• 대한수학회지
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• 제59권2호
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• pp.407-420
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• 2022

It is proved that every sufficiently large even integer can be represented as a sum of two squares of primes, two cubes of primes, two fourth powers of primes and 17 powers of 2.

• 제어로봇시스템학회논문지
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• 제22권6호
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• pp.429-434
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• 2016

This paper introduces a stabilization condition for polynomial fuzzy systems that guarantees $H_{\infty}$ performance under the imperfect premise matching. An $H_{\infty}$ control of polynomial fuzzy systems attenuates the effect of external disturbance. Under the imperfect premise matching, a polynomial fuzzy model and controller do not share the same membership functions. Therefore, a polynomial fuzzy controller has an enhanced design flexibility and inherent robustness to handle parameter uncertainties. In this paper, the stabilization conditions are derived from the polynomial Lyapunov function and numerically solved by the sum-of-squares (SOS) method. A simulation example and comparison of the performance are provided to verify the stability analysis results and demonstrate the effectiveness of the proposed stabilization conditions.

• 대한임베디드공학회논문지
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• 제16권4호
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• pp.119-127
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• 2021

The aim of this paper is to propose a less conservative stabilization condition for leader-following sampled-data control of wheeled mobile robot (WMR) systems by using a clock-dependent Lyapunov function (CDLF) with looped functionals. In the leader-following WMR system, the state and input of the leader robot are measured by digital devices mounted on the following robot, and they are utilized to construct the sampled-data controller of the following robot. To design the sampled-data controller, a stabilization condition is derived by using the CDLF with looped functionals, and formulated in terms of sum of squares (SOS). The considered Lyapunov function is a polynomial form with respect to the clock related to the transmitted sampling instants. As the degree of the Lyapunov function increases, the stabilization condition becomes less conservative. This ensures that the designed controller is able to stabilize the system with a larger maximum sampling interval. The simulation results are provided to demonstrate the effectiveness of the proposed method.

• 한국지능시스템학회논문지
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• 제22권3호
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• pp.300-304
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• 2012

본 논문은 리튬 폴리머 배터리 셀의 잔존충전용량을 추정하기 위한 비선형 관측기의 설계방법을 제시한다. 배터리 셀의 동적방정식은 비선형 전압원을 갖는 간단한 RC 전기회로로 모델하고 파라메터는 비선형 최적화기법을 이용하여 구한다. 관측기 이득은 제곱합 분해기법을 사용하여 오차의 동적방정식이 점근적으로 안정하고 추정오차 감소율이 설계자가 지정한 값 이하가 되도록 설계한다. 관측기의 성능을 입증하기 위하여 UDDS 전류 프로파일을 사용한 실험 데이터를 이용하여 모의실험을 수행하였다.

• 호남수학학술지
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• 제31권1호
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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.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.553-567
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• 2023

There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function E, we obtain the answer to this problem.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2016년도 춘계학술대회
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• pp.490-492
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• 2016

췌장 초음파 영상은 췌장비대증, 췌장지방증, 췌장암 등을 진단하기 위해서 사용된다. 췌장지방증의 진단은 췌장 초음파 영상에서 비장 실질보다 췌장 에코음영이 밝아진 경우 지방이 침착된 것으로 판단한다. 그리고 췌장암의 초음파 영상에 관한 연구는 활발히 이루어 졌지만 췌장 지방증에 관한 연구 사례는 미흡하다. 또한 췌장지방증은 그 진단 기준이 모호하고 숙련자의 주관적인 진단에 따른 오류가 많다. 이에 본 연구에서는 정상과 지방췌장의 영상에 GLCM algorithm을 적용하여 영상의 특징을 추출하고 추출된 특징값을 parameter를 이용하여 정량적인 분석을 하였다. GLCM algorithm을 이용하여 정상 89증례, 중등도 89증례, 고도 89증례 총 영상 267증례에 관심영역($5{\times}5pixel$)을 설정하고, 각 영상에서 Autocorrelation, Sum average, Sum of squares, Sum varience 4가지 parameter를 이용하여 분석하였다.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.865-873
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• 2009

Goodman([3]) presented the question of finding a best possible upper bound of the form $t(G)\;+\;t(G^c)$, where t(G) denote the number of triangles in given graph G. In this, the form of squares of degrees is appeared and many researches have been pursued as an application related to this. Here, we would like to deal with corollary related to the results of Nikiforov([6]).

• Communications for Statistical Applications and Methods
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• 제27권5호
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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.

• 산업경영시스템학회지
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• 제16권28호
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• pp.103-107
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• 1993

This paper studies computer programming for the analysis of data obtained by experiments using Orthogonal Arrays. The following items are considered in the computer programming : * significant digits in the computation of Sum of Squares, Mean Squares and Variance Ratios * containing the necessary F-distribution values in the program. * matching the rules of KS A 0021 and 3251 in the digit treatments etc. The running results of ANOVA Table and Pooled ANOVA Table of a fictitious example is added with the parts of a program. It should be mentioned that the main purpose of this paper is in the arousing of the discussion about significant digits concept in the computer programming for various kinds of Statistical Methods.