• 대한수학회지
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• 제47권6호
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• pp.1197-1222
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• 2010

There is a well-known classical reduction formula by Griffiths and Harris for Littlewood-Richardson coefficients, which reduces one part from each partition. In this article, we consider an extension of the reduction formula reducing two parts from each partition. This extension is a special case of the factorization theorem of Littlewood-Richardson coefficients by King, Tollu, and Toumazet (the KTT theorem). This case of the KTT factorization theorem is of particular interest, because, in this case, the KTT theorem is simply a reduction formula reducing two parts from each partition. A bijective proof using tableaux of this reduction formula is given in this paper while the KTT theorem is proved using hives.

• 대한수학회보
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• 제53권1호
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• pp.195-204
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• 2016

We prove, in this note, that a Zabavsky ring R is an elementary divisor ring if and only if R is a $B{\acute{e}}zout$ ring. Many known results are thereby generalized to much wider class of rings, e.g. [4, Theorem 14], [7, Theorem 4], [9, Theorem 1.2.14], [11, Theorem 4] and [12, Theorem 7].

• 대한수학회지
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• 제36권1호
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• pp.109-123
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• 1999

In this paper we prove a reduction theorem of the codimension for real submanifold of quaternionic projective space as a quaternionic analogue corresponding to those in Cecil [4], Erbacher [5] and Okumura [9], and apply the theorem to quaternionic CR- submanifold of quaternionic projective space.

• 대한수학회지
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• 제40권5호
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• pp.901-920
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• 2003

The notion of infinitely near singular points, classical in the case of plane curves, has been generalized to higher dimensions in my earlier articles ([5], [6], [7]). There, some basic techniques were developed, notably the three technical theorems which were Differentiation Theorem, Numerical Exponent Theorem and Ambient Reduction Theorem [7]. In this paper, using those results, we will prove the Finite Presentation Theorem, which the auther believes is the first of the most important milestones in the general theory of infinitely near singular points. The presentation is in terms of a finitely generated graded algebra which describes the total aggregate of the trees of infinitely near singular points. The totality is a priori very complex and intricate, including all possible successions of permissible blowing-ups toward the reduction of singularities. The theorem will be proven for singular data on an ambient algebraic shceme, regular and of finite type over any perfect field of any characteristics. Very interesting but not yet apparent connections are expected with many such works as ([1], [8]).

• Korean Journal of Mathematics
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• 제17권3호
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• pp.299-314
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• 2009

We investigate the multiple nontrivial solutions of the asymmetric beam equation $u_{tt}+u_{xxxx}=b_1[{(u + 2)}^+-2]+b_2[{(u + 3)}^+-3]$ with Dirichlet boundary condition and periodic condition on t. We reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions of the equation.

• 충청수학회지
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• 제22권4호
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• pp.675-687
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• 2009

We find the multiple nontrivial solutions of the equation of the form $u_{tt}-u_{xx}=b_1[(u+1)^{+}-1]+b_2[(u+2)^{+}-2]$ with Dirichlet boundary condition. Here we reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions.

• 호남수학학술지
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• 제30권3호
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• pp.443-468
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• 2008

We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system $\.{z}$ = $J(H_z(t,z))$. For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.

• 대한전자공학회논문지SD
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• 제41권4호
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• pp.57-66
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• 2004

본 논문에서는 RNS(residue number systems) 몽고메리 모듈라 곱셈기 기반의 2,048 비트 RSA 설계를 제안한다. RNS는 긴 워드에 대한 모듈라 연산을 짧은 워드로 분할하여 고속 병렬 모듈라 연산을 처리하는 시스템으로써 본 논문에서는 RNS 몽고메리 모듈라 곱셈 연산을 위해 Wallace 트리 모듈라 곱셈기 기반의 Montgomery reduction method(MRM)［1］와 33개의 64 비트 RNS base 를 도입하였다. 또한, 고속 RNS 모듈라 곱셈 연산을 위해 Chinese remainder theorem(CRT)［2］기반의 개선된 base extension 알고리즘을 제안한다. 본 논문에서 제시한 RNS 기반의 2,048 비트 RSA는 삼성 0.35㎛ 공정을 사용하여 기능을 검증하였으며 100㎒에서 2.53㎳ 연산 속도 결과를 얻었다.

• 대한전기학회논문지:시스템및제어부문D
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• 제53권5호
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• pp.368-373
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• 2004

Surface visualization can be useful, particularly for internet-based education and simulation system. Since the mesh data size directly affects the downloading and operational performance, the problem that should be solved for efficient surface visualization is to reduce the total number of polygons, constituting the surface geometry as much as Possible. In this paper, an efficient polygon reduction algorithm based on Stokes＇ theorem, and topology preservation to delete several adjacent vertices simultaneously for past polygon reduction is proposed. The algorithm is irrespective of the shape of polygon, and the number of the polygon. It can also reduce the number of polygons to the minimum number at one time. The performance and the usefulness for medical imaging application was demonstrated using synthesized geometrical objects including plane. cube. cylinder. and sphere. as well as a real human data.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.683-700
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• 2018

We get one theorem which shows existence of solutions for one-dimensional jumping problem involving p-Laplacian and Dirichlet boundary condition. This theorem is that there exists at least one solution when nonlinearities crossing finite number of eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigenfunctions of the p-Laplacian eigenvalue problem when 1 < p < ${\infty}$, variational reduction method and Leray-Schauder degree theory when $2{\leq}$ p < ${\infty}$.