• 호남수학학술지
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• 제8권1호
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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.

• 호남수학학술지
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• 제35권4호
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• pp.647-655
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• 2013

We obtain $C^{\infty}$-continuous paths of explicit Riemannian metrics $g_t$, $0{\leq}t$ < ${\varepsilon}$, whose scalar curvatures $s(g_t)$ decrease, where $g_0$ is a flat metric, i.e. a metric with vanishing curvature. Most of them can exist on tori of dimension ${\geq}3$. Some of them yield scalar curvature decrease on a ball in the Euclidean space.

• 정보보호학회논문지
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• 제12권2호
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• pp.3-10
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• 2002

Koblitz 타원곡선에서 스칼라 곱을 효율적으로 구현하기 위하여 프로베니우스 자기준동형 (Frobenius endomorphism)이 유용하게 사용된다. 스칼라 곱 연산시 스칼라를 이진 전개하는 대신에 프로베니우스 확장을 사용하여 고속연산을 가능하게 할 수 있으며 따라서 연산의 속도는 확장길이와 밀접한 관계가 있다. 본 논문은 스칼라의 프로베니우스 확장길이를 줄임으로써 스칼라 곱의 고속연산을 가능하게 하는 새로운 방법을 제안한다. 타원곡선의 위수를 노름(Norm)으로 갖는 원소대신 큰 소수 위수를 노름으로 갖는 원소를 사용하여 프로베니우스 확장길이를 최적화시키는 이 방법은 Solinas, Smart가 제안한 방법보다 프로베니우스 확장길이를 더 감소시킬 수 있다.

• ETRI Journal
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• 제27권5호
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• pp.617-627
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• 2005

This paper proposes an efficient scalar multiplication algorithm for hyperelliptic curves, which is based on the idea that efficient endomorphisms can be used to speed up scalar multiplication. We first present a new Frobenius expansion method for special hyperelliptic curves that have Gallant-Lambert-Vanstone (GLV) endomorphisms. To compute kD for an integer k and a divisor D, we expand the integer k by the Frobenius endomorphism and the GLV endomorphism. We also present improved scalar multiplication algorithms that use the new expansion method. By our new expansion method, the number of divisor doublings in a scalar multiplication is reduced to a quarter, while the number of divisor additions is almost the same. Our experiments show that the overall throughputs of scalar multiplications are increased by 15.6 to 28.3 % over the previous algorithms when the algorithms are implemented over finite fields of odd characteristics.

• 한국연소학회지
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• 제6권2호
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• pp.43-49
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• 2001

Instantaneous, three-dimensional scalar dissipation rates of the reaction progress variable are measured in turbulent premixed Bunsen flames of lean hydrocarbon/air mixtures with the two-sheet, two-dimensional Rayleigh scattering technique. The flames investigated are located in the turbulent flame-front regime on a newly proposed combustion diagram for premixed flames. The conditionally-averaged mean scalar dissipation rates, $N_{\zeta}$ are found to be lower than the calculated laminar values, indicating a locally broadened flame front. In agreement with previous measurements, the maximum of $N_{\zeta}$, decreases strongly with increasing Karlovitz numbers. The conditional probability density functions are close to a log-normal distribution for scalar dissipation rates conditioned at the progress variable value where the scalar dissipation is maximum in unstretched laminar flame calculations. The time scale for the Favre-averaged mean scalar dissipation rate decreases in general across the turbulent flame brush from the unburnt to burnt side.

• 대한수학회논문집
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• 제13권3호
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• pp.539-544
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• 1998

Let (M, g) be a noncompact complete Riemannian manifold of dimension n $\geq$ 3 with scalar curvature S, which is close to O. With conditions on a conformal invariant and scalar curvature of (M, g), we show that there exists a conformal metric (equation omitted), near g, whose scalar curvature (equation omitted) = 0 by gluing solutions of the corresponding partial differential equation on each bounded subsets $K_{i}$ with ∪$K_{i}$ = M.

• 대한수학회논문집
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• 제9권3호
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• pp.617-627
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• 1994

Algebraic spectral subspaces and admissible operators were introduced by K. B. Laursen and M. M. Neumann in 1988 [L88], [N]. These concepts are useful in automatic continuity problems of intertwining linear operators on Banach spaces. In this paper we characterize the algebraic spectral subspaces of generalized scalar operators. From this characterization we show that generalized scalar operators are admissible. Also we show that doubly power bounded operators are generalized scalar. And using the spectral capacity we show that a generalized scalar operator is decomposable. Then we give an example of an operator which is not admissible but decomposable.

• 대한수학회논문집
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• 제36권1호
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• pp.165-171
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• 2021

The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton (Mn, g, f, λ) with constant scalar curvature admitting a non-homothetic conformal vector field V leaving the potential vector field invariant. We show that in such manifolds the potential function f is constant and the scalar curvature of g is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field V, without constant scalar curvature assumption, we show that g has constant curvature and determines the potential function f explicitly.

• 충청수학회지
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• 제23권2호
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• pp.305-313
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• 2010

In this paper, we prove that if $T{\in}L$(X) is a generalized scalar operator then Ker $T^p$ is the quasi-nilpotent part of T for some positive integer $p{\in}{\mathbb{N}}$. Moreover, we prove that a generalized scalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent generalized scalar operator is nilpotent.

• 한국항공우주학회지
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• 제36권5호
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• pp.455-461
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• 2008

본 논문에서는 스칼라 필터와 적응 스칼라 필터의 성능을 비교 분석하였다. 외부 실험 과 비슷한 실험 환경을 만들기 위해서 GPS를 대신할 수 있는 초음파 의사위성을 사용하였다. 적응 스칼라 필터는 스칼라 필터와는 달리 적응기법을 사용하여 연속적으로 속도오차 공분산과 측정잡음 공분산을 추정한다. 실험결과, 적응 기법을 사용하여 위의 두 파라미터를 연속적으로 추정하는 적응 스칼라 필터의 위치 추정 성능이 스칼라 필터보다 더 좋다는 것을 확인하였다.