• 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.

• Honam Mathematical Journal
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• v.35 no.4
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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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.2
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• pp.3-10
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• 2002

For efficient implementation of scalar multiplication in Kobliz elliptic curves, Frobenius endomorphism is useful. Instead of binary expansion of scalar, using Frobenius expansion of scalar we can speed up scalar multiplication and so fast scalar multiplication is closely related to the expansion length of integral multipliers. In this paper we propose a new idea to reduce the length of Frobenius expansion of integral multipliers of scalar multiplication, which makes speed up scalar multiplication. By using the element whose norm is equal to a prime instead of that whose norm is equal to the order of a given elliptic curve we optimize the length of the Frobenius expansion. It can reduce more the length of the Frobenius expansion than that of Solinas, Smart.

• ETRI Journal
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• v.27 no.5
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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.

• Journal of the Korean Society of Combustion
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• v.6 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.5
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• pp.455-461
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• 2008

In this paper, the performance of a scalar filter and a scalar adaptive filter are analyzed. In order to make indoor experimental environment similar to outdoor test, ultrasonic sensors are used instead of GPS. The scalar adaptive filter, which is continuously estimating velocity error covariance and measurement noise covariance by using adaptive method, is different from the scalar filter. Experimental results show that the scalar adaptive filter has better position estimating performance than the scalar filter by estimating above two parameters with an adaptive method.