• Communications of the Korean Mathematical Society
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• v.15 no.2
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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.

• Honam Mathematical Journal
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• v.21 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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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.

• Honam Mathematical Journal
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• v.24 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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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.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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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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• v.34 no.3_4
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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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• v.43 no.2
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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.

• Journal of KIISE:Software and Applications
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• v.34 no.5
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• pp.397-406
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• 2007

The problem of finding an optimal alignment between sequence A and B can be solved by dynamic programming algorithm(DPA) efficiently. But, if the length of string was longer, the problem might not be solvable because it requires O(m*n) time and space complexity.(where, $m={\mid}A{\mid},\;n={\mid}B{\mid}$) For space, Hirschberg developed a linear space and quadratic time algorithm, so computer memory was no longer a limiting factor for long sequences. As computers's processor and memory become faster and larger, a method is needed to speed processing up, although which uses more space. For this purpose, we present an algorithm which will solve the problem in quadratic time and linear space. By using division method, It computes optimal alignment faster than LSA, although requires more memory. We generalized the algorithm about division problem for not being divided into integer and pruned additional space by entry/exit node concept. Through the proofness and experiment, we identified that our algorithm uses d*(m+n) space and a little more (m*n) time faster than LSA.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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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.