• Journal of the Korean Mathematical Society
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• v.60 no.2
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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.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.421-428
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• 2013

We observe the basic structure of the products of coefficients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result for semi-Armendariz rings. We introduce the concept of ${\alpha}$-skew n-semi-Armendariz ring, where ${\alpha}$ is a ring endomorphism. We prove that a ring R is ${\alpha}$-rigid if and only if the n by n upper triangular matrix ring over R is $\bar{\alpha}$-skew n-semi-Armendariz. This result are applicable to several known results.

• Kyungpook Mathematical Journal
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• v.62 no.1
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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.

• Honam Mathematical Journal
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• v.31 no.4
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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].

• Journal of the Korean Chemical Society
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• v.36 no.3
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• pp.405-411
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• 1992

The substitution reaction and structrue of products obtained from the reaction of Equatorial-Skew-[Co(TRDTRA)($OH_2$)] (TRDTRA = trimethylenediaminetriacetate) with $CN^-, NO^{-}_{2}$ and $NCS^-$ ions have been investigated by means of electronic absorption spectroscopy and theoretical calculation based on the Yamatera's theory. According to kinetic data, the substitution reaction order for the complexes such as $CN^-, NO^{-}_{2}$ and $NCS^-$ was the first order, respectively, and overall reaction order was second order. It has been determined that the structure of products having $CN^{-} and NO^{-}_{2}$ ions was Polar-Chair type complexes which were accompanying with isomerization and having $NCS^-$ ion was Equatorial-Skew type complex which was not accompanying with isomerization.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1251-1267
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• 2014

The semicommutative property of rings was introduced initially by Bell, and has done important roles in noncommutative ring theory. This concept was generalized to one of nil-semicommutative by Chen. We first study some basic properties of nil-semicommutative rings. We next investigate the structure of Ore extensions when upper nilradicals are ${\sigma}$-rigid ${\delta}$-ideals, examining the nil-semicommutative ring property of Ore extensions and skew power series rings, where ${\sigma}$ is a ring endomorphism and ${\delta}$ is a ${\sigma}$-derivation.

• Proceedings of the KSRS Conference
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• 2004.10a
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• pp.216-219
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• 2004

In this study, the concept and techniques to generate the level lA, lB and 2A image products have been reviewed. In particular, radiometric and geometric corrections and bands registration used to generate level lA, lB and 2A products have been focused in this study. Radiometric correction is performed to take into account radiometric gain and offset calculated by compensating the detector response non-uniformity. And, in order to compensate satellite altitude, attitude, skew effects, earth rotation and earth curvature, some geometric parameters for geometric corrections are computed and applied. Bands registration process using the matching function between a geometry, which is called 'reference geometry', and another one which is corresponds to the image to be registered is applied to images in case of multi-spectral imaging mode. In order to generate level-lA image products, a simple radiometric processing is applied to a level-0 image. Level-lB image has the same radiometry correction as a level-lA image, but is also issued from some geometric corrections in order to compensate skew effects, Earth rotation effects and spectral misregistration. Level-2A image is generated using some geo-referencing parameters computed by ephemeris data, orbit attitudes and sensor angles. Level lA image is tested by visual analysis. The difference between distances calculated level 1 B image and distances of real coordinate is tested. Level 2A image is tested Using checking points.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.459-460
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• 2012

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.373-382
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• 2006

In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}={f_i}\;\infty\limits_{i=1}$on circles is $h(f_{1,\infty})={\frac{lim\;sup}{n{\rightarrow}\infty}}\;\frac 1 n \;log\;{\prod}\limits_{i=1}^n|deg\;f_i|$. As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism f on a smooth 2-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.