• Journal for History of Mathematics
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• v.32 no.4
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.53 no.3
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• pp.297-302
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• 2008

Application of genotype by environment ($G\;{\times}\;E$) interaction would be used for identifying optimum test condition of the varietal adaptation in the establishment of breeding purpose. Yield and yield components were used to perform additive main effect and multiplicative interaction (AMMI) analysis. Significant difference for $G\;{\times}\;E$ interaction were observed for all variable examined. For yield, 0.18 of total sum of squares corresponded to $G\;{\times}\;E$ interaction. Correlation analysis was carried out between genotypic scores of the first interaction principal component axis (IPCA 1) for agronomic characters. Significant correlations were observed between IPCA 1 for yield and capsule bearing stem length (CBSL), number of capsule per plant (NOC). The biplot of grain yield means for IPCA1 which accounted for 34% of the variation in total treatment sums of squares showed different reaction according to $G\;{\times}\;E$ interaction, genotypes and environments. Taegu showed relatively lower positive IPCA1 scores, and it also showed smaller coefficient variation of yield mean where it is recommendable as a optimal site for the sesame cultivar adaptation and evaluation trial. In case of variables, Yangbaek and M1 showed relatively lower IPCA1 scores, but the score direction showed opposite each other on the graph. Ansan, Miryang1, Miryang4, and Miryang6 seemed to be similar group in view of yield response against IPCA1 scores. These results will be helpful to select experimental site for sesame in Korea to minimize $G\;{\times}\;E$ interaction for the selection of promising genotype with higher stability.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.431-440
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• 2013

We consider the problem of estimating the parameters of heavy tailed distributions. In general, maximum likelihood estimation(MLE) is the most preferred method of parameter estimation because it has good properties such as asymptotic consistency, normality and efficiency. However, MLE is not always the best solution because MLE is unstable or does not exist in some cases. This paper proposes another parameter estimation method, non-linear least squares(NLS) and compares its performance to MLE. The NLS estimator is achieved by minimizing sum of squared difference between empirical cumulative distribution function(CDF) and a theoretical distribution function. In this article, we compare the NLS method to MLE using simulated data from heavy tailed distributions. The NLS method is shown to perform better than MLE in Burr distribution when the sample size is small; in addition, it performs well in a Frechet distribution.

• Journal of Cadastre & Land InformatiX
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• v.45 no.2
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• pp.117-130
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• 2015

A least squares method for adjusting the horizontal network satisfies the conditions which is minimizing the sum of the squares of errors based on probability theory. This research compared accuracy of 3rd cadastral control points adjusted by traditional and least square method with respect to the result of Network-RTK. Test results showed the least square method more evenly distribute closure error than traditional method. Mean errors of least square and traditional adjusting method are 2.7cm, 2.2cm respectively. In addition, blunder in angle observations can be detected by comparing position errors which calculated by forward and backward initial coordinates. However, distance blunder cannot offer specific observation line occurred mistake because distance error propagates several observation lines which have similar directions.

• Imaging Science in Dentistry
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• v.53 no.1
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• pp.43-51
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• 2023

Purpose: This study aimed to assess texture analysis(TA) of cone-beam computed tomography (CBCT) images as a quantitative tool for the differential diagnosis of odontogenic and non-odontogenic maxillary sinusitis(OS and NOS, respectively). Materials and Methods: CBCT images of 40 patients diagnosed with OS (N=20) and NOS (N=20) were evaluated. The gray level co-occurrence (GLCM) matrix parameters, and gray level run length matrix texture (GLRLM) parameters were extracted using manually placed regions of interest on lesion images. Seven texture parameters were calculated using GLCM and 4 parameters using GLRLM. The Mann-Whitney test was used for comparisons between the groups, and the Levene test was performed to confirm the homogeneity of variance (α=5%). Results: The results showed statistically significant differences(P<0.05) between the OS and NOS patients regarding 3 TA parameters. NOS patients presented higher values for contrast, while OS patients presented higher values for correlation and inverse difference moment. Greater textural homogeneity was observed in the OS patients than in the NOS patients, with statistically significant differences in standard deviations between the groups for correlation, sum of squares, sum of entropy, and entropy. Conclusion: TA enabled quantitative differentiation between OS and NOS on CBCT images by using the parameters of contrast, correlation, and inverse difference moment.

• Asian-Australasian Journal of Animal Sciences
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• v.10 no.2
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• pp.240-244
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• 1997

This study was conducted in North Sulawesi, Indonesia to identify the factors affecting reproductive efficiency and to determine the contribution of each factor in reproductive efficiency of Indonesian native cows. Records of reproductive efficiency, body size (hip height, body weight, body length, heart girth) as well as age on one hundred and sixty seven Indonesian native cows (seventy six cows of the Bali breed and ninety one cows of the synthetic breed from unknown proportion of th Madura, the Sumba and the Ongole breeds) of 58 farmers were available in this research. The data were analyzed by covariance analysis using SAS package including reproductive efficiency as a dependent variable and breed, body size (hip height, body weight, body length, heart girth) and age of cows as independent variables. The contribution of each independent factor to dependent variable was estimated as the percentage of the sum of square in the corrected total sum of squares. The results showed that body weight and body size of cows would be considered as th most important factors affecting reproductive efficiency of Indonesian native cows. Therefore, the reproductive efficiency could be increased by 1) using cows that reached a target weight of at least 250 kg, 2) using cows with relatively well developed height at hip of at least 117 cm, heart girth of at least 150 cm, and body length of at least 125 cm, 3) keeping breeding cows that reach a target age of 24 months old with the maximum interval between postpartum and next breeding season of 90 days for each year, and 4) using good nutritional feeding to reach the optimum weight and body condition.

