• Title/Summary/Keyword: $L_p$-metric

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THE BROUWER AND SCHAUDER FIXED POINT THEOREMS FOR SPACES HAVING CERTAIN CONTRACTIBLE SUBSETS

  • Park, Sehie
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.83-89
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    • 1993
  • Applications of the classical Knaster-Kuratowski-Mazurkiewicz theorem [KKM] and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde[L]. Recently, this concept has been extended to pseudo-convex spaces, contractible spaces, or spaces having certain families of contractible subsets by Horvath[H1-4]. In the present paper we give a far-reaching generalization of the best approximation theorem of Ky Fan[F1, 2] to pseudo-metric spaces and improved versions of the well-known fixed point theorems due to Brouwer [B] and Schauder [S] for spaces having certain families of contractible subsets. Our basic tool is a generalized Fan-Browder type fixed point theorem in our previous works [P3, 4].

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The Stability Constant of 1, 7, 10, 16-Tetraoxa-4, 13-Diazacyclooctadecane-Uranium (Ⅵ) Complex in Aqueous Solution

  • Suh, Moo-Yul;Eom, Tae-Yoon;Kim, Si-Joong
    • Bulletin of the Korean Chemical Society
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    • v.4 no.5
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    • pp.231-234
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    • 1983
  • The stability constant for the complex of $UO_2^{2+}$ with a macrocyclic aminoether ligand, 1,7,10,16-tetraoxa-4,13-diazacyclooctadecane, has determined in aqueous solution. The conductivity and pH metric measurements suggest that the ligand forms a stable 1:1 complex with $UO_2^{2+}$ ion, and the complex is an ionic form, $UO_2L^{2+}$, in aqueous solution. The fact that the ligand does not form a complex with lanthanides, such as $Ce^{3+}$, $Sm^{3+}$, and $Nd^{3+}$ ions, in aqueous solution suggests a possibility of separation of the lanthanide elements from uranium matrix using the macrocyclic aminoether ligand.

Estimation of Gene Effects in Four Bivoltine Silkworm (Bombyx mori L.) Crosses

  • Malik, G.N.;Singh, T.P.;Rufaie, S.Z.Haque;Aijaz, M.;Dar, H.U.
    • International Journal of Industrial Entomology and Biomaterials
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    • v.8 no.1
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    • pp.113-115
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    • 2004
  • Six generations (P$_1$, P$_2$, F$_1$, BC$_1$, BC$_2$ and F$_2$) of four bivoltine silkworm crosses (SKAU-R-1 ${\times}$ Yakwei, SKAU-R-6 ${\times}$ Yakwei, CSR$_2$ ${\times}$ CSR$_4$ and SH$_{6}$${\times}$ NB$_4$D$_2$) were evaluated in a completely randomized block design with 5 replications for each treatment. The generation mean 2 in respect of 3 metric traits (single cocoon weight, single shell weight, and shell ratio %), were subjected to Cavallis joint scaling test. Additive dominance model was found to be adequate in CSR$_2$${\times}$CSR$_4$ and SH$_{6}$${\times}$ NB$_4$D$_2$ for single cocoon weight and shell weight and SKAU-R-6 ${\times}$ Yakwei for shell ratio(%). Whereas, in rest of the crosses epistasis was evident in the traits under investigation. Magnitude of additive gene effect (d) was greater than dominance(h) in SH$_{6}$${\times}$NB$_4$D$_2$ and SKUA-R-6${\times}$Yakwei for shell ratio (%) and in CSR$_2$${\times}$ CSR$_4$ for shell weight. Thus selection for these traits in early segregating generations of these crosses would be effective for obtaining considerable genetic gain. gain.

Lebesgue-Stieltjes Measures and Differentiation of Measures

  • Jeon, Won-Kee
    • Honam Mathematical Journal
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    • v.8 no.1
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    • pp.51-74
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    • 1986
  • The thery of measure is significant in that we extend from it to the theory of integration. AS specific metric outer measures we can take Hausdorff outer measure and Lebesgue-Stieltjes outer measure connecting measure with monotone functions.([12]) The purpose of this paper is to find some properties of Lebesgue-Stieltjes measure by extending it from $R^1$ to $R^n(n{\geq}1)$ $({\S}3)$ and differentiation of the integral defined by Borel measure $({\S}4)$. If in detail, as follows. We proved that if $_n{\lambda}_{f}^{\ast}$ is Lebesgue-Stieltjes outer measure defined on a finite monotone increasing function $f:R{\rightarrow}R$ with the right continuity, then $$_n{\lambda}_{f}^{\ast}(I)=\prod_{j=1}^{n}(f(b_j)-f(a_j))$$, where $I={(x_1,...,x_n){\mid}a_j$<$x_j{\leq}b_j,\;j=1,...,n}$. (Theorem 3.6). We've reached the conclusion of an extension of Lebesgue Differentiation Theorem in the course of proving that the class of continuous function on $R^n$ with compact support is dense in $L^p(d{\mu})$ ($1{\leq$}p<$\infty$) (Proposition 2.4). That is, if f is locally $\mu$-integrable on $R^n$, then $\lim_{h\to\0}\left(\frac{1}{{\mu}(Q_x(h))}\right)\int_{Qx(h)}f\;d{\mu}=f(x)\;a.e.(\mu)$.

