• Title/Summary/Keyword: Unit Vector

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SOME EIGENFORMS OF THE LAPLACE-BELTRAMI OPERATORS IN A RIEMANNIAN SUBMERSION

  • MUTO, YOSIO
    • Journal of the Korean Mathematical Society
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    • v.15 no.1
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    • pp.39-57
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    • 1978
  • It is given in the Lecture Note [1] of Berger, Gauduchon and Mazet that, if ${\pi}$n: (${\tilde{M}}$, ${\tilde{g}}$)${\rightarrow}$(${\tilde{M}}$, ${\tilde{g}}$) is a Riemannian submersion with totally geodesic fibers, ${\Delta}$ and ${\tilde{\Delta}}$ are Laplace operators on (${\tilde{M}}$, ${\tilde{g}}$) and (M, g) respectively and f is an eigenfunction of ${\Delta}$, then its lift $f^L$ is also an eigenfunction of ${\tilde{\Delta}}$ with the common eigenvalue. But such a simple relation does not hold for an eigenform of the Laplace-Beltrami operator ${\Delta}=d{\delta}+{\delta}d$. If ${\omega}$ is an eigenform of ${\Delta}$ and ${\omega}^L$ is the horizontal lift of ${\omega}$, ${\omega}^L$ is not in genera an eigenform of the Laplace-Beltrami operator ${\tilde{\Delta}}$ of (${\tilde{M}}$, ${\tilde{g}}$). The present author has obtained a set of formulas which gives the relation between ${\tilde{\Delta}}{\omega}^L$ and ${\Delta}{\omega}$ in another paper [7]. In the present paper a Sasakian submersion is treated. A Sasakian manifold (${\tilde{M}}$, ${\tilde{g}}$, ${\tilde{\xi}}$) considered in this paper is such a one which admits a Riemannian submersion where the base manifold is a Kaehler manifold (M, g, J) and the fibers are geodesics generated by the unit Killing vector field ${\tilde{\xi}}$. Then the submersion is called a Sasakian submersion. If ${\omega}$ is a eigenform of ${\Delta}$ on (M, g, J) and its lift ${\omega}^L$ is an eigenform of ${\tilde{\Delta}}$ on (${\tilde{M}}$, ${\tilde{g}}$, ${\tilde{\xi}}$), then ${\omega}$ is called an eigenform of the first kind. We define a relative eigenform of ${\tilde{\Delta}}$. If the lift ${\omega}^L$ of an eigenform ${\omega}$ of ${\Delta}$ is a relative eigenform of ${\tilde{\Delta}}$ we call ${\omega}$ an eigenform of the second kind. Such objects are studied.

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Bacillus cereus ASK-202에서 cloning 된 agarase의 물리 ${\cdot}$ 화학적 특성

  • Hwang, Seon-Hui;Ha, Sun-Deuk;Kim, Bong-Jo;Gong, Jae-Yeol
    • 한국생물공학회:학술대회논문집
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    • 2002.04a
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    • pp.534-537
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    • 2002
  • An agarase gene from Bacillus cereus ASK202 was expressed in high levels by E. coli BL21(DE3)/pEBA1 using pET28a(+) vector system with the inducible T7 promoter in the presence of isopropyl- ${\beta}$ -thiogalactopyranoside. The open reading frame encodes 761 amino acid residues with a calculated molecular weight of 83,300 daltons and a potential signal peptide about 36 amino acid residues at the N-terminus. E. coli BL21(DE3)/pEBA1 produce 1280 unit/ ${\ell}$ of agarase. The optimum physical condition for the agarase activity was pH 5.6, and $40^{\circ}C$, respectively. The agarase activity was stable up pH $4.0{\sim}9.0$ and $4{\sim}40^{\circ}C$. The km and maximum rate of metabolism for agar were 0.068mg/$m{\ell}$ and 0.094mg/$m{\ell}{\cdot}min$, respectively.

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Categorization of Korean News Articles Based on Convolutional Neural Network Using Doc2Vec and Word2Vec (Doc2Vec과 Word2Vec을 활용한 Convolutional Neural Network 기반 한국어 신문 기사 분류)

  • Kim, Dowoo;Koo, Myoung-Wan
    • Journal of KIISE
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    • v.44 no.7
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    • pp.742-747
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    • 2017
  • In this paper, we propose a novel approach to improve the performance of the Convolutional Neural Network(CNN) word embedding model on top of word2vec with the result of performing like doc2vec in conducting a document classification task. The Word Piece Model(WPM) is empirically proven to outperform other tokenization methods such as the phrase unit, a part-of-speech tagger with substantial experimental evidence (classification rate: 79.5%). Further, we conducted an experiment to classify ten categories of news articles written in Korean by feeding words and document vectors generated by an application of WPM to the baseline and the proposed model. From the results of the experiment, we report the model we proposed showed a higher classification rate (89.88%) than its counterpart model (86.89%), achieving a 22.80% improvement. Throughout this research, it is demonstrated that applying doc2vec in the document classification task yields more effective results because doc2vec generates similar document vector representation for documents belonging to the same category.