• Imaging Science in Dentistry
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• v.53 no.2
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• pp.109-115
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• 2023

Purpose: The aim of this study was to evaluate changes in the trabecular bone through texture analysis and compare the texture analysis characteristics of different areas in patients with medication-related osteonecrosis of the jaw (MRONJ). Materials and Methods: Cone-beam computed tomographic images of 16 patients diagnosed with MRONJ were used. In sagittal images, 3 regions were chosen: active osteonecrosis(AO); intermediate tissue (IT), which presented a zone of apparently healthy tissue adjacent to the AO area; and healthy bone tissue (HT) (control area). Texture analysis was performed evaluating 7 parameters: secondary angular momentum, contrast, correlation, sum of squares, inverse moment of difference, sum of entropies, and entropy. Data were analyzed using the Kruskal-Wallis test with a significance level of 5%. Results: Comparing the areas of AO, IT, and HT, significant differences (P<0.05) were observed. The IT and AO area images showed higher values for parameters such as contrast, entropy, and secondary angular momentum than the HT area, indicating greater disorder in these tissues. Conclusion: Through texture analysis, changes in the bone pattern could be observed in areas of osteonecrosis. The texture analysis demonstrated that areas visually identified and classified as IT still had necrotic tissue, thereby increasing the accuracy of delimiting the real extension of MRONJ.

• Journal of the korean Society of Automotive Engineers
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• v.14 no.5
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• pp.95-106
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• 1992

Active control of acoustic noise is an application area of adaptive digital signal processing with increasingly interest along the last year. This work studies the implementation of the multichannel LMS filter and the application of this algorithm for the reduction of the noise inside a vechicle cabin using a number of 'secondary sources' drived by adaptive filtering of a reference noise source. Firstly, we propose the use of an adaptive method for the time-varient optimal convergence factor. Secondly, we propose the use of adaptive delayed inverse model to estimate the elastic-acoustic transfer function presented in vechicle cabin. The original, primary source is often periodic, with a known fundamental frequency. A suitably filtered reference signal can thus be used to drive the secondary sources. An algorithm is presented for adapting the coefficients of an FIR filter feeding such a secondary source in such a way as to minimize the output of a suitably placed microphone. In this algorithm, the coefficients of adaptive filter driving an array of secondary sources can be adapted to minimize the sum of the squares of the outputs of a number of error microphones. The multichannel LMS algorithm displays that such an algorithm is considered suitable to used for the global suppression of noise in vehicle cabin.

• Horticulture, Environment, and Biotechnology : HEB
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• v.59 no.6
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• pp.919-927
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• 2018

To compare the antioxidant properties and flavonols in various parts; dry skin (DS) and edible portion (EP), of 8 red onions (Allium cepa L, ROs), total content of phenolics (TPC), flavonoids (TFC), and anthocyanins (TAC) and DPPH radical scavenging properties were estimated and the content of six flavonols were quantified by HPLC-PDA analysis. The major component of DS and EP of RO was quercetin and quercetin-4'-glucoside, respectively. Score plots of the PCA and PLS-DA were segregated by flavonols content and antioxidant properties according to the EP and DS of ROs. Loading plot of the PCA showed that the quercetin and sum of flavonol content were highly correlated with antioxidant activity of ROs. Therefore, flavonol content and antioxidant activity can be used as markers for distinct parts of ROs.

• International journal of steel structures
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• v.18 no.5
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• pp.1508-1524
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• 2018

Hysteretic energy dissipating devices (HEDDs) have been increasingly applied to building construction to improve the seismic performance. The seismic responses of such damped structures are significantly affected by HEDD's structural properties. An accurate investigation on the propagation of HEDD's structural properties is required for reasonable evaluation of the seismic performance of a structure. This study aims to develop simplified methods that can estimate the collective uncertainty-propagation to the seismic response of damped structures employing HEDDs. To achieve this, three- and six-story steel moment-resisting frames were selected and the propagations of the individual HEDD's property-uncertainties were evaluated when they are subjected to various levels of seismic demand. Based on the result of individual uncertainty-propagations, a simplified method is proposed to evaluate the variation of seismic response collectively propagated by HEDD's property-uncertainties and is verified by comparing with the exact collective uncertainty-propagation calculated using the Monte Carlo simulation method. The proposed method, called as a modified SRSS method in this study, is established from a conventional square root of the sum of the squares (SRSS) method with the relative contributions of the individual HEDD's property-uncertainty propagations. This study shows that the modified SRSS method provides a better estimation than the conventional SRSS method and can significantly reduce computational time with reasonable accuracy compared with the Monte Carlo simulation method.