• Title/Summary/Keyword: geometric mean

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SOME INTEGRATIONS ON NULL HYPERSURFACES IN LORENTZIAN MANIFOLDS

  • Massamba, Fortune;Ssekajja, Samuel
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.229-243
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    • 2019
  • We use the so-called pseudoinversion of degenerate metrics technique on foliated compact null hypersurface, $M^{n+1}$, in Lorentzian manifold ${\overline{M}}^{n+2}$, to derive an integral formula involving the r-th order mean curvatures of its foliations, ${\mathcal{F}}^n$. We apply our formula to minimal foliations, showing that, under certain geometric conditions, they are isomorphic to n-dimensional spheres. We also use the formula to deduce expressions for total mean curvatures of such foliations.

Robust Radiometric and Geometric Correction Methods for Drone-Based Hyperspectral Imaging in Agricultural Applications

  • Hyoung-Sub Shin;Seung-Hwan Go;Jong-Hwa Park
    • Korean Journal of Remote Sensing
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    • v.40 no.3
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    • pp.257-268
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    • 2024
  • Drone-mounted hyperspectral sensors (DHSs) have revolutionized remote sensing in agriculture by offering a cost-effective and flexible platform for high-resolution spectral data acquisition. Their ability to capture data at low altitudes minimizes atmospheric interference, enhancing their utility in agricultural monitoring and management. This study focused on addressing the challenges of radiometric and geometric distortions in preprocessing drone-acquired hyperspectral data. Radiometric correction, using the empirical line method (ELM) and spectral reference panels, effectively removed sensor noise and variations in solar irradiance, resulting in accurate surface reflectance values. Notably, the ELM correction improved reflectance for measured reference panels by 5-55%, resulting in a more uniform spectral profile across wavelengths, further validated by high correlations (0.97-0.99), despite minor deviations observed at specific wavelengths for some reflectors. Geometric correction, utilizing a rubber sheet transformation with ground control points, successfully rectified distortions caused by sensor orientation and flight path variations, ensuring accurate spatial representation within the image. The effectiveness of geometric correction was assessed using root mean square error(RMSE) analysis, revealing minimal errors in both east-west(0.00 to 0.081 m) and north-south directions(0.00 to 0.076 m).The overall position RMSE of 0.031 meters across 100 points demonstrates high geometric accuracy, exceeding industry standards. Additionally, image mosaicking was performed to create a comprehensive representation of the study area. These results demonstrate the effectiveness of the applied preprocessing techniques and highlight the potential of DHSs for precise crop health monitoring and management in smart agriculture. However, further research is needed to address challenges related to data dimensionality, sensor calibration, and reference data availability, as well as exploring alternative correction methods and evaluating their performance in diverse environmental conditions to enhance the robustness and applicability of hyperspectral data processing in agriculture.

MEAN-VALUE PROPERTY AND CHARACTERIZATIONS OF SOME ELEMENTARY FUNCTIONS

  • Matkowski, Janusz
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.263-273
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    • 2013
  • A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

Mercury Level in Hair of Primary School Children in Korea and China

  • Park, Hee-Jin;Kim, Dae-Seon;Moon, Jeong-Suk;Yang, Won-Ho;Son, Bu-Soon
    • Molecular & Cellular Toxicology
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    • v.4 no.3
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    • pp.235-245
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    • 2008
  • Exposure to mercury was assessed in 125 Korean (Gwangju and Busan) and 373 Chinese primary school students (Xinguang village, Goumen town) using hair mercury analysis from November 2006 to September 2007. The geometric mean concentration of mercury was higher among Korean children with recording 0.73 ${\mu}g$/g, compared to Chinese children of 0.12 ${\mu}g$/g, which indicated statistically difference (P<0.01). The mean concentration of Korean children living near incineration facilities was higher by recording 0.76 ${\mu}g$/g while the average concentration of their counterpart in Korea reached 0.69 ${\mu}g$/g. In case of Chinese children, those who are living near power plants showed higher level with posting 0.16 ${\mu}g$/g while the others recorded 0.10 ${\mu}g$/g (P<0.01). Intake of fish was found to be related to hair mercury level. In case of Korean children, those with high fish intake recorded 0.79 ${\mu}g$/g in terms of the geometric mean concentration while the others with low fish intake posted 0.61 ${\mu}g$/g. Among Chinese children, those who often eat fish recorded 0.13 ${\mu}g$/g compared to the others with low fish intake of 0.11 ${\mu}g$/g. On the other hand, amalgam dental fillings have limited influence on mean hair mercury level. As for vaccination, within a month of vaccination, the geometric mean concentration of Korean children reached 0.76 ${\mu}g$/g, and in case of 15 days after injection, the level was 1.20 ${\mu}g$/g. In China, the level of children at one month after receiving injection stood at 0.15 ${\mu}g$/g while the level within 15 days was 0.13 ${\mu}g$/g. Multiple regression analysis showed that BMI, passive smoking, and fish consumption are closely related to hair mercury level among the Korean subjects. In China, hair mercury level was affected by age, location, passive smoking, fish consumption, and vaccination. Explanatory power was 21.6% with $R^2$=0.216.

