• 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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-46
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• 2023

Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant (α₁, α₂)-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit (α₁, α₂)-metrics on spheres. We mainly show that a Sp(n + 1)-invariant (α₁, α2)-metric on S⁴ⁿ⁺³ = Sp(n + 1)/Sp(n) is geodesic orbit with respect to Sp(n + 1) if and only if it is Sp(n + 1)Sp(1)-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.339-348
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• 2023

It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R₁ × R₂, where R₁, R₂ are rings which satisfy R₁ is a semi-simple Artinian ring and R₂ is square-free as a right R₂-module and all idempotents of R₂ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.275-296
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• 2017

All rings considered here are commutative rings with identity and all modules considered here are unital left modules. A submodule N of an R-module M is said to be extended to M if $N=aM$ for some ideal a of R and it is said to be fully invariant if ${\varphi}(L){\subseteq}L$ for every ${\varphi}{\in}End(M)$. An R-module M is called a [resp., fully invariant] multiplication module if every [resp., fully invariant] submodule is extended to M. The class of fully invariant multiplication modules is bigger than the class of multiplication modules. We deal with prime submodules and associated prime submodules of fully invariant multiplication modules. In particular, when M is a nonzero faithful multiplication module over a Noetherian ring, we characterize the zero-divisors of M in terms of the associated prime submodules, and we show that the set Aps(M) of associated prime submodules of M determines the set $Zdv_M(M)$ of zero-dvisors of M and the support Supp(M) of M.

• Journal of the HCI Society of Korea
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• v.1 no.2
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• pp.27-33
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• 2006

This paper presents a new approach to translation and rotation invariant feature extraction for image texture retrieval. For the rotation invariant feature extraction, we invent angular projection along angular frequency in Polar coordinate system. The translation and rotation invariant feature vector for representing texture images is constructed by the averaged magnitude and the standard deviations of the magnitude of the Fourier transform spectrum obtained by the proposed angular projection. In order to easily implement the angular projection, the Radon transform is employed to obtain the Fourier transform spectrum of images in the Polar coordinate system. Then, angular projection is applied to extract the feature vector. We present our experimental results to show the robustness against the image rotation and the discriminatory capability for different texture images using MPEG-7 data set. Our Experiment result shows that the proposed rotation and translation invariant feature vector is effective in retrieval performance for the texture images with homogeneity, isotropy and local directionality.

• Journal of Digital Contents Society
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• v.19 no.9
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• pp.1787-1793
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• 2018

Shadow is a common phenomenon observed in natural scenes, but it has a negative influence on image analysis such as object recognition, feature detection and scene analysis. Therefore, the process of detecting and removing shadows included in digital images must be considered as a pre-processing process of image analysis. In this paper, the existing methods for acquiring 1D invariant images, one of the feature elements for detecting and removing shadows contained in a single natural image, are described, and a method for obtaining 1D invariant images based on linear regression has been proposed. The proposed method calculates the log of the band-ratio between each channel of the RGB color image, and obtains the grayscale image line by linear regression. The final 1D invariant images were obtained by projecting the log image of the band-ratio onto the estimated grayscale image line. Experimental results show that the proposed method has lower computational complexity than the existing projection method using entropy minimization, and shadow detection and removal based on 1D invariant images are performed effectively.

• Journal of Broadcast Engineering
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• v.17 no.1
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• pp.26-36
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• 2012

Since shape of an object in an image carries important information in contents based image retrieval (CBIR), many shape description methods have been proposed to retrieve images using shape information. Among the existing shape based image retrieval methods, the method which employs invariant Zernike moment desciptor (IZMD) showed better performance compared to other methods which employ traditional Zernike moments descriptor in CBIR. In this paper, we propose a new image retrieval method which applies invariant angular radial transform descriptor (IARTD) to obtain higher performance than the method which employs IZMD in CBIR. IARTD is a rotationally invariant feature which consists of magnitudes and alligned phases of angular radial transform coefficients. To produce rotationally invariant phase coefficients, a phase correction scheme is performed while extracting the IARTD. The distance between two IARTDs is defined by combining the differences of the magnitudes and the aligned phases. Through the experiment using MPEG-7 shape dataset, the average bull's eye performance (BEP) of the proposed method is 0.5806 while the average BEPs of the exsiting methods which employ IZMD and traditional ART are 0.4234 and 0.3574, respectively.

• East Asian mathematical journal
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• v.19 no.1
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• pp.121-131
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• 2003

We extend the characterization for the analytic Besov space obtained by Nowak to the invariant harmonic Besov space.

• Journal of KIISE:Software and Applications
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• v.30 no.3_4
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• pp.212-218
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• 2003

State invariant is a property that holds in every reachable state. It can be used not only in understanding and analyzing complex software systems, but it can also be used for system verifications such as checking safety, liveness, and consistency. For these reasons, there are many vital researches for deriving state invariant from finite state machine models. In previous works every reachable state is to be considered to generate state invariant. Thus it is likely to be too complex for the user to understand. This paper seeks to answer the question `how to simplify state invariant\ulcorner`. Since the complexity of state invariant is strongly dependent upon the size of states to be considered, so the smaller the set of states to be considered is, the shorter the length of state invariant is. For doing so, we let the user focus on some interested scopes rather than a whole state space in a model. Computation Tree Logic(CTL) is used to specify scopes in which he/she is interested. Given a scope in CTL, mixed reachability analysis is used to find out a set of states inside it. Obviously, a set of states calculated in this way is a subset of every reachable state. Therefore, we give a weaker, but comprehensible, state invariant.

• KIPS Transactions on Software and Data Engineering
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• v.4 no.10
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• pp.431-438
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• 2015

In this paper we address the symmetric-invariant problem in boundary image matching. Supporting symmetric transformation is an important factor in boundary image matching to get more intuitive and more accurate matching results. However, the previous boundary image matching handled rotation transformation only without considering symmetric transformation. In this paper, we propose symmetric-invariant boundary image matching which supports the symmetric transformation as well as the rotation transformation. For this, we define the concept of image symmetry and formally prove that rotation-invariant matching of using a symmetric image always returns the same result for every symmetric angle. For efficient symmetric transformation, we also present how to efficiently extract the symmetric time-series from an image boundary. Finally, we formally prove that our symmetric-invariant matching produces the same result for two approaches: one is using the time-series extracted from the symmetric image; another is using the time-series directly obtained from the original image time-series by symmetric transformation. Experimental results show that the proposed symmetric-invariant boundary image matching obtains more accurate and intuitive results than the previous rotation-invariant boundary image matching. These results mean that our symmetric-invariant solution is an excellent approach that solves the image symmetry problem in time-series domain.