• East Asian mathematical journal
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• v.5 no.1
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• International Commerce and Information Review
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• v.9 no.2
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• pp.65-86
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• 2007

This paper reviews the properties and application methods of widely used types of risk measures, identifies the rationale and business-side effects of hedging, derives the theoretical formula of optimal hedging ratio, and analyzes the various functional aspects of VaR(Value-at-risk) as a risk measure and a hedging tool. Especially this paper focuses on the characteristics of VaR compared with other risk measures in terms of their own principal determinants and identifies its stronger aspects in the dimension of hedging strategy tools. As well, this paper provides the detailed processes deriving the optimal hedge ratios based on the distributional parameters and risk factors. In addition, this paper presents the detailed and substantial processes of estimating the minimum variance hedge ratio and minimum-VaR hedge ratio using the actual data and shows that the minimum variance hedge ratio proves helpful for many cases although it is not appropriate for the non-linear portfolio including the option contracts. We demonstrate the trade-off relationship between the minimum variance hedge strategy and the minimum-VaR hedge strategy in their hedging costs and performances through calculation of the respective VaRs and variances of unhedged and hedged portfolios and the optimal hedge ratio and hedging effectiveness values for the given long position in US Dollar with the short position in Euro.

• Journal of Sasang Constitutional Medicine
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• v.8 no.1
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• pp.101-186
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• 1996

The clinical application of constitutional Diagnosis is the most important part of Sasang constitutional medicine. It has been studied in various way. However, the study of morphologic characteristics on the face is applied for the first time. For quantitative analysis of the correlation between the sasang constitution and the shape of the face, the head-facial part of 170 cases were measured by Martin's measurement and analysis of a) the measurement value of height and the component ratio from the Gnathion to each part of face by constitution. b) the measurement value of depth and the component ratio from T-projected to each part of the face by constitution. c) the measurement value of breadth and component ratio between each parts of the facial breadth by constitution. d) the ratio of square on every part of face by constitution. e) the characteristics on each part of the face by constitution. f) the contour line of the forehead. g) the result of discriminant analysis about the constitution. Authors obtained the results from the study as follows; 1. The characteristics of Taeum-IN (1) The measurement value of Height, Breadth, T-Projected had a tendency to maximum value in general. (2) The value of lower opthal height and the square of lower opthal part was maximum. (3) The value of Pronasal T-projected length and Subnasal T-projected length was minimum, so Taeum-In has characteristics of depression in middle face, nasal part. (4) In the ratio of Breadth, T-Projected, T-Projected was minimum. (5) It was maximum that the square of nose, Alare, Middle face, Lower face and it was minimum that the square of eye. The square of nose, Alare, Middle facc, Lower face was maximum and the square of eye was minimum. (6) The curvature of the eyebrow was minimum. (7) The projection of jaw (Pogonion T-projection length) was maximum. (8) The breadth of eye was minimum. (9) There was a tendency that the projection of the forehead to the right in general. 2. The characteristics of Soeum-In (1) In all cases of projected length the measurement value was minimum. (2) The value of lower opthal height and the square of lower opthal part was minimum. (3) By the Pupulare T-projected length, the value of Pronasal T-projected length and Subnasal T-projected length was minimum, so the Soeum In's face shape is flat. (4) The square of eye, mouth, forehead was maximum and the square of nose, Alare, Middle face, Lower face was minimum. (5) The curvature of the eyebrow was maximum. (6) The projection of mouth was minimum. (7) The jaw was flat. (8) The breadth of eye was maximum. (9) There was a tendency that the projection of the forehead to the left in general. 3. The characteristics of Soyang-In. (1) In most cases of 고경 length the measurement value was minimum. (2) By the Pupulare T-projected length, each ratio of projected length was maximum, so the Soyang-In's face shape has many protrusions (3) In the ratio of Breadth, T-Projected, T-Projected was maximum. (4) The square of mouth was minimum. (5) The inclination of the forehead was minimum. (6) The projection of mouth was maximum. (7) The breadth of eye was minimum. (8) There was a tendency that the projection of the forehead to the left in general. (9) The middle face was protruded. 4. Discriminant about the constitution. According to the result of discriminant, the accuracy probability of discriminant was 85.58% in total and Taeum-In was 90.5%, Soeum-In was 70.8%, Soyang-In was 89.5%. The accuracy probability of discriminant about 3 constitutional group increased by 49.03% than the accident probility 36.55% 5. Suggestion (1) The study which gather and analysis the data should be continued. (2) The study which subdivide the characteristics of each part of the face by the constitution should be continued. (3) The analysis method about Moire should be supplement. (4) The study about the morphologic characteristics of the whole body should be continued. (5) Computer program of constitution diagnosis should be developed. (6) To increase utility of this method, the measurement should be automation.

