• Bulletin of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.227-234
• /
• 1998

Criteria are derived for the existence of a unique invariant oprobability distribution of a class of nonlinear pth-order autoregressive oprocesses, which reformulate those of Tweedie's. It will be shown that the criteria in this paper are easily applicable to the linear or piecewise linear case so that some of the earlier results are immediate consequences of our main results.

• The Pure and Applied Mathematics
• /
• v.19 no.2
• /
• pp.199-209
• /
• 2012

For a locally compact higher rank graph ${\Lambda}$, we construct a two-sided path space ${\Lambda}^{\Delta}$ with shift homeomorphism ${\sigma}$ and its corresponding path groupoid ${\Gamma}$. Then we find equivalent conditions of aperiodicity, cofinality and irreducibility of ${\Lambda}$ in (${\Lambda}^{\Delta}$, ${\sigma}$), ${\Gamma}$, and the groupoid algebra $C^*({\Gamma})$.

• Journal of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.101-112
• /
• 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
• /
• v.5 no.1
• /
• pp.195-201
• /
• 1992

Let G(A) denote a generalized Kac Moody Lie algebra associated to a symmetrizable generalized Cartan matrix A. In this paper, we study on representations of G(A). Highest weight modules and the category O are described. In the main theorem we show that some G(A) modules from the category O are completely reducible. Also a criterion for irreducibility of highest weight modules is obtained. This was proved in [3] for the case of Kac Moody Lie algebras.

• Honam Mathematical Journal
• /
• v.29 no.3
• /
• pp.351-366
• /
• 2007

Let R be a commutative ring and let M be an R-module. Let X = Spec(M) be the prime spectrum of M with Zariski topology. Our main purpose in this paper is to specify the topological dimensions of X, where X is a Noetherian topological space, and compare them with those of topological dimensions of $Supp_{R}$(M). Also we will give a characterization for the irreducibility of X and we obtain some related results.

• Journal of the Korean Data and Information Science Society
• /
• v.22 no.6
• /
• pp.1233-1240
• /
• 2011

An augmented asymmetric power GARCH(p, q) process is considered and conditions for stationarity, geometric ergodicity and ${\beta}$-mixing property with exponential decay rate are obtained.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.429-437
• /
• 2019

Dilcher and Stolarsky [1] recently studied a sequence resembling the Chebyshev polynomials of the first kind. In this paper, we follow their some research directions to the Chebyshev polynomials of the second kind. More specifically, we consider a sequence resembling the Chebyshev polynomials of the second kind in two different ways, and investigate its properties including relations between this sequence and the sequence studied in [1], zero distribution and the irreducibility.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1129-1147
• /
• 2021

This paper aims to analyze the PTG module for the finite-dimensional odd Contact superalgebra over a field of prime characteristic by using the method of Hu and Shen's mixed product realization. The general acting law in odd Contact superalgebra is obtained. In addition, the structure and irreducibility of graded module for odd Contact superalgebra are discussed.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.83-96
• /
• 2013

Let K be a number field and fix a prime number $p$. For any set S of primes of K, we here say that an elliptic curve E over K has S-reduction if E has bad reduction only at the primes of S. There exists the set $B_{K,p}$ of primes of K satisfying that any elliptic curve over K with $B_{K,p}$-reduction has no $p$-torsion points under certain conditions. The first aim of this paper is to construct elliptic curves over K with $B_{K,p}$-reduction and a $p$-torsion point. The action of the absolute Galois group on the $p$-torsion subgroup of E gives its associated Galois representation $\bar{\rho}_{E,p}$ modulo $p$. We also study the irreducibility and surjectivity of $\bar{\rho}_{E,p}$ for semistable elliptic curves with $B_{K,p}$-reduction.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.777-788
• /
• 2018

A simple poset is a poset whose linear discrepancy increases if any relation of the poset is removed. In this paper, we investigate more important properties of simple posets such as its width and height which help to construct concrete simple poset of linear discrepancy l. The simplicity of a poset is similar to the ld-irreducibility of a poset. Hence, we investigate which posets are both simple and ld-irreducible. Using these properties, we characterize n-posets of linear discrepancy n - k for k = 2, 3, and, lastly, we also characterize a poset of linear discrepancy 3 with simple posets and ld-irreducible posets.