Ensemble Learning with Support Vector Machines for Bond Rating (회사채 신용등급 예측을 위한 SVM 앙상블학습)

  • Kim, Myoung-Jong
    • Journal of Intelligence and Information Systems
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    • v.18 no.2
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    • pp.29-45
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    • 2012
  • Bond rating is regarded as an important event for measuring financial risk of companies and for determining the investment returns of investors. As a result, it has been a popular research topic for researchers to predict companies' credit ratings by applying statistical and machine learning techniques. The statistical techniques, including multiple regression, multiple discriminant analysis (MDA), logistic models (LOGIT), and probit analysis, have been traditionally used in bond rating. However, one major drawback is that it should be based on strict assumptions. Such strict assumptions include linearity, normality, independence among predictor variables and pre-existing functional forms relating the criterion variablesand the predictor variables. Those strict assumptions of traditional statistics have limited their application to the real world. Machine learning techniques also used in bond rating prediction models include decision trees (DT), neural networks (NN), and Support Vector Machine (SVM). Especially, SVM is recognized as a new and promising classification and regression analysis method. SVM learns a separating hyperplane that can maximize the margin between two categories. SVM is simple enough to be analyzed mathematical, and leads to high performance in practical applications. SVM implements the structuralrisk minimization principle and searches to minimize an upper bound of the generalization error. In addition, the solution of SVM may be a global optimum and thus, overfitting is unlikely to occur with SVM. In addition, SVM does not require too many data sample for training since it builds prediction models by only using some representative sample near the boundaries called support vectors. A number of experimental researches have indicated that SVM has been successfully applied in a variety of pattern recognition fields. However, there are three major drawbacks that can be potential causes for degrading SVM's performance. First, SVM is originally proposed for solving binary-class classification problems. Methods for combining SVMs for multi-class classification such as One-Against-One, One-Against-All have been proposed, but they do not improve the performance in multi-class classification problem as much as SVM for binary-class classification. Second, approximation algorithms (e.g. decomposition methods, sequential minimal optimization algorithm) could be used for effective multi-class computation to reduce computation time, but it could deteriorate classification performance. Third, the difficulty in multi-class prediction problems is in data imbalance problem that can occur when the number of instances in one class greatly outnumbers the number of instances in the other class. Such data sets often cause a default classifier to be built due to skewed boundary and thus the reduction in the classification accuracy of such a classifier. SVM ensemble learning is one of machine learning methods to cope with the above drawbacks. Ensemble learning is a method for improving the performance of classification and prediction algorithms. AdaBoost is one of the widely used ensemble learning techniques. It constructs a composite classifier by sequentially training classifiers while increasing weight on the misclassified observations through iterations. The observations that are incorrectly predicted by previous classifiers are chosen more often than examples that are correctly predicted. Thus Boosting attempts to produce new classifiers that are better able to predict examples for which the current ensemble's performance is poor. In this way, it can reinforce the training of the misclassified observations of the minority class. This paper proposes a multiclass Geometric Mean-based Boosting (MGM-Boost) to resolve multiclass prediction problem. Since MGM-Boost introduces the notion of geometric mean into AdaBoost, it can perform learning process considering the geometric mean-based accuracy and errors of multiclass. This study applies MGM-Boost to the real-world bond rating case for Korean companies to examine the feasibility of MGM-Boost. 10-fold cross validations for threetimes with different random seeds are performed in order to ensure that the comparison among three different classifiers does not happen by chance. For each of 10-fold cross validation, the entire data set is first partitioned into tenequal-sized sets, and then each set is in turn used as the test set while the classifier trains on the other nine sets. That is, cross-validated folds have been tested independently of each algorithm. Through these steps, we have obtained the results for classifiers on each of the 30 experiments. In the comparison of arithmetic mean-based prediction accuracy between individual classifiers, MGM-Boost (52.95%) shows higher prediction accuracy than both AdaBoost (51.69%) and SVM (49.47%). MGM-Boost (28.12%) also shows the higher prediction accuracy than AdaBoost (24.65%) and SVM (15.42%)in terms of geometric mean-based prediction accuracy. T-test is used to examine whether the performance of each classifiers for 30 folds is significantly different. The results indicate that performance of MGM-Boost is significantly different from AdaBoost and SVM classifiers at 1% level. These results mean that MGM-Boost can provide robust and stable solutions to multi-classproblems such as bond rating.

