• 호남수학학술지
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• 제44권1호
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• pp.1-16
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• 2022

In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

• 대한수학회보
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• 제40권3호
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• pp.365-371
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• 2003

In this paper, some limit functions of the iteration of the skew product in the stable sets are investigated, which is associated with finitely generated semigroup for the class M, under some additional conditions.

• 대한수학회지
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• 제60권2호
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권1호
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• pp.25-33
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• 2001

Let G be a finite group with a probability measure. We investigate the random walks on G in terms of ergodicity of the associated skew product transformation.

• Communications for Statistical Applications and Methods
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• 제29권3호
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• pp.333-351
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• 2022

The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and Student's-t distributions as special cases. In this work, we propose an EM-type algorithm for computing the maximum likelihood estimates for skew-t linear regression models with censored response. In contrast with previous proposals, this algorithm uses analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of a truncated skew-t distribution, and can be computed using the R library MomTrunc. The standard errors, the prediction of unobserved values of the response and the log-likelihood function are obtained as a by-product. The proposed methodology is illustrated through the analyses of simulated and a real data application on Letter-Name Fluency test in Peruvian students.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.43-55
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• 2022

Let R be a *-ring and n ≥ 1 be an integer. The objective of this paper is to introduce the notion of n-skew centralizing maps on *-rings, and investigate the impact of these maps. In particular, we describe the structure of prime rings with involution '*' such that _*[x, d(x)]_n ∈ Z(R) for all x ∈ R (for n = 1, 2), where d : R → R is a nonzero derivation of R. Among other related results, we also provide two examples to prove that the assumed restrictions on our main results are not superfluous.

• 대한수학회논문집
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• 제37권2호
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• pp.385-397
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• 2022

Let (M, [ , ]) be a finite dimensional Malcev algebra over an algebraically closed field 𝔽 of characteristic 0. We first prove that, (M, [ , ]) (with [M, M] ≠ 0) is simple if and only if ind(M) = 1 (i.e., M admits a unique (up to a scalar multiple) invariant scalar product). Further, we characterize the form of skew-symmetric biderivations on simple Malcev algebras. In particular, we prove that the simple seven dimensional non-Lie Malcev algebra has no nontrivial skew-symmetric biderivation.

• 호남수학학술지
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• 제31권4호
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• pp.591-599
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• 2009

For given ${\alpha},{\omega}\;{\in}\;{\mathbb{R}}$ and ${\beta}$ > 1, let $T_{{\beta},{\alpha},{\omega}}$ be the skew-product transformation on the torus, [0, 1) ${\times}$ [0, 1) defined by (x, y) ${\longmapsto}\;({\beta}x,y+{\alpha}x+{\omega})$ (mod 1). In this paper, we give a criterion of ergodicity and weakly mixing for the transformation $T_{{\beta},{\alpha},{\omega}}$ when the natural extension of the given ${\beta}$-transformation can be viewed as a generalized baker's transformation, i.e., they flatten and stretch and then cut and stack a two-dimensional domain. This is a generalization of theorems in [10].

• 한국정보처리학회논문지
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• 제6권6호
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• pp.1468-1480
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• 1999

데이터베이스 시스템에서 조인 연산은 시스템의 성능에 영향을 주는 가장 복잡하고 소모적인 연산이다. 데이터베이스 시스템의 향상을 위한 많은 병렬 처리 알고리즘들이 제안되었으나 기존의 방법들은 AVS(Attribute Value Skew)와 JPS(Join Product Skew) 등과 같은 데이터 편지를 고려하고 있지 않다. 따라서 데이터 편재의 상황에서 기존의 방법들은 조인 연산 중에 노드들 간의 부하 불균형으로 인하여 그 성능이 급격하게 저하된다. 본 논문에서는 병렬 조인 시에 AVS와 JPS를 고려하여 노드간에 균등하게 부하를 분산하는 방법과 이를 이용한 효율적인 병렬 조인 알고리즘을 제안한다. 제안된 알고리즘은 먼저 기존의 샘플링 방법을 이용하여 조인 연산의 입력과 결과 릴레이션의 데이터 분포를 예측하고, 이를 기반으로 데이터 값에 대한 조인 비용을 산출한다. 그리고 히스토그램 균등화 기법을 이용하여 국부적인 조인 과정에서 노드들 간에 부하 균등을 성취할 수 있도록 데이터를 각 노드에 재 분재한다. 본 논문에서는 성능 평가를 위하여 제안된 알고리즘과 기존의 대표적인 알고리즘들을 위한 모의 실험 모델을 제시하고 모의 실험 결과를 기술한다. 성능 측정 결과 제안된 알고리즘이 기존의 알고리즘들에 비해서 데이터 편재의 상황에서 성능이 우수한 것으로 나타났다.

• 대한수학회보
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• 제48권1호
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• pp.157-167
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• 2011

For a ring endomorphism of a ring R, Krempa called $\alpha$ rigid endomorphism if $a{\alpha}(a)$ = 0 implies a = 0 for a $\in$ R, and Hong et al. called R an $\alpha$-rigid ring if there exists a rigid endomorphism $\alpha$. Due to Rege and Chhawchharia, a ring R is called Armendariz if whenever the product of any two polynomials in R[x] over R is zero, then so is the product of any pair of coefficients from the two polynomials. The Armendariz property of polynomials was extended to one of skew polynomials (i.e., $\alpha$-Armendariz rings and $\alpha$-skew Armendariz rings) by Hong et al. In this paper, we study the relationship between $\alpha$-rigid rings and extended Armendariz rings, and so we get various conditions on the rings which are equivalent to the condition of being an $\alpha$-rigid ring. Several known results relating to extended Armendariz rings can be obtained as corollaries of our results.