac{p_1}{p_2})4$ and binary quadratic forms such as $p_2^{h+(2_{p_1})/4}=x^2-2p_1y^2$, where $h+(2p_1)$ is the narrow class number of $\mathbb{Q}(\sqrt{2p_1})$. The results are also very useful for numerical computations.

Relationships between Cellulose Decomposition and Soil Environmental Factors in Three Coniferous Plantations (3수종의 침엽수조림지내 셀룰로오스 분해와 토양 환경요인과의 관계)

  • Kim, Choon-Sig
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.14 no.1
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    • pp.39-44
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    • 2012
  • This study was carried out to determine the relationships between cellulose decomposition and soil environmental factors in larch (Larix leptolepis) and pine (red pine: Pinus densiflora; rigitaeda pine: P. rigida ${\times}$ P. taeda) species planted in the same year (1963). The variation of cellulose mass loss with soil temperature, soil pH, soil $CO_2$ efflux rates, and soil water content was measured monthly for 4 months (July, August, September and October 2006) from three coniferous plantations. Mean mass loss rates during the study period were generally more rapid in rigitaeda pine (6.5 $mg\;g^{-1}\;day^{-1}$) than in red pine (6.2 $mg\;g^{-1}\;day^{-1}$) or larch (6.1 $mg\;g^{-1}\;day^{-1}$) plantations, although the mass loss rates were not significantly different among three tree species (P > 0.05). Cellulose mass loss rates among three tree species were positively correlated with soil temperature (red pine: r = 0.77, P < 0.05; rigitaeda pine: r = 0.59, P < 0.05; larch: r = 0.48, P < 0.05) at the 20 cm soil depth, while the mass loss rates were negatively correlated with soil pH (red pine: r = -0.63, P < 0.05; rigitaeda pine: r = -0.47, P < 0.05; larch: r = -0.43, P < 0.05). There was a significant correlation between cellulose mass loss and soil $CO_2$ efflux rates except for regitaeda pine plantation, while no significant correlation (P > 0.05) between cellulose mass loss and soil water content in larch or rigitaeda pine. The results suggest that cellulose mass loss rates in soil layers depend on the different soil environmental factors caused by tree species.