Construction of Farmlands Spatial Information for Reasonable Adjustment of Farmland Use (합리적인 농지이용조정을 위한 농지공간정보구축)

  • Chung, Hoi-Hoon;Na, Sang-Il;Lee, Sang-Hyun;Choi, Jin-Yong
    • Journal of Korean Society of Rural Planning
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    • v.15 no.4
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    • pp.213-220
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    • 2009
  • Farmland spatial data are needed as a basic information in conducting rational use of farmlands in regional scale. This study develops a method that can be used to make up such farmland spatial data in a simple way and to develop a technique to manage them in a unitary way, and examines the effectiveness of the technique by applying it to the case area. A method that Web-Service Raster Image and Digital Cadastal Map can be utilized as a base map was devised. It was designed applying the vector system, in which one lot of farmland is area unit. Raster image and field survey data were combined to increase the accuracy of data. The lot boundaries of the existing boundary map were adjusted to the shapes of actual farmlands using GIS edition function. A proper farmland use classification system to the area characteristics was established and data obtained from the field survey were coded. Usually it is very difficult to identify the size of one lot of actual farmland in the existing space data, based on the results of the case study, the result map showed actual topography very realistically. Also the frequently occurring lot divisions and the serious topographical modifications by natural disasters frequently have made it impossible to survey farmlands on the catastral map in the field. But the final map had a great usefulness in that it may solve such problems by expressing the filed survey results graphically.

Molecular Cloning and Nucleotide Sequence of the Gene Encoding Fusion(F) Protein of the Thermostable Newcastle Disease Virus Isolated from a Diseased Pheasant (꿩에서 분리된 Newcastle Disease Virus 내열성주 (CBP)의 Fusion(F) 유전자 클론닝과 염기서열 분석)

  • Chang, Kyung-Soo;Jun, Moo-Hyung;Song, Hee-Jong;Kim, Kui-Hyun;Park, Jong-Hyeon
    • The Journal of Korean Society of Virology
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    • v.28 no.3
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    • pp.233-245
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    • 1998
  • The gene encoding F protein of CBP-1 strain, a heat-stable Newcastle disease virus (NDV) isolated from the diseased pheasants in Korea, was characterized by reverse transcription-polymerase chain reaction (RT-PCR), nucleotide and amino acid sequences. Virus RNA was prepared from the chorioallatoic fluid infected with NDV CBP-1 virus and cDNA was amplified by RT-PCR, cloned and sequenced to analyze. The PCR was sensitive as to detect the virus titer above $2^5$ hemagglutination unit. 1.7kb (1,707bp) size of the cDNA was amplified and cloned into BamHI site of pVL1393 Baculo transfer vector. The nucleotide sequences for F protein were determined by dye terminator cyclic sequencing using four pairs of primers, and 553 amino acid sequences were predicted. In comparison of the nucleotide sequence of F gene of CBP-1 with those of other NDV strains, the homology revealed 88.8%, 98.5% and 98.7% with Kyojungwon (KJW), Texas GB and Beaudette C strains, respectively. As the deduced 553 amino acid sequences of F protein of CBP-1 were compared with those of other NDV strains, the homology appeared 89.9%, 98.7% and 98.9% with KJW, Texas GB and Beaudette C strains, respectively. The putative protease cleavage site (112-116) was R-R-Q-K-R, indicating that CBP-1 strain is velogenic type. The amino acid sequences include 6 sites of N-asparagine-linked glycosylation and 13 cysteine residues. These data indicate that the genotype of CBP-1 strain is more closely associated with the strains of Texas GB and Beaudette C than KJW strain.

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Digital Mapping Based on Digital Ortho Images (수치정사투영영상을 이용한 수치지도제작)

  • 이재기;박경식
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.18 no.1
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    • pp.1-9
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    • 2000
  • In the recent day, the necessity and the effective usage are increased rapidly, and it is applied in many other fields as well as in the field of ortho-photo map. In this study, we extract each objects on the aerial image and automatically classify graphic information to produce digital map using only digital ortho-image without particular drawing devices for producing digital map. For this purpose, we have applied a lot of the image processing techniques and fuzzy theory, classified outline and lane of road and building, and had each layer according to each feature. Especially, in the case of the building, the outer vector lines extracted by pixel unit at the building were very complex, but we have developed the program to be expressed by I-dimensional linear type between building corners. In the result of this study, we could not extract and recognize all of the object on the image all together, but we have got the error within 50cm using semi-automatic technique. Therefore, this method will be used effectively in producing 1/5,000 digital map.

