• 한국수학사학회지
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• 제34권2호
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• pp.39-54
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• 2021

One of the topics in school mathematics is the relation between the roots and the coefficients of equations. It deals with the way to find the roots out of the coefficients of equations. One of the concepts derived from the theory of equations is symmetric functions. Symmetry is a kind of functionality of human cognition. It is, in mathematics, geometrically related to the congruence and the similarity of figures, and algebraically a kind of invariants. We look at stories on the appearance of symmetric functions through the development of the theory of equations.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.57-79
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• 2023

We investigate the existence and uniform attractivity of solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. Using the technique of measures of noncompactness and a fixed point theorem of Darbo type we prove the existence of solutions of these equations in the Banach space of continuous and bounded functions on the nonnegative real half axis. Our results extend and improve some known results in the recent literature. An example illustrating the main result is presented in the last section.

• 충청수학회지
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• 제26권4호
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• pp.869-878
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• 2013

We study boundedness of solutions of dynamic equations on time scales by using Lyapunov-type functions.

• 대한수학회지
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• 제48권6호
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• pp.1269-1283
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• 2011

For a class of quasilinear elliptic equations we establish the existence of multiple solutions by variational methods.

• 대한수학회논문집
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• 제24권2호
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• pp.239-245
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• 2009

We estimate the positive real zeros of certain trinomial equations and then deduce zeros bounds of some lacunary polynomials.

• 대한수학회지
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• 제35권4호
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• pp.881-890
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• 1998

Sufficient conditions for forced oscillations of the solutions of impulsive nonlinear parabolic differential-difference equations are obtained.

• 대한수학회지
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• 제38권1호
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• pp.147-162
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• 2001

This paper establishes exponential decay estimates for the solution of a stationary magnetohydrodynamics equations in a semi-infinite pipe flow when homogeneous lateral surface boundary conditions are applied.

• 유기물자원화
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• 제21권2호
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• pp.88-96
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• 2013

본 연구의 목적은 고형폐기물의 메탄발생 특성을 나타내기 위한 1차 반응식과 S형태 식들의 적합성을 평가하는 것이다. S형태 식은 수정 Gompertz와 Logistic 식을 사용하였다. 모델의 적합성을 평가하기 위해 잔차제곱합, 표준제곱근 오차, Akaike's information criterion 등의 통계분석을 실시하였다. AIC (Akaike's information criterion)는 모델의 변수 개수 차이에 따른 모델 적합성을 비교하기 위하여 적용하였다. 1차 반응식의 경우 지체기를 고려하지 않을 때보다 고려하였을 경우 잔차제곱합과 표준제곱근 오차는 감소하는 것으로 나타났다. 그러나 1차 반응식의 경우 S형태 식보다 AIC가 상대적으로 높게 나타났다. 이는 S형태 식이 1차 반응식보다 메탄발생특성을 나타낼 때에 더욱 적합한 것으로 사료된다.

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.185-196
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• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• Nutrition Research and Practice
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• 제16권5호
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• pp.565-576
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• 2022

BACKGROUND/OBJECTIVES: Various accelerometer equations are used to predict energy expenditure (EE). On the other hand, the development of these equations and their validation studies have been conducted primarily without including older adults. This study assessed the accuracy of 8 ActiGraph accelerometer equations to predict the energy cost of walking in older adults. SUBJECTS/METHODS: Thirty-one participants with a mean age of 74.3 ± 3.3 yrs were enrolled in this study (20 men and 11 women). The participants completed 8 walking activities, including 5 treadmill and 3 self-paced walking activities. The EE was measured using a portable indirect calorimeter, with each participant simultaneously wearing the ActiGraph accelerometer. Eight ActiGraph equations were assessed for accuracy by comparing the predicted EE with indirect calorimetry results. RESULTS: All equations resulted in an overall underestimation of the EE across the activities (bias -1 to -1.8 kcal·min^-1 and -0.7 to -1.8 metabolic equivalents [METs]), as well as during treadmill-based (bias -1.5 to -2.9 kcal·min^-1 and -0.9 to -2.1 METs) and self-paced (bias -1.2 to -1.7 kcal·min-1 and -0.2 to -1.3 METs) walking. In addition, there were higher rates of activity intensity misclassifications, particularly among vigorous physical activities. CONCLUSIONS: The ActiGraph equations underestimated the EE for walking activities in older adults. In addition, these equations inaccurately classified the activities based on their intensities. The present study suggests a need to develop ActiGraph equations specific to older adults.