• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1185-1189
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• 2008

In this paper we show that the polynomial of degree 9 called generalized algebraicity is a polynomial identity for $3{\times}3$ matrices. ([5])

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.201-209
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• 2009

In this paper, we prove the stability of the functional equation $$\sum_{i=0}^3_3C_i(-1)^{3-i}f(ix+y)=0$$ in the sense of Th.M.Rassias on the punctured domain. Also, we investigate the superstability of the functional equation.

• Journal of the Korea institute for structural maintenance and inspection
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• v.10 no.3
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• pp.165-175
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• 2006

To analyze the deformation and failure of slopes, generally, two types of model, Polynomial model and Growth model, are applied. These two models are focused on the behavior of the slope by time. Therefore, this research is more focused on predicting of slope failure than analyzing the slope behavior by time. Generally, Growth model is used to analyze the soil slope, to the contrary, Polynomial model is used for rock slope. However, 3-degree polynomial($y=ax^3+bx^2+cx+d$) is suggested to combine two models in this research. The main trait of this model is having an asymptote. The fields to adopt this model are Gosujae Danyang(soil slope) and Youngduk slope(rock slope), which are the cut-slope near national road. Data from Gosujae are shown the failure traits of soil slope, to the contrary, those of Youngduk slope are shown the traits of rock slope. From the real-time monitoring data of the slope, 3-degree polynomial is proved as excellent system to analyze the failure and behavior of slope. In case of Polynomial model, even if the order of polynomials is increased, the $R^2$ value and shape of the curve-fitted graph is almost the same.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.165-182
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• 2014

After algebraic expressions for the roots of 3rd and 4th degree polynomial equations were given in the mid 16th century, seeking such a formula for the 5th and greater degree equations had been one main problem for algebraists for almost 200 years. Lagrange made careful and thorough investigation of various solving methods for equations with the purpose of finding a principle which could be applicable to general equations. In the process of doing this, he found a relation between the roots of the original equation and its auxiliary equation using permutations of the roots. Lagrange's ingenious idea of using permutations of roots of the original equation is regarded as the key factor of the Abel's proof of unsolvability by radicals of general 5th degree equations and of Galois' theory as well. This paper intends to examine Lagrange's contribution in the theory of polynomial equations, providing a detailed analysis of various solving methods of Lagrange and others before him.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.101-112
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• 2010

In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. In this paper, we consider the polynomials with coefficients in a field and divisibility of a polynomial by a polynomial with a certain degree is equivalent to the existence of common solution to a system of Diophantine equations. As an application we construct a family of irreducible quartics over $\mathbb{Q}$ which are not of Eisenstein type.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.887-900
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• 2013

In this paper, we investigate the stability for the functional equation f(3x+y)-3f(2x+y)+3f(x+y)-f(y)=0 in the sense of M. S. Moslehian and Th. M. Rassias.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.269-283
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• 2013

In this paper, we investigate a stability of the functional equation $$\sum^3_{i=0}_3C_i(-1)^{3-i}f(ix+y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.231-236
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• 2018

A polynomial, $p(z)=a_0z^n+a_1z^{n-1}+{\cdots}+a_{n-1}z+a_n$, with real coefficients is called a stable or a Hurwitz polynomial if all its zeros have negative real parts. We show that if a polynomial is a Hurwitz polynomial then so is the polynomial $q(z)=a_nz^n+a_{n-1}z^{n-1}+{\cdots}+a_1z+a_0$ (with coefficients in reversed order). As consequences, we give simple ratio checking inequalities that would determine unstability of a polynomial of degree 5 or more and extend conditions to get some previously known results.

• Journal of Power System Engineering
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• v.3 no.4
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• pp.69-78
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• 1999

In the single-input and single-output system, the parameter of plant is scalar polynomial, but in the multiple input and multiple output, it accompanies, being matrix polynomial, the consideration of observable controlability index or problems non-commutation in matrix polynomial as well as degree, and it is more complex to deal with. Therefore, it is thought that a full research on the single-input and single-output system is not sufficient. This paper proposes that problems of minimum variance self-tuning regulator by using numerical calculation example of multivariable system and pole assignment self-tuning regulator.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.