• 호남수학학술지
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• 제41권3호
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• pp.651-659
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• 2019

A certain class of polynomials with integer coefficients are considered. If one of the coefficients is large enough in modulus with additional assumptions, then the irreducibility over the field of rationals is proved.

• 대한수학회논문집
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• 제21권3호
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• pp.533-541
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• 2006

We consider a autoregressive moving average process of order p and q with Markov switching coefficients and find sufficient conditions for irreducibility of the process. Identifying small sets is also examined.

• 통합자연과학논문집
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• 제7권4호
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• pp.283-285
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• 2014

We investigate irreducibility of the quadrinomial $F_m(x)=x^{2m}-x^{m+1}-x^{m-1}-1$ where m is an even integer ${\geq}2$ using only basic techniques that can be often used in many classes of polynomials.

• 대한수학회지
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• 제50권6호
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• pp.1213-1222
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• 2013

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group G over a field $\mathbb{K}$ where the group G is a semidirect product of a normal abelian subgroup N and a subgroup H. The main results are proved with the assumption that char $\mathbb{K}$ does not divide |G| but there is no assumption made of $\mathbb{K}$ being algebraically closed.

• 충청수학회지
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• 제24권4호
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• pp.713-724
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• 2011

We investigate the irreducibility of iterate and composite polynomials. For this purpose discriminant and resultant are computed by means of the norm function.

• 대한수학회보
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• 제51권6호
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• pp.1615-1623
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• 2014

Let $G{\leq}S_n$ and ${\chi}$ be any nonzero complex valued function on G. We first study the irreducibility of the generalized matrix polynomial $d^G_{\chi}(X)$, where $X=(x_{ij})$ is an n-by-n matrix whose entries are $n^2$ commuting independent indeterminates over $\mathbb{C}$. In particular, we show that if $\mathcal{X}$ is an irreducible character of G, then $d^G_{\chi}(X)$ is an irreducible polynomial, where either $G=S_n$ or $G=A_n$ and $n{\neq}2$. We then give a necessary and sufficient condition for the equality of two generalized matrix functions on the set of the so-called ${\chi}$-singular (${\chi}$-nonsingular) matrices.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.1-12
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• 1994

We consider the markov process ${X_n}$ on R which is genereated by $X_{n+1} = f(X_n) + \epsilon_{n+1}$. Sufficient conditions for irreducibility and geometric ergodicity are obtained for such Markov processes. In additions, when ${X_n}$ is geometrically ergodic, the functional central limit theorem is proved for every bounded functions on R.

• 대한수학회보
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• 제53권3호
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• pp.833-842
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• 2016

For a certain kind of reciprocal polynomials $P(x),Q(x){\in}{\mathbb{Z}}[x]$, their sums are considered. We demonstrate that the Mahler measure of polynomials plays a role to prove the irreducibility of the sums over the field of rationals.

• Journal of the Korean Data and Information Science Society
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• 제18권1호
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• pp.211-218
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• 2007

Nonlinear ARMA model $X_n\;=\;h(X_{n-1},{\cdots},X_{n-p},e_{n-1},{\cdots},e_{n-p})+e_n$ is considered and easy-to-check sufficient condition for strict stationarity of {$X_n$} without some irreducibility or continuity assumption is given. Threshold ARMA(p, q) and momentum threshold ARMA(p, q) models are examined as special cases.

• 대한수학회지
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• 제48권5호
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• pp.1065-1081
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• 2011

For any field F, a polynomial f $\in$ F[$x_1,x_2,{\ldots},x_k$] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F, i.e., irreducible over every algebraic extension of F. We present some results giving new integrally indecomposable classes of polygons. Consequently, we have some criteria giving many types of absolutely irreducible bivariate polynomials over arbitrary fields.