• East Asian mathematical journal
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• v.24 no.4
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• pp.377-387
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• 2008

We consider associative ring R (not necessarily commutative). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were introduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.315-318
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• 2006

In this paper we present the simple updating formulas for a sum of product and a sum of cross product when a new value is added on or a specific value is eliminated from the original data. The sample variance and correlation for the new data set are derived by new computing formulas. Any statistic which is a function of the sum of product and a sum of cross product also can be updated by proposed method even though the original data is not available.

• Communications of Mathematical Education
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• v.21 no.1 s.29
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• pp.51-64
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• 2007

In this study we generalize the law of cosine(in any triangle the square of one side is equal to the sum of the squares of the other sides minus twice their product times the cosine of their included angle), We find the following generalized law of cosine: in any polygon the square of one side is equal to the sum of the squares of the other sides minus twice their products times the cosines of their included angles, and prove it using vector.

• Knowledge Management Research
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• v.21 no.1
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• pp.27-40
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• 2020

Response surface methodology (RSM) empirically studies the relationship between a response variable and input variables in the product or process development phase. The ultimate goal of RSM is to find an optimal condition of the input variables that optimizes (maximizes or minimizes) the response variable. RSM can be seen as a knowledge management tool in terms of creating and utilizing data, information, and knowledge about a product production and service operations. In the field of product or process development, most real-world problems often involve a simultaneous consideration of multiple response variables. This is called a multiple response surface (MRS) problem. Various approaches have been proposed for MRS optimization, which can be classified into loss function approach, priority-based approach, desirability function approach, process capability approach, and probability-based approach. In particular, the loss function approach is divided into univariate and multivariate approaches at large. This paper focuses on the univariate approach. The univariate approach first obtains the mean square error (MSE) for individual response variables. Then, it aggregates the MSE's into a single objective function. It is common to employ the weighted sum or the Tchebycheff metric for aggregation. Finally, it finds an optimal condition of the input variables that minimizes the objective function. When aggregating, the relative weights on the MSE's should be taken into account. However, there are few studies on how to determine the weights systematically. In this study, we propose an interactive procedure to determine the weights through considering a decision maker's preference. The proposed method is illustrated by the 'colloidal gas aphrons' problem, which is a typical MRS problem. We also discuss the extension of the proposed method to the weighted MSE (WMSE).

• Structural Engineering and Mechanics
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• v.9 no.3
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• pp.269-288
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• 2000

The governing differential equations for free vibration of multi-step orthotropic shear plates with variably distributed mass, stiffness and viscous damping are established. It is shown that a shear plate can be divided into two independent shear bars to determine the natural frequencies and mode shapes of the plate. The jk-th natural frequency of a shear plate is equal to the square root of the square sum of the j-th natural frequency of a shear bar and the k-th natural frequency of another shear bar. The jk-th mode shape of the shear plate is the product of the j-th mode shape of a shear bar and the k-th mode shape of another shear bar. The general solutions of the governing equations of the orthotropic shear plates with various boundary conditions are derived by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. A numerical example demonstrates that the present methods are easy to implement and efficient. It is also shown through the numerical example that the selected expressions are suitable for describing the distributions of stiffness and mass of typical multi-storey buildings.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.444-449
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• 1996

The semiconductor, which is precision product, requires many inspection processes. The surface conditions of the semiconductor chip affect on the functions of the semiconductors. The defects of the chip surface are cracks or voids. As general inspection method requires many inspection procedure, the inspection system which searches immediately and precisely the defects of the semiconductor chip surface is required. We suggest the detection algorithm for inspecting the surface defects of the semiconductor surface. The proposed algorithm first regards the semiconductor surface as random texture and point spread function, and secondly presents the character of texture by linear estimation theorem. This paper assumes that the gray level of each pixel of an image is estimated from a weighted sum of gray levels of its neighbor pixels by linear estimation theorem. The weight coefficients are determined so that the mean square error is minimized. The obtained estimation window(two-dimensional estimation window) characterizes the surface texture of semiconductor and is used to discriminate the defects of semiconductor surface.

• Smart Media Journal
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• v.12 no.11
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• pp.134-144
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• 2023

Nowadays, Deep Learning (DL) technology is being used in several government departments. South Korea imports a lot of seafood. If the demand for fishery products is not accurately predicted, then there will be a shortage of fishery products and the price of the fishery product may rise sharply. So, South Korea's Ministry of Ocean and Fisheries is attempting to accurately predict seafood imports using deep learning. This paper introduces the solution for the fish import prediction in South Korea using the Long Short-Term Memory (LSTM) method. It was found that there was a huge gap between the sum of consumption and export against the sum of production especially in the case of two species that are Hairtail and Pollock. An import prediction is suggested in this research to fill the gap with some advanced Deep Learning methods. This research focuses on import prediction using Machine Learning (ML) and Deep Learning methods to predict the import amount more precisely. For the prediction, two Deep Learning methods were chosen which are Artificial Neural Network (ANN) and Long Short-Term Memory (LSTM). Moreover, the Machine Learning method was also selected for the comparison between the DL and ML. Root Mean Square Error (RMSE) was selected for the error measurement which shows the difference between the predicted and actual values. The results obtained were compared with the average RMSE scores and in terms of percentage. It was found that the LSTM has the lowest RMSE score which showed the prediction with higher accuracy. Meanwhile, ML's RMSE score was higher which shows lower accuracy in prediction. Moreover, Google Trend Search data was used as a new feature to find its impact on prediction outcomes. It was found that it had a positive impact on results as the RMSE values were lowered, increasing the accuracy of the prediction.

