• 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.

• The Journal of the Acoustical Society of Korea
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• v.43 no.4
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• pp.466-475
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• 2024

Matched-Field Processing (MFP) is a model-based approach that requires accurate knowledge of the ocean environment and array geometry (e.g., array tilt) to localize underwater acoustic sources. Consequently, it is inherently sensitive to model mismatches. In contrast, the waveguide invariant-based approach (also known as array invariant) offers a simple and robust means for source-range estimation in shallow waters. This approach solely exploits the beam angles and travel times of multiple arrivals separated in the beam-time domain, requiring no modeling of the acoustic fields, unlike MFP. This paper extends the waveguide invariant-based approach to shallow water environments featuring a shallow pit, where the waveguide invariant is not defined due to the complex bathymetry. An in-depth performance analysis is conducted using experimental data and numerical simulations.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.289-294
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• 2009

We show that on a Hermitian surface M, if M is weakly *-Einstein and has J-invariant Ricci tensor then M is Einstein, and vice versa. As a consequence, we obtain that a compact *-Einstein Hermitian surface with J-invariant Ricci tensor is $K{\ddot{a}}hler$. In contrast with the 4- dimensional case, we show that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold which is not weakly *-Einstein.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.309-323
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• 2003

In this paper, We characterize a semi-invariant sub-manifold of codimension 3 satisfying ∇$\varepsilon$A = 0 in a complex projective space CP$\^$n+1/, where ∇$\varepsilon$A is the covariant derivative of the shape operator A in the direction of the distinguished normal with respect to the structure vector field $\varepsilon$.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.213-219
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• 2013

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, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.921-925
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• 2011

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 $D{\equiv}21$ (mod 36).

• 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).

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.867-873
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• 2024

A pseudo-Riemannian solvmanifold is a solvable Lie group endowed with a left invariant pseudo-Riemannian metric. In this short note, we investigate the nilpotency of the Ricci operator of pseudo-Riemannian solvmanifolds. We focus on a special class of solvable Lie groups whose Lie algebras can be expressed as a one-dimensional extension of a nilpotent Lie algebra ℝD⋉n, where D is a derivation of n whose restriction to the center of n has at least one real eigenvalue. The main result asserts that every solvable Lie group belonging to this special class admits a left invariant pseudo-Riemannian metric with nilpotent Ricci operator. As an application, we obtain a complete classification of three-dimensional solvable Lie groups which admit a left invariant pseudo-Riemannian metric with nilpotent Ricci operator.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.761-771
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• 2005

In this paper we present another characterization of (${\pm}1$)-invariant sequences. We also introduce truncated Fibonacci and Lucas sequences of the second kind and show that a sequence $x\;{\in}\;R^{\infty}$ is (-1)-invariant(l-invariant resp.) if and only if $D[_x^0]$ is perpendicular to every truncated Fibonacci(truncated Lucas resp.) sequence of the second kind where $$D=diag((-1)^0,\; (-1)^1,\;(-1)^2,{\ldots})$$.