• Journal of the Korean Mathematical Society
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• v.59 no.2
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.6
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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.

• IEMEK Journal of Embedded Systems and Applications
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• v.16 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.3
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• pp.300-304
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• 2012

This paper presents a nonlinear observer design method for SOC(state-of-charge) estimation of Lithium polymer battery cell. The dynamic equation of the battery cell is modeled as a simple RC electrical circuit with a nonlinear voltage source and the parameters are obtained via nonlinear optimization. Using the sum of squares decomposition, the observer gain is designed such that the error dynamics is asymptotically stable and the decay rate is below the prescribed value. In order to illustrate the performance of the observer, a computer simulation is performed using the experimental data with the UDDS(urban dynamometer driving schedule) current profile.

• 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.

• Journal of applied mathematics & informatics
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• v.41 no.3
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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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2016.05a
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• pp.490-492
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• 2016

Pancreatic ultrasound imaging is used to diagnose pancreatic hyperplasia, pancreatic steatosis, pancreatic cancer and the like. If the diagnosis of pancreatic steatosis is pancreatic parenchyma echo shades splashes spleen than in the pancreas ultrasound it determines that the fat is deposited. And research on ultrasound imaging of pancreatic cancer but is actively conducted research studies on pancreatic steatosis is insufficient In addition, pancreatic steatosis is often an error in accordance with the diagnostic criteria are vague and subjective diagnosis of the artisan. This study was a quantitative analysis using the feature value extracting a feature of an image extracted by applying a parameter to the algorithm GLCM image of the normal and pancreatic fat. Setting a region of interest ($5{\times}5pixel$) in the mild 89 case, moderate 89 case, severe 89 case, total image 267 case using GLCM algorithm, and using the Autocorrelation, Sum average, Sum of squares, Sum varience 4 kinds parameter in each image It was analyzed.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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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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• 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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.16 no.28
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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.