• Korean Journal of Mathematics
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• v.28 no.4
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• pp.649-671
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• 2020

In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on ℝd, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on ℝd in the W-invariant case.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.751-767
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• 2022

This paper deals with the Paneitz-Branson operator in compact Riemannian manifolds with negative Yamabe invariant. We start off by providing a new criterion for the positivity of the Paneitz-Branson operator when the Yamabe invariant of the manifold is negative. Another result stated in this paper is about the existence of a metric on a manifold of dimension 5 such that the Paneitz-Branson operator has multiple negative eigenvalues. Finally, we provide new inequalities related to the upper bound of the mean value of the Q-curvature.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.3
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• pp.177-182
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• 2013

This paper proposes an input-constrained reference tracking control of a converter model. To this end, first it is shown that the bilinear converter model can be equivalently represented by a linear uncertain model belonging to a polytopic set. Then, an input-constrained tracking control scheme for the linear uncertain model is designed based on recently proposed tracking control scheme. The control scheme yields not only a stabilizing control gain but also a feasible and invariant set for the converter model. Finally, simulation results show that the state trajectory always stays in the feasible and invariant set and that the output tracks the given reference while satisfying the input constraint.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.763-777
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• 2000

We investigate the existence of group invariant solutions of the Emden-Fowler equation, - u=$\mid$x$\mid$$\sigma$$\mid$u$\mid$p-1u in B, u=0 on B and u(gx)=u(x) in B for g G. Here B is the unit ball in n 2, 1$\sigma$ 0 and G is a closed subgrop of the orthogonal group. A soultion of the problem is called a G in variant solution. We prove that there exists a G invariant non-radial solution if and only if G is not transitive on the unit sphere.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1-4
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• 2004

The dual-mode strategy has been adopted in many constrained MPC methods. The size of stabilizable regions of states of MPC methods depends on the size of underlying feasible and positively invariant set and number of control moves. These results, however, could be conservative because the definition of positive invariance does not allow temporal leave of states from the set, In this paper, a concept of periodic invariance is introduced in which states are allowed to leave a set temporarily but return into the set in finite steps. The periodic invariance can defined with respect to sets of different state feedback gains. These facts make it possible for the periodically invariant sets to considerably larger than ordinary invariant sets. The periodic invariance can be defined for systems with polyhedral model uncertainties. We derive a MPC method based on these periodically invariant sets. Some numerical examples are given to show that the use of periodic invariance yields considerably larger stabilizable sets than the case of using ordinary invariance.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.3
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• pp.1155-1172
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• 2015

In this paper, we propose a novel saliency detection framework based on illumination invariant features to improve the accuracy of the saliency detection under the different light conditions. The proposed algorithm is divided into three steps. First, we extract the illuminant invariant features to reduce the effect of the illumination based on the local sensitive histograms. Second, a preliminary saliency map is obtained in the CIE Lab color space. Last, we use the region growing method to fuse the illuminant invariant features and the preliminary saliency map into a new framework. In addition, we integrate the information of spatial distinctness since the saliency objects are usually compact. The experiments on the benchmark dataset show that the proposed saliency detection framework outperforms the state-of-the-art algorithms in terms of different illuminants in the images.

• International Journal of Control, Automation, and Systems
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• v.3 no.3
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• pp.502-507
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• 2005

The dual-mode strategy has been adopted in many constrained MPC (Model Predictive Control) methods. The size of stabilizable regions of states of MPC methods depends on the size of underlying feasible and positively invariant sets and the number of control moves. The results, however, may perhaps be conservative because the definition of positive invariance does not allow temporal departure of states from the set. In this paper, a concept of periodic invariance is introduced in which states are allowed to leave a set temporarily but return into the set in finite time steps. The periodic invariance can be defined with respect to sets of different state feedback gains. These facts make it possible for the periodically invariant sets to be considerably larger than ordinary invariant sets. The periodic invariance can be defined for systems with polyhedral model uncertainties. We derive a MPC method based on these periodically invariant sets. Some numerical examples are given to show that the use of periodic invariance yields considerably larger stabilizable sets than the case of using ordinary invariance.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.7
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• pp.1690-1704
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• 2013

An affine invariant descriptor is proposed, which is able to well represent the affine covariant regions. Estimating main orientation is still problematic in many existing method, such as SIFT (scale invariant feature transform) and SURF (speeded up robust features). Instead of aligning the estimated main orientation, in this paper ellipse orientation is directly used. According to ellipse orientation, affine covariant regions are firstly divided into 4 sub-regions with equal angles. Since affine covariant regions are divided from the ellipse orientation, the divided sub-regions are rotation invariant regardless the rotation, if any, of ellipse. Meanwhile, the affine covariant regions are normalized into a circular region. In the end, the gradients of pixels in the circular region are calculated and the partition-based descriptor is created by using the gradients. Compared with the existing descriptors including MROGH, SIFT, GLOH, PCA-SIFT and spin images, the proposed descriptor demonstrates superior performance according to extensive experiments.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.449-457
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• 2020

We focus on the interations of the weighted Berezin transform T_α on L^p(τ), where τ is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(τ) the space of radial integrable functions played important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of T_α on L¹_R(τ) and observe differences between the iterations of T_α on L1(τ) and L^p(τ) for 1 < p < ∞.