• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.907-925
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• 2012

In this paper the boundedness for a large class of multi-sublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calder$\acute{o}$n-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.353-358
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• 2000

To achieve the requirement for high fuel economy and low emissions, the research for GDI engines is recently very brisk in the whole world. This study was performed to measure distribution of average particle size in non-evaporating spray. The 2-D fluorescence/scattering images of fuel spray were captured simultaneously by visualization system composed of a laser sheet, a doubling prism, optical filters, and an ICCD camera. Using the ratio of the two light intensities, particle size distribution was obtained. The SMD measured by fluorescence/scattering technique was compared with it obtained by PDA. The experimental results show that the spray structure of GDI injector and temporal SMD distribution.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.6
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• pp.167-174
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• 1997

The penetration depth and the size distribution of the droplets of fuel sprays are important in the operation of spark-ignition MPI engines. A fluorescence/scattering image technique for droplet sizing was applied to measure th edroplet size distribution in non-evaporating gasoline sprays. The fluorescence and scattering lights were imaged simultaneously by the two-dimensional visualization system composed of a laser sheet, a doubling prism, optical filters, and a CCD camera. Quantitative droplet size distributions were extracted from evaluating the ratio of the two light densities. The mean droplet size measured by the fluorescence/scattering technique was compared with the result obtained by the enlarged photographs of droplets. The fluorescence/scattering image technique also gives the useful information of the characteristics of droplet impingement in a inclined wall.

• Advances in aircraft and spacecraft science
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• v.2 no.2
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• pp.125-168
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• 2015

Dynamic aeroelastic behavior of structurally nonlinear Joined Wings is presented. Three configurations, two characterized by a different location of the joint and one presenting a direct connection between the two wings (SensorCraft-like layout) are investigated. The snap-divergence is studied from a dynamic perspective in order to assess the real response of the configuration. The investigations also focus on the flutter occurrence (critical state) and postcritical phenomena. Limit Cycle Oscillations (LCOs) are observed, possibly followed by a loss of periodicity of the solution as speed is further increased. In some cases, it is also possible to ascertain the presence of period doubling (flip-) bifurcations. Differences between flutter (Hopf's bifurcation) speed evaluated with linear and nonlinear analyses are discussed in depth in order to understand if a linear (and thus computationally less intense) representation provides an acceptable estimate of the instability properties. Both frequency- and time-domain approaches are compared. Moreover, aerodynamic solvers based on the potential flow are critically examined. In particular, it is assessed in what measure more sophisticated aerodynamic and interface models impact the aeroelastic predictions. When the use of the tools gives different results, a physical interpretation of the leading mechanism generating the mismatch is provided. In particular, for PrandtlPlane-like configurations the aeroelastic response is very sensitive to the wake's shape. As a consequence, it is suggested that a more sophisticate modeling of the wake positively impacts the reliability of aerodynamic and aeroelastic analysis. For SensorCraft-like configurations some LCOs are characterized by a non-synchronous motion of the inner and outer portion of the lower wing: the wing's tip exhibits a small oscillation during the descending or ascending phase, whereas the mid-span station describes a sinusoidal-like trajectory in the time-domain.