• Journal of Technologic Dentistry
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• v.21 no.1
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• pp.67-75
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• 1999

The purpose of this study is to evaluate the friction coefficients between abutment materials and clasp materials, and to an estimation formula for retention force. The coefficients of friction between three clasp materials and four abutment materials were measured under various conditions, polished and sandblasted and wet and dry. The measurement was repeated for each combination up to a total measurement of 1200 times. Estimation formula for retention force is measured as sum of two terms, which the one time is proportional to the product of friction coefficient ${\mu}$ and undercut u and the other term is proportional to u-squared. Two proportional coefficient were obtained by least square method. The results are as follows: 1. Friction coefficients were ranged from 0.08 to 0.53 under various conditions. 2. Friction coefficients of non-metal abutment materials are greater in wet conditions than dry conditions. 3. Friction coefficients of sandblasted clasp against abutment are greater than that of polished clasp. 4. Clasp retention force can be estimated with the model as F=$F_d(3.0{\mu}u+1.5u^2/h)$ with minor error.

• Korean Journal of Agricultural and Forest Meteorology
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• v.25 no.1
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• pp.28-36
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• 2023

Solar radiation that is measured at relatively small number of weather stations is one of key inputs to crop models for estimation of crop productivity. Solar radiation products derived from GK-2A and Himawari 8 satellite data have become available, which would allow for preparation of input data to crop models, especially for assessment of crop productivity under an agrivoltaic system where crop and power can be produced at the same time. The objective of this study was to compare the degree of agreement between the solar radiation products obtained from those satellite data. The sub hourly products for solar radiation were collected to prepare their daily summary for the period from May to October in 2020 during which both satellite products for solar radiation were available. Root mean square error (RMSE) and its normalized error (NRMSE) were determined for daily sum of solar radiation. The cumulative values of solar radiation for the study period were also compared to represent the impact of the errors for those products on crop growth simulations. It was found that the data product from the Himawari 8 satellite tended to have smaller values of RMSE and NRMSE than that from the GK-2A satellite. The Himawari 8 satellite product had smaller errors at a large number of weather stations when the cumulative solar radiation was compared with the measurements. This suggests that the use of Himawari 8 satellite products would cause less uncertainty than that of GK2-A products for estimation of crop yield. This merits further studies to apply the Himawari 8 satellites to estimation of solar power generation as well as crop yield under an agrivoltaic system.

• Asian-Australasian Journal of Animal Sciences
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• v.21 no.3
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• pp.392-403
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• 2008

Four ruminally fistulated Hanwoo steers were used to determine the effects of level and degradability of dietary protein on ruminal fermentation, blood metabolites and concentration of soluble non-ammonia nitrogen (SNAN) in ruminal (RD) and omasal digesta (OD). Experiments were conducted in a $4{\times}4$ Latin square design with a $2{\times}2$ factorial arrangement of treatments. Factors were protein supplements with two ruminal crude protein (CP) degradabilities, corn gluten meal (CGM) that was low in degradability (rumen-degraded protein (RDP), 23.4% CP) or soybean meal (SBM) that was high in degradability (RDP, 62.1% CP), and two feeding levels of CP (12.2 or 15.9% dry matter). Ruminal fermentation rates and plasma metabolite concentrations were determined from the RD collected at 2-h intervals and from the blood taken by jugular puncture, respectively. The SNAN fractions (free amino acid, peptide and soluble protein) in RD and OD collected at 2-h intervals were assessed by ninhydrin assay. Mean ruminal ammonia concentrations were 40.5, 74.8, 103.4 and 127.0 mg/L for low CGM, high CGM, low SBM and high SBM, respectively, with statistically significant differences (p<0.01 for CP level and p<0.001 for CP degradability). Blood urea nitrogen concentrations were increased by high CP level (p<0.001) but unaffected by CP degradability. There was a significant (p<0.05) interaction between level and degradability of CP on blood albumin concentrations. Albumin was decreased to a greater extent by increasing degradability of low CP diets (0.26 g/dl) compared with high CP diets (0.02 g/dl). Concentrations of each SNAN fraction in RD (p<0.01) and OD (p<0.05) for high CP diets were higher than those for low CP diets, except for peptides but concentrations of the sum of peptide and free amino acid in RD and OD were significantly higher (p<0.05) for high CP diets than for low CP diets. Soybean meal diets increased free amino acid and peptide concentrations in both RD (p<0.01) and OD (p<0.05) compared to CGM diets. High level and greater degradability of CP increased (p<0.001) mean concentrations of total SNAN in RD and OD. These results suggest that RDP contents, increased by higher level and degradability of dietary protein, may increase release of free amino acids, peptides and soluble proteins in the rumen and omasum from ruminal degradation and solubilization of dietary proteins. Because SNAN in OD indicates the terminal product of ruminal metabolism, increasing CP level and degradability appears to increase the amount of intestine-available nitrogen in the liquid phase.