• Journal for History of Mathematics
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• v.34 no.2
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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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• v.28 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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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.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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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.

• Journal of the Korea Organic Resources Recycling Association
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• v.21 no.2
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• pp.88-96
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• 2013

The objective of this research was to evaluate the suitability of sigmoidal and firstorder kinetic equations for simulating the methane production from solid wastes. The sigmoidal kinetic equations used were modified Gompertz and Logistic equations. Statistical criteria used to evaluate equation performance were analysis of goodness-of-fit (Residual sum of squares, Root mean squared error and Akaike's Information Criterion). Akaike's Information Criterion (AIC) was employed to compare goodness-of-fit of equations with same and different numbers of parameters. RSS and RMSE were decreased for first-order kinetic equation with lag-phase time, compared to the first-order kinetic equation without lag-phase time. However, first-order kinetic equations had relatively higher AIC than the sigmoidal kinetic equations. It seemed that the sigmoidal kinetic equations had better goodness-of-fit than the first-order kinetic equations in order to simulate the methane production.

• Kyungpook Mathematical Journal
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• v.28 no.2
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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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• v.16 no.5
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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.