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ISFRNet: A Deep Three-stage Identity and Structure Feature Refinement Network for Facial Image Inpainting

  • Yan Wang;Jitae Shin
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.17 no.3
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    • pp.881-895
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    • 2023
  • Modern image inpainting techniques based on deep learning have achieved remarkable performance, and more and more people are working on repairing more complex and larger missing areas, although this is still challenging, especially for facial image inpainting. For a face image with a huge missing area, there are very few valid pixels available; however, people have an ability to imagine the complete picture in their mind according to their subjective will. It is important to simulate this capability while maintaining the identity features of the face as much as possible. To achieve this goal, we propose a three-stage network model, which we refer to as the identity and structure feature refinement network (ISFRNet). ISFRNet is based on 1) a pre-trained pSp-styleGAN model that generates an extremely realistic face image with rich structural features; 2) a shallow structured network with a small receptive field; and 3) a modified U-net with two encoders and a decoder, which has a large receptive field. We choose structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), L1 Loss and learned perceptual image patch similarity (LPIPS) to evaluate our model. When the missing region is 20%-40%, the above four metric scores of our model are 28.12, 0.942, 0.015 and 0.090, respectively. When the lost area is between 40% and 60%, the metric scores are 23.31, 0.840, 0.053 and 0.177, respectively. Our inpainting network not only guarantees excellent face identity feature recovery but also exhibits state-of-the-art performance compared to other multi-stage refinement models.

The Effects of Ankle Taping on Ankle Angular Velocity, Ground Reaction Force and Postural Stability during Jump Landing on Athlete with Functional Ankle Instability (기능적 발목 불안정성을 가진 선수에게 발목 테이핑이 점프 후 착지 시 발목 각속도, 지면반력과 자세 안정성에 미치는 영향)

  • Kim, Kyoung-Hun;Cho, Joon-Heang
    • Korean Journal of Applied Biomechanics
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    • v.19 no.3
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    • pp.519-528
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    • 2009
  • The effects of taping on the use of such measures for prevention have already been comprehensively described in the literature. However, few studies have analyzed ground reaction forces and postural stability with functional ankle instability subject during dynamic activities with ankle taping The purpose of this study was to identify the effects of ankle taping on ground reaction force and postural stability during jump landing. Fourteen players who has ankle instability were participated in this study. we used vicon and force platform. The application of taping who has ankle instability decreased DF and inversion angular velocity and peak vertical ground reaction force during landing. It also improved A-P cop, M-L cop in stability. The findings of this study support the use of taping as part of injury prevention for subject with functional ankle instability in clinical setting.

Spectrophotometric Quantitative Analysis of Cu(II) Ion Using N,N'-bis(4-methoxysalicylidene)phenylendiamine (N,N'-bis(4-methoxysalicylidene)phenylendiamine를 이용한 Cu(II) 이온의 분광학적 분석)

  • Kim, Sun-Deuk;Seol, Jong-Min
    • Journal of the Korean Chemical Society
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    • v.56 no.2
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    • pp.228-235
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    • 2012
  • A $N_2O_2$ Schiff base ligand, N,N'-bis(4-methoxysalicylidene)phenylendiamine (4-$CH_3O$-salphen) was synthesized. Using the 4-$CH_3O$-salphen, the spectrophoto-metric quantitative analysis of Cu(II) ion in aqueous solution was performed. The optimum condition for the quantitative analysis of Cu(II) ion was determined as the following; the concentration of 4-$CH_3O$-salphen is $2.0{\times}10^{-4}\;mol/L$, ratio between solvent DMSO and water is 50/50(v/v), pH is 5.5. After 1 hr water incubation at $55^{\circ}C$ and then the absorbance measurements at 388 nm, a calibration curve (${\varepsilon}=3.6{\times}10^4\;mol^{-1}cm^{-1}$) with a correlation coefficient ($R^2$=0.9963) was obtained in this condition. Using this optimized condition, the quantitative analysis of Cu(II) ion was performed with various samples such as hot spring water, semiconductor factory waste water and treated water from sewage treatment plant. The average value of the measured values agreed well with standard value with a range of 0.6~5.4%. The limit of determination was 31.77 ng/mL ($5.0{\times}10^{-7}\;mol/L$).

