• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.651-655
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• 1996

Lagrange's famous Four Square Theorem [L] says that every positive integer can be represented by the sum of four squares. This marvelous theorem was generalized by Mordell [M1] and Ko [K1] as follows : every positive definite integral quadratic form of two, three, four, and five variables is represented by the sum of five, six, seven, and eight squares, respectively. And they tried to extend this to positive definite integral quadratic forms of six or more variables.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.593-602
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• 2021

We use a kind of modified Hurwitz class numbers to express the number of representing a positive integer by some ternary quadratic forms such as the sum of three squares, and the Fourier coefficients of weight 2 modular forms of prime level with trivial character.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.109-124
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• 2009

Based on the observed data for Clarithromycin released, three commonly used inflow models: the power, the exponential, and the logarithmic models are considered. Among them, the power model is used most in practice for simplicity. Using the numerical parameter estimation techniques, the parameters appeared in the model equations are estimated. Through the numerical estimation results using the several experimental data sets, the exponential model turns out to be best among the three models. More specifically, the sum of squares of absolute errors and the sum of squares of relative errors for the exponential model are reduced by 80-95 % for the experimental data sets and 60-90 % for the noise added data sets compared with those for the power and logarithmic models. A typical experimental data set is used in this paper to show the estimation method and its numerical results. The proposed numerical method and its algorithm are designed for estimating the parameters appeared in the model differential equations for which the exact form of the solution is unknown in general. The methodology developed can be applied to more general cases such as the nonlinear ordinary differential equations or the partial differential equations.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.37-49
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• 2004

We are interested in the problem of fitting a sphere to a set of data points in the three dimensional Euclidean space. In Spath [6] a descent algorithm already have been given to find the sphere of best fit in least squares sense of minimizing the orthogonal distances to the given data points. In this paper we present another new algorithm which computes a parametric represented sphere in order to minimize the sum of the squares of the distances to the given points. For any choice of initial approximations our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.941-947
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• 2009

Let q be a power of 16. Every polynomial $P\in\mathbb{F}_q$[t] is a strict sum $P=A^2+A+B^3+C^3+D^3+E^3$. The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial $Q\in\mathbb{F}_q$[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: $Q=F^2+F+tG^2$. This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation $Q=F^2$+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.

• Korea journal of population studies
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• v.28 no.2
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• pp.131-164
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• 2005

The central focus of this research paper is to explore the recent structural core empirical unemployment reason of IT new professional manpower who graduated in higher education level in Korea. The final goal of this issue is to estimate and analyze rambling impediment in IT manpower labor market between 26 detail occupations and between detail occupations and 3 educational levels of new graduates and entrants who entered in IT 6 occupational groups composing 26 particular occupations. This study uses the 2004 data published by the Ministry of ICT and relies upon both one-way analysis of variance and two-way analysis variance to tackle the issue. According to the ANOVA results, 2 main points were delineated In the one-way analysis of variance method. the total sum of squares (SST) is decomposed into two major components: within sum of squares (SSW) (6 detail occupations, 85%) and between sum of squares (SSG) (26 detail occupation, 15%) The other major finding is that total sum of squares (SST) is decomposed into three major components: between detail occupations (SSG) (19.3%), between educations (SSB) and errors (SSE) (56%) in IT SIW development design group.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.25
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• pp.103-113
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• 1992

This paper is to study the various diagnostic measures for detecting outliers and influential cases in linear regression. In this paper we review the most common diagnostic measures and show the inter-relationships the exist among them. Based on the PRESS(Predicted REsidual Sum of Squares ) offered by Allen(1974) as a criterion for model selection, we propose three measures for detecting outliers and influential cases. Examples are given illustrating various diagnostic measures including Proposed measures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1426-1435
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• 2003

Design goal is to find the one that has the highest probability of success and the smallest variation. A robustness index has been proposed to satisfy these conditions. The two-step optimization process of the target problem requires a scaling factor. The search process of a scaling factor is replaced with the making of the decoupled design between the mean and the standard deviation. The decoupled design matrix is formed from the sensitivity or the sum of squares. After establishing the design matrix, the robust design process has a new three-step one. The first is ″reduce variability,″ the second is ″make the candidate designs that satisfy constraints and move the mean on the target,″ and the final is ″select the best robust design using the proposed robustness index.″ The robust design process is verified by three examples and the results using the robustness index are compared with those of other indices.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.566-571
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• 2009

A calibration method for multiple sets of stereo vision cameras is proposed. To measure the three-dimensional shape of a very long object, measuring the object at different viewpoints and registration of the data are necessary. In this study, two lasers beams generate two strings of calibration targets, which form straight lines in the world coordinate system. An evaluation function is defined to calculate the sum of the squares of the distances between each transformed target and the fitted line representing the laser beam to each target, and the distances between points appearing in the data sets of two adjacent viewpoints. The calculation process for the approximation method based on data linearity is presented. The experimental results show the effectiveness of the method.