• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.401-413
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• 2002

In this paper, we consider hyperstructures (H,.) defined on the set H = {e, a, b}. We study the hyperstructure of H when every element is one of a scalar unit, a unit or a weak scalar. On those conditions the $H_{\upsilon}$-quasigroups are classified. And we obtain the 15 minimal $H_{\upsilon}$-groups and 2 non-quasi $H_{\upsilon}$-semigroups For these we use the Mathematica 3.0 computer programs.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.541-549
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• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.867-871
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• 2013

It has been conjectured that, on a compact 3-dimensional orientable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker $s^{\prime}^*_g{\neq}0$, which generalizes the previous partial results.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.585-600
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• 2011

In this paper we derive an integral formula on an (n + 3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere $S^{4m+3}$. Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• Honam Mathematical Journal
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• v.8 no.1
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• pp.1-19
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• 1986

We show that a (possibly unbounded) linear operator, T, is scalar on the real line (spectral operator of scalar type, with real spectrum) if and only if (iT) generates a uniformly bounded semigroup and $(1-iT)(1+iT)^{-1}$ is scalar on the unit circle. T is scalar on [0, $\infty$) if and only if T generates a uniformly bounded semigroup and $(1+T)^{-1}$ is scalar on [0,1). By analogy with these results, we define $C^0$-scalar, on the real line, or [0. $\infty$), for an unbounded operator. We show that a generator of a positive-definite group is $C^0$-scalar on the real line. and a generator of a completely monotone semigroup is $C^0$-scalar on [0, $\infty$). We give sufficient conditions for a closed operator, T, to generate a positive-definite group: the sequence < $\phi(T^{n}x)$ > $_{n=0}^{\infty}$ must equal the moments of a positive measure on the real line, for sufficiently many positive $\phi$ in $X^{*}$, x in X. If the measures are supported on [0, $\infty$), then T generates a completely monotone semigroup. On a reflexive Banach lattice, these conditions are also necessary, and are equivalent to T being scalar, with positive projection-valued measure. T generates a completely monotone semigroup if and only if T is positive and m-dispersive and generates a bounded holomorphic semigroup.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.117-123
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• 2004

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1087-1094
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• 2016

On a compact n-dimensional manifold M, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, after derivng an interesting curvature identity, we show that the conjecture is true in dimension three and four when g is weakly Einstein. In higher dimensional case $n{\geq}5$, we also show that the conjecture is true under an additional Ricci curvature bound. Moreover, we prove that the manifold is isometric to a standard n-sphere when it is n-dimensional weakly Einstein and the kernel of the linearized scalar curvature operator is nontrivial.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.303-311
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• 1998

We study the conformally flat unit vector bundle $E_1$ of constant scalar curvature for the bundle ${\pi}:E^{n+2}{\rightarrow}M^n$ over an Einstein manifold M.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.30 no.2
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• pp.179-187
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• 2020

The FBC(Fixed-Base Comb) is a method to efficiently operate scalar multiplication, a core operation for signature generations of the ECDSA(Elliptic Curve Digital Signature Algorithm), utilizing precomputed lookup tables. Since the FBC refers to the table depending on the secret information and the values of the table are publicly known, an adversary can perform HCA(Horizontal Correlation Analysis), one of the single trace side channel attacks, to reveal the secret. However, HCA is a statistical analysis that requires a sufficient number of unit operation traces extracted from one scalar multiplication trace for a successful attack. In the case of the scalar multiplication for signature generations of ECDSA, the number of unit operation traces available for HCA is significantly fewer than the case of the RSA exponentiation, possibly resulting in an unsuccessful attack. In this paper, we propose an improved HCA on lookup table based scalar multiplication algorithms such as FBC. The proposed attack improves HCA by increasing the number of unit operation traces by determining such traces for the same intermediate value through collision analysis. The performance of the proposed attack increases as more secure elliptic curve parameters are used.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.1153-1156
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• 1998

We describe a design of a simple but efficient floatingpoint processing architecture expoiting concurrent execution of scalar instructions for high performance in general-purpose microprocessors. This architecture employs 3 stage pipeline asyncronously working with integer processing unit to regulate instruction flows between two arithmetic units.