• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2001.11a
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• pp.139-143
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• 2001

본 논문은 작은 홀수 표수를 갖는 유한체에서 정의된 타원곡선의 스칼라 곱 연산속도를 향상시키는 새로운 방법을 소개한다. 본 논문에서 제안하는 알고리즘은 스칼라의 프로베니우스 자기준동형 (Frobenius endomorphsim) 확장길이를 줄이는 최근의 방법들을 개선한 방법이다.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.9-17
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• 2001

A ring R is called right mininjective if every isomorphsim between simple right ideals is given by left multiplication by an element of R. In this paper we consider that the necessary and sufficient condition for that Trivial extension of R by V, i.e. T(R; V ) is mininjective. We also study the split null extension R and S by V.

• East Asian mathematical journal
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• v.37 no.5
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• pp.585-590
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• 2021

This paper consider the Jacobian variety of a hyperelliptic curve over a finite field with the formal structure of the mixed type. We present the Newton polygon of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety. It gives an useful tool for finding the local decomposition of the Jacobian variety into isotypic components.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.583-590
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• 2021

In this work we give new upper and lower bounds for the numerical radius of a complex square matrix A using the entries and the trace of A.

• East Asian mathematical journal
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• v.38 no.5
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• pp.611-616
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• 2022

This paper considers the Jacobian variety of a hyperelliptic curve over a finite field with mixed symmetric formal type. We present the Newton polygon of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety. It gives a useful tool for finding the local decomposition of the Jacobian variety into isotypic components.

• The Journal of the Korea Contents Association
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• v.12 no.3
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• pp.434-441
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• 2012

An analytic solution to the extended mild-slope equation was derived for waves propagating over an axi-symmetric pit. The water depth inside the pit was in proportion to a power of radial distance from the center of pit. The equation was transformed into the ordinary differential equation using the method of separation of variables. The coefficients of differential terms were expressed as an explicit form composing of the phase and group velocities. The bottom curvature and the square of bottom slope terms, which were added to the extended mild-slope equation, were expressed as power series. Finally, using the Frobenius series, the analytic solution to the extended mild-slope equation was derived. The present analytic solution was validated by comparing with the numerical solution obtained from FEM.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9A
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• pp.1322-1328
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• 1999

In this paper, we propose a Multiple Signal Classification(MUSIC) in conjunction with signal enhancement (SE-MUSIC) for solving the direction-of-arrival estimation problem of multiple incoherent plane waves incident on a uniform linear array. The proposed SE-MUSIC algorithms involve the following main two-step procedure : ( i )to find the enhanced matrix that possesses the prescribed properties and which lies closest to a given covariance matrix estimate in the Frobenius norm sense and (ii) to apply the MUSIC to the enhanced matrix. Simulation results are illustrated to demonstrate the better resolution and statistical performance of the proposed method than MUSIC at lower SNR.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.6
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• pp.959-967
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• 1999

In this paper, we propose a Linear Prediction Method(LPM) in conjunction with signal enhancement for solving the direction-of-arrival estimation problem of multiple incoherent plane waves incident on a uniform linear array. The basic idea of signal enhancement is that of finding the covariance matrix of given rank that lies closest to a given estimated matrix in Frobenius norm sense. It is well known that LPM has a high-resolution performance in general applications, while it provides a lower statistical performance in lower SNR environment. To solve this problem, the LPM combined with signal enhancement approach is herein proposed. Simulation results are illustrated to demonstrate the better performance of the proposed method than conventional LPM.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.125-138
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• 2018

This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.423-445
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• 2021

In this paper, a new form of poly-Genocchi polynomials is defined by means of polylogarithm, namely, the Apostol-type poly-Genocchi polynomials of higher order with parameters a, b and c. Several properties of these polynomials are established including some recurrence relations and explicit formulas, which are used to express these higher order Apostol-type poly-Genocchi polynomials in terms of Stirling numbers of the second kind, Apostol-type Bernoulli and Frobenius polynomials of higher order. Moreover, certain differential identity is obtained that leads this new form of poly-Genocchi polynomials to be classified as Appell polynomials and, consequently, draw more properties using some theorems on Appell polynomials. Furthermore, a symmetrized generalization of this new form of poly-Genocchi polynomials that possesses a double generating function is introduced. Finally, the type 2 Apostolpoly-Genocchi polynomials with parameters a, b and c are defined using the concept of polyexponential function and several identities are derived, two of which show the connections of these polynomials with Stirling numbers of the first kind and the type 2 Apostol-type poly-Bernoulli polynomials.