ON SOME GEOMETRIC PROPERTIES OF QUADRIC SURFACES IN EUCLIDEAN SPACE

  • Ali, Ahmad T.;Aziz, H.S. Abdel;Sorour, Adel H.
    • Honam Mathematical Journal
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    • v.38 no.3
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    • pp.593-611
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    • 2016
  • This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.

Input energy spectrum damping modification factors

  • Onur Merter;Taner Ucar
    • Earthquakes and Structures
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    • v.26 no.3
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    • pp.219-228
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    • 2024
  • This study examines damping modification factors (DMFs) of elastic input energy spectra corresponding to a set of 116 earthquake ground motions. Mean input energy per mass spectra and mean DMFs are presented for both considered ground motion components. Damping ratios of 3%, 5%, 10%, 20%, and 30% are used and the 5% damping ratio is considered the benchmark for DMF computations. The geometric mean DMFs of the two horizontal components of each ground motion are computed and coefficients of variation are presented graphically. The results show that the input energy spectra-based DMFs exhibit a dependence on the damping ratio at very short periods and they tend to be nearly constant for larger periods. In addition, mean DMF variation is obtained graphically for also the damping ratio, and mathematical functions are fitted as a result of statistical analyses. A strong correlation between the computed DMFs and the ones from predicted equations is observed.

Exposure Assessment of Airborne Dust in Manufacturing Industries Using Silicon Carbide in Korea (우리나라 실리콘카바이드 취급사업장의 공기 중 분진 노출평가)

  • Lee, Jun Jung;Phee, Young Gyu
    • Journal of Korean Society of Occupational and Environmental Hygiene
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    • v.21 no.3
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    • pp.177-183
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    • 2011
  • Occupational exposure to silicon carbide dust of manufacturing industries has seldom been evaluated in Korea. Accordingly, we evaluated various silicon carbide dust concentrations in the breathing zone of workers between May 2010 and July 2010. To compare silicon carbide dust concentrations, three dust samplers including the Institute of Occupational Medicine (IOM) sampler, 37mm cassette sampler, and Aluminum cyclone sampler were used. A total of 5 manufacturing industries producing abrasive and refractory materials using silicon carbide were investigated. The geometric mean concentrations were 2.04, 0.97, and $0.48mg/m^3$ in inhalable, total and respirable silicon carbide dust, respectively. The geometric mean concentrations of silicon carbide in abrasive material manufacturing industries were slightly higher than that of refractory manufacturing industries, and finishing operations were higher than that of other operations. It was found that the results of exposure assessment in airborne dust at manufacturing industries using silicon carbide in Korea showed exceeding rate to American Conference of Governmental Industrial Hygienists Threshold Limit Value ($3mg/m^3$) was 10% in respirable dust samples. Therefore, with the consideration of the close relationship between smaller dust size and the occurrence of occupational respiratory diseases, it is suggested to promulgate the new occupational exposure limit for respirable silicon carbide dust.

Serological Survey of Cattle on Bovine Viral Diarrhea in Young Dong Province (강원 영동지역 우 바이러스성 설사병의 혈청학적 조사)

  • 이종오;한영도;육심용;김연수;장상문;정재영;김동훈
    • Korean Journal of Veterinary Service
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    • v.14 no.2
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    • pp.148-153
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    • 1991
  • To investigate epidemological sitution of bovine viral diarrhea infection, serological survey in cattle being raised in Young Dong province were conducted. Bovine sera collected ramdomly from August 1990 to December 1990 were tested for bovine viral diarrhea virus serum neutralizing antibody titers. The results were as follows 1. BVDV SN antibody levels were considerably varies and positive rate was 58(108 heads out of 186) 2. BVDV SN antibodies to breeds of cattle was various and positive rates showed that diary cattle, beef, native cattle(Korean) were 67.52%, 59.38%, 27.00% respectively followed in that order. 3. In the regional prevalence of BVD SN antibodies in cattle, Alpine(92%) was the highest, Young Dong south(59%) middle(44%), and North 30% followed in that order 4. In the age relatated prevalence of BVD SN antibodies, the younger than 6 month old group was the highest 65.7%, and older than 25 month old group was also at 62.2%. Then, 7 to 12 moth old group and 13 to 24 month old group showed to 58.5%, 52.1% respectively. 5. The geometric mean titer (log2) of 108 cattle serum samples showing positive BVD SN antibodies was 4.3. 6. In the geometric mean titer(log2) according to age, younger than 6 month old group (5.2) was the highest, then 7 to 12 month old group 2.8(SD=1.94 standard deviation) was lowliest.

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