• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1963-1971
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• 2015

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras. Denote by W(a) the numerical range of an element $a{\in}\mathcal{A}$. We show that the condition W(ax) = W(bx), ${\forall}x{\in}\mathcal{A}$ implies that a = b. Using this, among other results, it is proved that if ${\phi}$ : $\mathcal{A}{\rightarrow}\mathcal{B}$ is a surjective map such that $W({\phi}(a){\phi}(b){\phi}(c))=W(abc)$ for all a, b and $c{\in}\mathcal{A}$, then ${\phi}(1){\in}Z(B)$ and the map ${\psi}={\phi}(1)^2{\phi}$ is multiplicative.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.8
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• pp.790-797
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• 2010

Mode transition of the axi-symmetric screech tone in the low supersonic Mach number range from 1.0 to 1.20 is numerically analyzed. The axi-symmetric Navier-Stokes equations and the k-e turbulence model are solved in the cylindrical coordinate system. The dispersion-relation-preserving(DRP) scheme is applied for space discretization and the optimized four levels marching method are used for time integration. At low supersonic Mach numbers with an axi-symmetric A1 mode in the simulation, it is shown that acoustic propagation due to the nonlinear effects is seen in the lateral direction and the screech tone frequency is the same as the vortex passing frequency due to the generation of intense large-scale vortical motions.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.445-448
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• 2006

The effects of surface roughness on a spatially-developing turbulent boundary layer (TBL) were investigated by performing direct numerical simulations of TBLs over rough and smooth walls. The Reynolds number based on the momentum thickness was varied in the range $Re_{\theta}=300{\sim}1400$. The roughness elements used were periodically arranged two-dimensional spanwise rods, and the roughness height was $k=1.5{\theta}_{in}$, which corresponds to $k/{\delta}=0.045{\sim}0.125$. To avoid generating a rough wall inflow, which is prohibitively difficult, a step change from smooth to rough was placed $80{\theta}_{in}$ downstream from the inlet. The spatially-developing characteristics of the rough-wall TBL were examined. Along the streamwise direction, the friction velocity approached a constant value and a self-preserving form of the turbulent stress was obtained. Introduction of the roughness elements affected the turbulent stress not only in the roughness sublayer but also in the outer layer. Despite the roughness-induced increase of the turbulent stress in the outer layer, the roughness had only a relatively small effect on the anisotropic Reynolds stress tensor in the outer layer. Inspection of the triple products of the velocity fluctuations revealed that introducing the roughness elements onto the smooth wall had a marked effect on vertical turbulent transport across the whole TBL. By contrast, good surface similarity in the outer layer was obtained for the third-order moments of the velocity fluctuations.

• Journal of the Korean earth science society
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• v.34 no.5
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• pp.393-401
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• 2013

Spherical harmonics power spectrum of the geopotential field of Gaussian-bell type on the sphere was investigated using integral formula that is associated with Legendre polynomials. The geopotential field of Gaussian-bell type is defined as a function of sine of angular distance from the bell's center in order to guarantee the continuity on the global domain. Since the integral-formula associated with the Legendre polynomials was represented with infinite series of polynomial, an estimation method was developed to make the procedure computationally efficient while preserving the accuracy. The spherical harmonics power spectrum was shown to vary significantly depending on the scale parameter of the Gaussian bell. Due to the accurate procedure of the new method, the power (degree variance) spanning over orders that were far higher than machine roundoff was well explored. When the scale parameter (or width) of the Gaussian bell is large, the spectrum drops sharply with the total wavenumber. On the other hand, in case of small scale parameter the spectrum tends to be flat, showing very slow decaying with the total wavenumber. The accuracy of the new method was compared with theoretical values for various scale parameters. The new method was found advantageous over discrete numerical methods, such as Gaussian quadrature and Fourier method, in that it can produce the power spectrum with accuracy and computational efficiency for all range of total wavenumber. The results of present study help to determine the allowable maximum scale parameter of the geopotential field when a Gaussian-bell type is adopted as a localized function.