Assessment of Apartment Building Construction Workers' Noise Exposure (아파트 건설노동자 소음 노출평가)

  • Taesun Kang
    • Journal of Korean Society of Occupational and Environmental Hygiene
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    • v.33 no.3
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    • pp.308-316
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    • 2023
  • Objectives: The aim of this study is to measure and assess the occupational noise exposure levels among construction workers at apartment building construction sites in South Korea. Methods: Noise exposure assessments were conducted for 139 construction workers across 10 different trades at 53 apartment building construction sites in the northern part of Gyeonggi-do. Assessments were carried out using a noise dosimeter set with a 90 dB criterion, an 80 dB threshold, and a 5 dB exchange rate over a period of more than 6 hours(LMOEL) Results: The mean LMOEL (equivalent continuous noise level over 8 hours) for the 139 dosimeter samples was 87.8 ± 4.3 dBA. The mean noise exposure level for each construction trade, referred to as the trade mean, was also calculated. Significant differences in noise exposure levels were observed between construction trades (ANOVA, p < 0.001). The highest LMOEL values were recorded for concrete chippers (93.2 ± 2.6 dBA), followed by ironworkers (88.4 ± 0.7 dBA), concrete finishers (88.3 ± 2.7 dBA), masonry workers (87.7 ± 1.9 dBA), pile driver operators (85.6 ± 1.7 dBA), concrete carpenters (84.9 ± 2.4 dBA), interior carpenters (83.5 ± 2.1 dBA), and other groups (81.4 ± 2.2 dBA). Conclusions: The findings suggest that nearly all construction workers in this study are at risk of Noise-Induced Hearing Loss (NIHL). Moreover, the study establishes that construction trades can serve as a useful metric for assessing noise exposure levels at apartment construction sites.

Water Quality and Ecosystem Health Assessments in Urban Stream Ecosystems (도심하천 생태계에서의 수질 및 생태건강성 평가)

  • Kim, Hyun-Mac;Lee, Jae-Hoon;An, Kwang-Guk
    • Korean Journal of Environmental Biology
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    • v.26 no.4
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    • pp.311-322
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    • 2008
  • The objectives of the study were to analyze chemical water quality and physical habitat characteristics in the urban streams (Miho and Gap streams) along with evaluations of fish community structures and ecosystem health, throughout fish composition and guild analyses during 2006$\sim$2007. Concentrations of BOD and COD averaged 3.5 and 5.7 mg L$^{-1}$, in the urban streams, while TN and TP averaged 5.1 mg L$^{-1}$ and 274 ${\mu}g$ L$^{-1}$, indicating an eutrophic state. Especially, organic pollution and eutrophication were most intense in the downstream reach of both streams. Total number of fish was 34 species in the both streams, and the most abundant species was Zacco platypus (32$\sim$42% of the total). In both streams, the relative abundance of sensitive species was low (23%) and tolerant and omnivores were high (45%, 52%), indicating an typical tolerance and trophic guilds of urban streams in Korea. According to multi-metric models of Stream Ecosystem Health Assessments (SEHA), model values were 19 and 24 in Miho Stream and Gap Stream, respectively. Habitat analysis showed that QHEI (Qulatitative Habitat Evaluation Index) values were 123 and 135 in the two streams, respectively. The minimum values in the SEHA and QHEI were observed in the both downstreams, and this was mainly attributed to chemical pollutions, as shown in the water quality parameters. The model values of SEHA were strongly correlated with conductivity (r=-0.530, p=0.016), BOD (r=-0.578, p< 0.01), COD (r=-0.603, p< 0.01), and nutrients (TN, TP: r>0.40, p<0.05). This model applied in this study seems to be a useful tool, which could reflect the chemical water quality in the urban streams. Overall, this study suggests that consistent ecological monitoring is required in the urban streams for the conservations along with ecological restorations in the degradated downstrems.

Studies on the Manifestation of Hybrid vigour and Combining Ability in Polyvoltine X Bivoltine (cross breed) Hybrids of Mulberry Silkworm Bombyx mori L.

  • Seshagiri, S.V.;Naik, S. Sankar;Seetharamulu, J.;Goel, A.K.;Raju, P.J.
    • International Journal of Industrial Entomology and Biomaterials
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    • v.24 no.1
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    • pp.7-16
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    • 2012
  • To meet the local requirement i.e. the tropical stress of Andhra Pradesh and marginal farmers, twenty four new hybrid combinations were tested in Line x Tester method involving eight newly developed polyvoltine oval lines viz., MSO1, MSO2, MSO3, MSO4, MSO5, MSO6, MSO7 and MSO8 and three bivoltine silkworm breeds viz., APS12, APS45 and APS8 as testers. These hybrids were reared to evaluate their performance. Data for eight economically important metric traits viz., fecundity, cocoon yield per 10,000 larvae by number, cocoon yield per 10,000 larvae by weight, survival rate, cocoon weight, cocoon shell weight, cocoon shell ratio and filament length was recorded. General combining ability (gca), specific combining ability (sca) and heterosis were analyzed. Further, the relative merit of the hybrids for all the traits under study was also assessed adopting Evaluation Index method. Based on combining ability effects, heterosis and evaluation index, five hybrid combinations viz., MSO3 $\times$ APS45, MSO1 $\times$ APS12, MSO7 $\times$ APS8, MSO2 $\times$ APS45 and MSO1 $\times$ APS45 were selected for further evaluation in different seasons.