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The Analysis of Swing Plane of Elite Golfers During Drive Swing (엘리트 골프 선수의 드라이버 스윙 시 스윙 평면 분석)

  • Lim, Young-Tae
    • Korean Journal of Applied Biomechanics
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    • v.19 no.1
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    • pp.59-66
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    • 2009
  • The purpose of this study was to evaluate flatness of swing plane and determine swing plane type using 3-D swing plane analysis from young elite male golf players. This study also investigate the possibility of determination of swing plane using other kinematic parameters except flatness. As results, no correlations was found between flatness and handicap. Comparison of flatness between single plane and multiple plane swing group were performed and found a significant difference. The error range of flatness, 10cm, which was used for distinguish swing plane type was effective since significant differences were found at MB, EB, and EF. These differences were typical characteristics to classify two swing styles. Other kinematic parameters such as unit vector components of shaft and displacement of shaft end point also compared per event but found no significant differences. However, the moving patterns of these parameters during a golf swing showed such characteristics of each swing plane type well that these parameters could be used to determine swing style as an indirect barometers.

Energy analysis-based core drilling method for the prediction of rock uniaxial compressive strength

  • Qi, Wang;Shuo, Xu;Ke, Gao Hong;Peng, Zhang;Bei, Jiang;Hong, Liu Bo
    • Geomechanics and Engineering
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    • v.23 no.1
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    • pp.61-69
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    • 2020
  • The uniaxial compressive strength (UCS) of rock is a basic parameter in underground engineering design. The disadvantages of this commonly employed laboratory testing method are untimely testing, difficulty in performing core testing of broken rock mass and long and complicated onsite testing processes. Therefore, the development of a fast and simple in situ rock UCS testing method for field use is urgent. In this study, a multi-function digital rock drilling and testing system and a digital core bit dedicated to the system are independently developed and employed in digital drilling tests on rock specimens with different strengths. The energy analysis is performed during rock cutting to estimate the energy consumed by the drill bit to remove a unit volume of rock. Two quantitative relationship models of energy analysis-based core drilling parameters (ECD) and rock UCS (ECD-UCS models) are established in this manuscript by the methods of regression analysis and support vector machine (SVM). The predictive abilities of the two models are comparatively analysed. The results show that the mean value of relative difference between the predicted rock UCS values and the UCS values measured by the laboratory uniaxial compression test in the prediction set are 3.76 MPa and 4.30 MPa, respectively, and the standard deviations are 2.08 MPa and 4.14 MPa, respectively. The regression analysis-based ECD-UCS model has a more stable predictive ability. The energy analysis-based rock drilling method for the prediction of UCS is proposed. This method realized the quick and convenient in situ test of rock UCS.

Multivariate empirical distribution plot and goodness-of-fit test (다변량 경험분포그림과 적합도 검정)

  • Hong, Chong Sun;Park, Yongho;Park, Jun
    • The Korean Journal of Applied Statistics
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    • v.30 no.4
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    • pp.579-590
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    • 2017
  • The multivariate empirical distribution function could be defined when its distribution function can be estimated. It is known that bivariate empirical distribution functions could be visualized by using Step plot and Quantile plot. In this paper, the multivariate empirical distribution plot is proposed to represent the multivariate empirical distribution function on the unit square. Based on many kinds of empirical distribution plots corresponding to various multivariate normal distributions and other specific distributions, it is found that the empirical distribution plot also depends sensitively on its distribution function and correlation coefficients. Hence, we could suggest five goodness-of-fit test statistics. These critical values are obtained by Monte Carlo simulation. We explore that these critical values are not much different from those in text books. Therefore, we may conclude that the proposed test statistics in this work would be used with known critical values with ease.

Secretion of Bacillus subtilis Endo-1,4-$\beta$-D-Glucanase in Yeast Using Promoter and Signal Sequence of Glucoamylase Gene (Glucoamylase 유전자의 promoter 와 분비신호서열을 이용한 Bacillus subtilis Endo-1-4$\beta$-D-Glucanase 의 효모에서 분비)

  • 안종석;강대욱;황인규;박승환;박무영;민태익
    • Korean Journal of Microbiology
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    • v.30 no.5
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    • pp.403-409
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    • 1992
  • For the development of a glucanolytic yeast strain. the seceretion of endo-1.4-$\beta$-D-glucanase (CMCase) of Bacillus subtilis was performed in yeast using glucoamylase gene (STA1) of Saccharomyces diastaticus. A 1.7 kb-DNA fragment of STA1 gene containing authentic promoter, signal sequence, threonine serine-rich (TS) region and N-terminal region (98 amino acids) of mature glucoamylase was ligated to YEp 24. E. coli-yeast shuttle vector. And then. CMCase structural gene of B. subtilis was fused in frame with the 1.7 kb-DNA fragment of STA1 gene, resulting in recombinant plasmid pYES('24. Yeast transformant harboring pYESC24 had no CMCase activity. So. we deleted TS region and N-terminal region of mature glucoamylase existing between signal sequence and CMCase structural gene in pYESC24. consequently constructed recombinant plasmid pYESC11. The yeast transformed with the newly constructed recombinant plasmid pYESC11 efficiently secreted CMCase to extracellular medium. After 4 days culture. total CMCase activity of this transformant was 44.7 units/ml and over 93% of total CMCase activity was detected in culture supernatant.

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