• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.161-170
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• 2022

For an arbitrary ample divisor A in smooth del Pezzo surface S of degree 2, we completely compute alpha invariant along curves when the ample divisor A is birational type.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.1-13
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• 1999

The purpose of this paper is to show that if the Fatou set F(f) of a CF-meromorphic function f has two completely invariant components, then they are the only components of F(f) and that the Julia set of the entire transcendental function $E_{\lambda}(z)={\lambda}e^z$ for 0 < ${\lambda}$ < $\frac{1}{e}$ contains a Cantor bouquet by employing the Devaney and Tangerman's theorem[10].

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.195-203
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• 2023

Special examples of harmonic manifolds that are not symmetric, proving that the conjecture posed by Lichnerowicz fails in the non-compact case have been intensively studied. We completely classify homogeneous structures on Damek-Ricci spaces equipped with the left invariant metric.

• Journal of the Institute of Convergence Signal Processing
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• v.4 no.3
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• pp.21-26
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• 2003

A new method to realize 3-dimensional object pattern recognition system using Fourier-based feature extractor has been proposed. The procedure to obtain the invariant feature vector is as follows ; A closed surface is generated by tracing the surface of object using the 3-dimensional polar coordinate. The centroidal distances between object's geometrical center and each closed surface points are calculated. The distance vector is translation invariant. The distance vector is normalized, so the result is scale invariant. The Fourier spectrum of each normalized distance vector is calculated, and the spectrum is rotation invariant. The Fourier-based feature generating from above procedure completely eliminates the effect of variations in translation, scale, and rotation of 3-dimensional object with closed-surface. The experimental results show that the proposed method has a high accuracy.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.20-27
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• 1987

The hierarchical approach method is proposed to sperate each different time scale sub-systems from linear time invariant multi-parameter singular perturbation systems. By means of this proposal, the original multi-parameter singular perturbation systems is completely separated into independent subsystems with each different time scale. It is also investigated that the controllability of the system is invariant. And this paper applies singular perturbation methods to the minimum control effort problem for linear time invariant systems with constrained controls. Also near-optimum control theory, which is based on dividing the total time interval with the time scales respectively, is proposed. As a result, the time scale separation method is show to be particularly useful in a near optimum design which can be otained through a decentralized control structure.

• East Asian mathematical journal
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• v.34 no.3
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• pp.305-316
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• 2018

Let R be a ring with identity. A right ideal ideal I of a ring R is called ref lexive (resp. completely ref lexive) if $aRb{\subseteq}I$ implies that $bRa{\subseteq}I$ (resp. if $ab{\subseteq}I$ implies that $ba{\subseteq}I$) for any $a,\;b{\in}R$. R is called ref lexive (resp. completely ref lexive) if the zero ideal of R is a reflexive ideal (resp. a completely reflexive ideal). Let K(R) (called the ref lexive radical of R) be the intersection of all reflexive ideals of R. In this paper, the following are investigated: (1) Some equivalent conditions on an reflexive ideal of a ring are obtained; (2) reflexive (resp. completely reflexive) property is Morita invariant; (3) For any ring R, we have $K(M_n(R))=M_n(K(R))$ where $M_n(R)$ is the ring of all n by n matrices over R; (4) For a ring R, we have $K(R)[x]{\subseteq}K(R[x])$; in particular, if R is quasi-Armendaritz, then R is reflexive if and only if R[x] is reflexive.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.11
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• pp.1612-1619
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• 2017

In this note, a complete proof of Utkin's theorem is presented for SI(single input) uncertain nonlinear systems. The invariance theorem with respect to the two nonlinear transformation methods so called the two diagonalization methods is proved clearly, comparatively, and completely for SI uncertain nonlinear systems. With respect to the sliding surface and control input transformations, the equation of the sliding mode i.e., the sliding surface is invariant, which is proved completely. Through an illustrative example and simulation study, the usefulness of the main results is verified. By means of the two nonlinear transformation methods, the same results can be obtained.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.3
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• pp.63-69
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• 1998

In this paper, a new input method is proposed to improve shift-invariant property of a photorefractive correlator andwe implemented real-time optical pattern recognition system using it. In the conventional photorefractive correlator, it is vrey difficult to satisfy the Bragg condition in the pattern recognition process. So, correlation peak is decreased heavily for the shift of input image. If a liquid crystal television(LCTV) without an anlyzer is used as input device, we can get the correlation result regardless of shift of input image because beam path is not changed during storage of holographic filter and correlation process. Also recording time of a holographic matched filter in photorefractive crystal is reduced and the correlation peak is increased because incident beam on the LCTV is transmitted completely. Therefore total optical efficiency is improved. We compared and analyzed the correlation results of proposed photorefractive correlator by computer simulation and optical experiment. We used a BaTiO$_{3}$ single crystal which has high diffraction efficiency in optical experiment.

• Economic and Environmental Geology
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• v.5 no.2
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• pp.77-86
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• 1972

The system NaAlSiO_4-KAlSiO_4-SiO_2-H_2O, Bowen's "Petrogeny's Residua System" of course is extremely important in understanding the phase relationships of igneous and metamorphic rock in the continental crust. The phase relationships in this system, however, have not been completely established in the P-T range above the Mohorovicic discontinuity. They need to be established. In this study, the most probable sequence of P-T curves around a quaternary invariant point(~5Kb/${\sim}635^{\circ}C$) in the system using Schreinemakers' rule, is deduced, essentially on the basis of Morse's(1969a and b) experimental data. Possible modifications of the sequence of the P-T curves considering likely changes of the invariant chemogram are also considered. It is concluded that the sequence of P-T curves around the invariant point (~5Kb/${\sim}635^{\circ}C$) is (L), (Anl), (Or), (V), (Ne) and (Ab) on the P-T projection, where the P-T curve (L) is extended towards lower P-T regions, and the (Anl) curve is extended towards a region of higher temperature and lower pressure from the invariant point respectively.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 2000.11b
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• pp.279-286
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• 2000

The objective of this research is to detect the papaya fruits on tree in an orchard. The detection of papaya on natural background is difficult because colors of fruits and background such as leaves are similarly green. We cannot separate it from leaves by color information. Therefore, this research will use shape information instead. First, we detect an interested object by detecting its boundary using edge detection technique. However, the edge detection will detect every objects boundary in the image. Therefore, shape description technique will be used to describe which one is the interested object boundary. The good shape description should be invariant in scaling, rotating, and translating. The successful concept is to use Fourier series, which is called "Fourier Descriptors". Elliptic Fourier Descriptors can completely represent any shape, which is selected to describe the shape of papaya. From the edge detection image, it takes a long time to match every boundary directly. The pre-processing task will reduce non-papaya edge to speed up matching time. The deformable template is used to optimize the matching. Then, clustering the similar shapes by the distance between each centroid, papaya can be completely detected from the background.