• 대한수학회논문집
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• 제15권2호
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• pp.349-355
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• 2000

In this paper we generalize the Whitehead theorem which says that a homology equivalence implies a homotopy equivalence for nilpotent spaces. We make some theorems on a homotopy equivalence of non-nilpotent spaces, e.g., the solvable space or space satisfying the condition (T**) or space X with $\pi$1(X) Engel, or locally nilpotent space with some properties. Furthermore we find some conditions that the Wall invariant will be trivial.

• 호남수학학술지
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• 제21권1호
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• pp.171-177
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• 1999

We find the properties of the defects and textures in an ordered medium. Especially, the space X, e.g., the residually solvable space or space satisfying the conditions ($T^{**}$) with respect to the defect and texture.

• 대한수학회보
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• 제21권2호
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• pp.91-95
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• 1984

Let D$^{p}$ be the space of distributions of $L^{p}$-growth and S the space of tempered destributions in $R^{n}$: D$^{p}$, 1.leq.P.leq..inf., is the dual of the space $D^{p}$ which we discribe later. We denote by O$_{c}$(S:S') the space of convolution operators in S. In [8] S. Sznajder and Z. Zielezny proved the following necessary conditions for convolution operators in O$_{c}$(S:S) to be solvable in S.

• 호남수학학술지
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• 제24권1호
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• pp.93-101
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• 2002

The $S^1$-Eule characteristics of X is defined by $\bar{\chi}_{S^1}(X)\;{\in}\;HH_1(ZG)$, where G is the fundamental group of connected finite $S^1$-compact manifold or connected finite $S^1$-finite complex X and $HH_1$ is the first Hochsch ild homology group functor. The purpose of this paper is to find several cases which the $S^1$-Euler characteristic has a homotopic invariant.

• 대한수학회지
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• 제58권6호
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• pp.1407-1419
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• 2021

The Iwasawa decomposition NAK of the Lie group G = SO₀(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.

• 대한수학회지
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• 제33권4호
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• pp.1047-1067
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• 1996

In this paper, we are interested in left invariant flat affine structures on Lie groups. These structures has been studied by many authors in different contexts. One of the fundamental questions is the existence of complete affine structures for solvable Lie groups G, raised by Minor [15]. But recently Benoist answered negatively even for the nilpotent case [1]. Also moduli space of such structures for lower dimensional cases has been studied by several authors, sometimes with compatible metrics [5,10,4,12].

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• ETRI Journal
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• 제43권2호
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• pp.344-356
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• 2021

CRAFT is a tweakable block cipher introduced in 2019 that aims to provide strong protection against differential fault analysis. In this paper, we show that CRAFT is vulnerable to side-channel cube attacks. We apply side-channel cube attacks to CRAFT with the Hamming weight leakage assumption. We found that the first half of the secret key can be recovered from the Hamming weight leakage after the first round. Next, using the recovered key bits, we continue our attack to recover the second half of the secret key. We show that the set of equations that are solvable varies depending on the value of the key bits. Our result shows that 99.90% of the key space can be fully recovered within a practical time.

• 한국정보과학회논문지:소프트웨어및응용
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• 제34권5호
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• pp.397-406
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• 2007

두 서열 A와 B간의 최적정렬을 찾는 문제는 동적프로그래밍 알고리즘을 사용하여 효과적으로 해결 될 수 있다. 하지만, 길이가 각각 m, n인 두 서열, $S_1$, $S_2$를 정렬하기 위해서는 O(m*n)의 시간과 공간 복잡도를 갖기 때문에 서열의 길이가 길어질 경우에는 시간과 공간 비용 문제로 인해 적용 할 수 없게 된다. 실제 계산상에 제한요소로 작용하는 공간비용 문제를 해결하기 위해 Hirschberg에 의해 제시된 선형공간 알고리즘은 이 문제를 O(n*m)의 시간복잡도와 O(n+m)의 공간복잡도로서 해결하였다. 컴퓨터 기술의 발전으로 CPU의 처리속도가 향상되고, 사용가능한 주기억장치의 공간이 확대됨에 따라, 기억공간은 더 사용하더라도 처리속도는 높일 수 있는 방법이 필요하다. 이를 위해, 본 논문에서는 공간 분할 방법을 통하여 공간 소모는 선형공간 알고리즘보다 많지만, 처리 속도는 빠른 O(n*m)의 시간과 O(n+m)의 공간비용을 갖는 알고리즘을 제안한다. 또한 분할 시 서열의 길이변화에 따른 분할 수(d) 문제를 일반화하고, 입/출구 노드 개념을 이용하여 불필요한 연산을 제거하였다. 선형공간 알고리즘이 (m+n)의 공간으로 2*m*n에 가까운 속도를 갖는데 비해, 본 알고리즘은 (m+n)*d의 공간으로 m*n에 가까운 결과를 보임을 증명과 실험결과로부터 확인한다.

• Advances in aircraft and spacecraft science
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• 제5권1호
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• pp.73-105
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• 2018

A particular type of constant speed helical trajectory, with variable ascension rate, is proposed. Such trajectories are candidates of choice as motion primitives in automatic airplane trajectory planning; they can also be used by airplanes taking off or landing in limited space. The equations of motion for airplanes flying on such trajectories are exactly solvable. Their solution is presented, together with an analysis of the restrictions imposed on the geometrical parameters of the helical paths by the dynamical abilities of an airplane. The physical quantities taken into account are the airplane load factor, its lift coefficient, and the thrust its engines can produce. Formulas are provided for determining all the parameters of trajectories that would be flyable by a particular airplane, the final altitude reached, and the duration of the trajectory. It is shown how to construct speed interval tables, which would appreciably reduce the calculations to be done on board the airplane. Trajectories are characterized by their angle of inclination, their radius, and the rate of change of their inclination. Sample calculations are shown for the Cessna 182, a Silver Fox like unmanned aerial vehicle, and the F-16 Fighting Falcon.