• Research in Mathematical Education
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• v.27 no.1
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• pp.75-92
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• 2024

Mathematical argument has been given much attention in the research literature as a mediating construct between reasoning and proof. However, there have been relatively less efforts made in the research that examined the nature of empirical arguments represented in textbooks and how students perceive them as proofs. Cases of point include Intermediate Value Theorem [IVT] and Maximum-Minimum theorem [MMT] in grade 11 in Korea. In this study, using Toulmin's framework (1958), the author analyzed the substance of the empirical arguments provided for both MMT and IVT to draw comparisons between the nature of datum, claims, and warrants among empirical arguments offered in textbooks. Also, an online survey was administered to learn about how students view as proofs the empirical arguments provided for MMT and IVT. Results indicate that nearly half of students tended to accept the empirical arguments as proofs. Implications are discussed to suggest alternative approaches for teaching MMT and IVT.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.229-241
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• 1997

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.8
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• pp.644-649
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• 2013

For effective DC-free coding in the optical storage systems, the Guided Scrambling algorithm is widely used. To reduce digital discrepancy of the coded sequence, functions of digital sum value (DSV) are used as criteria to choose the best candidate. Among these criteria, the minimum digital sum value (MDSV), minium squared weight (MSW), and minimum threshold overrun (MTO) are popular methods for effective DC-suppression. In this paper, we formulate integer programming models that are equivalent to MDSV, MSW, and MTO GS coding. Incorporating the MDSV integer programming model in MaxMin setting, we develop an integer programming model that computes the worst case MDSV bound given scrambling polynomial and control bit size. In the simulation, we compared the worst case MDSV bound for different scrambling polynomial and control bit sizes. We find that careful selection of scrambling polynomial and control bit size are important factor to guarantee the worst case MDSV performance.

• Atmosphere
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• v.26 no.4
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• pp.697-709
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• 2016

This study estimates and evaluates the extreme value of 30 m-resolution daily maximum and minimum temperatures over South Korea, using inverse distance weighting (IDW), parameter-elevation regression on independent slopes model (PRISM) and generalized extreme value (GEV) method. The three experiments are designed and performed to find the optimal estimation strategy to obtain extreme value. First experiment (EXP1) applies GEV firstly to automated surface observing system (ASOS) to estimate extreme value and then applies IDW to produce high-resolution extreme values. Second experiment (EXP2) is same as EXP1, but using PRISM to make the high-resolution extreme value instead of IDW. Third experiment (EXP3) firstly applies PRISM to ASOS to produce the high-resolution temperature field, and then applies GEV method to make high resolution extreme value data. By comparing these 3 experiments with extreme values obtained from observation data, we find that EXP3 shows the best performance to estimate extreme values of maximum and minimum temperatures, followed by EXP1 and EXP2. It is revealed that EXP1 and EXP2 have a limitation to estimate the extreme value at each grid point correctly because the extreme values of these experiments with 30 m-resolution are calculated from only 60 extreme values obtained from ASOS. On the other hand, the extreme value of EXP3 is similar to observation compared to others, since EXP3 produces 30m-resolution daily temperature through PRISM, and then applies GEV to that result at each grid point. This result indicates that the quality of statistically produced high-resolution extreme values which are estimated from observation data is different depending on the combination and procedure order of statistical methods.

• Journal of the Korea Institute of Military Science and Technology
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• v.2 no.2
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• pp.271-278
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• 1999

An alternative panel flutter approach utilizing minimum angle is presented. The minimum angle is the lowest value among the angles between modes i and j at a certain pressure condition. This method utilizes eigenvectors rather than eigenvalues. Cross-ply composite plates are considered in this study. A remarkable result of this investigation is that the angle always dropped gradually to zero for all presented examples

• Journal of The Korea Institute of Healthcare Architecture
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• v.23 no.1
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• pp.15-24
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• 2017

Purpose: Korea is expected to enter an aged society in 2018 and then a super-aged society in early 2025. The country's aging is progressing faster than any other country in the world. However, the foundation of the elderly friendly industry is weak, and measures at the government level are urgently needed. Especially, housing problems of the elderly are one of the most urgent measures to be taken. Korea does not have the minimum residential area standard for the elderly, and the current general minimum residential area standard is based on the survey of the housing situation without scientific evidence. Therefore, both standards need to be revised as soon as possible based on scientific evidence. Methods: The minimum residential area standard has been calculated following Karl H. E. Kroemer's Min or Max design also being called as-single cut and dual cut theory- as the maximum population value and minimum population value theory of Ernest J. McCormick. Therefore there is a need for a formula made using a few key factors, such as corresponding dimension, practical dimension, clearance, spare dimension, integrated dimension. These elements can be defined and used as formulas to calculate minimum residential area standards. Results: Assuming the results of the spatial variability in this study showed that it is possible to raise the standard of living in a terms of sustainable minimum size for the young, old and all residents. Implications: The government should set a minimum residential area standard with scientific grounds and set up a policy improving the life of people who live in an needy residential environment.

• Steel and Composite Structures
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• v.37 no.4
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• pp.463-479
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• 2020

Currently, there are many lateral resisting systems utilized in resisting lateral loads being produced in an earthquake. Such systems can significantly reduce the roof's displacement when placed at an optimum location. Since in the design of tall buildings, the minimum distance between adjacent buildings is important. In this paper, the critical excitation method is used to determine the best location of the belt truss system while calculating the minimum required distance between two adjacent buildings. For this purpose, the belt truss system is placed at a specific story. Then the critical earthquakes are computed so that the considered constraints are satisfied, and the value of roof displacement is maximized. This procedure is repeated for all stories; i.e., for each, a critical acceleration is computed. From this set of computed roof displacement values, the story with the least displacement is selected as the best location for the belt truss system. Numerical studies demonstrate that absolute roof displacements induced through critical accelerations range between 5.36 to 1.95 times of the San Fernando earthquake for the first example and 7.67 to 1.22 times of the San Fernando earthquake for the second example. This method can also be used to determine the minimum required distance between two adjacent buildings to eliminate the pounding effects. For this purpose, this value is computed based on different standard codes and compared with the results of the critical excitation method to show the ability of the proposed method.