• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.1001-1017
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• 2021

In this paper, we first apply parabolic inequalities and a maximum principle to give a new proof for symmetry and monotonicity of solutions to fractional elliptic equations with gradient term by the method of moving planes. Under the condition of suitable initial value, by maximum principles for the fractional parabolic equations, we obtain symmetry and monotonicity of positive solutions for each finite time to nonlinear fractional parabolic equations in a bounded domain and the whole space. More generally, if bounded domain is a ball, then we show that the solution is radially symmetric and monotone decreasing about the origin for each finite time. We firmly believe that parabolic inequalities and a maximum principle introduced here can be conveniently applied to study a variety of nonlocal elliptic and parabolic problems with more general operators and more general nonlinearities.

• Korean Journal of Optics and Photonics
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• v.11 no.6
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• pp.385-389
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• 2000

A phase-retardation function which was derived from Wigner distribution function (WDF) is used to increase a focal depth of a radially symmetric optical system. The WDF for one-dimensional signal is represented as a two-dimensional function of phasespace ($\chi,\zeta$), and a normalized irradiance is described as a form of the Strehl ratio (SR). The increase in the focal depth is accomplished by delivering a shearing tilt a that represents a characteristic of free space propagation with simple manipulation in the WDF space. In this paper we propose a method for evaluating the focal depth quantitatively by representing the phaseretardation function in terms of the focal depth term. In order to verify the validity of the proposed method, we compared the numerically analyzed result with that of J. Sochki's study. study.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.839-865
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• 2013

We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v&gt;0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.

• Journal of the Optical Society of Korea
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• v.18 no.1
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• pp.60-64
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• 2014

We report the generation of 3.3-mW single-cycle terahertz (THz) pulses at 1-kHz repetition rate via optical rectification in MgO-doped prism-cut stoichiometric LiNbO3. Efficient pulse-front tilting of 800-nm pulses was realized by an optimized single-lens focusing scheme for radially-symmetric propagation of THz beams. In this geometry, nearly-diffraction-limited THz Gaussian beams with electric field strength as high as 350 kV/cm were generated. The pump-to-THz energy conversion efficiency of $1.36{\times}10^{-3}$ and the extremely high signal-to-noise ratio of ~1:15000 achieved are among the best results for 1-kHz single-cycle terahertz pulse generation ever demonstrated in room temperature operation.

• Nuclear Engineering and Technology
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• v.52 no.11
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• pp.2460-2470
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• 2020

To study the thermophysical and neutronic properties of thorium-plutonium fuel, a conceptual design of a hybrid facility consisting of a subcritical Th-Pu reactor core and a source of additional D-D neutrons that places on the axis of the core is proposed. The source of such neutrons is a column of high-temperature plasma held in a long magnetic trap for D-D fusionreactions. This article presents computer simulation results of generation of thermonuclear neutrons in the plasma, facility neutronic properties and the evolution of a fuel nuclide composition in the reactor core. Simulations were performed for an axis-symmetric radially profiled reactor core consisting of zones with various nuclear fuel composition. Such reactor core containing a continuously operating stationary D-D neutron source with a yield intensity of Y = 2 × 10¹⁶ neutrons per second can operate as a nuclear hybrid system at its effective coefficient of neutron multiplication 0.95-0.99. Options are proposed for optimizing plasma parameters to increase the neutron yield in order to compensate the effective multiplication factor decreasing and plant power in a long operating cycle (3000-day duration). The obtained simulation results demonstrate the possibility of organizing the stable operation of the proposed hybrid 'fusion-fission' facility.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1999.10a
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• pp.27-27
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• 1999

To illustrate the global variation of the droplet mean diameters and the turbulent flow characteristics in counterflowing internal mixing pneumatic nozzle, the experimental measurements at five axial downstream locations(i.e., at Z=30, 50, 80, 120, and 170mm) were made using a PDPA(Phase Doppler Particle Analyzer) under the different air injection pressures ranging from 40 ㎪ to 120 ㎪. A nozzle with axi-symmetric tangential-drilled four holes at an angle of 15$^{\circ}$ has been designed and manufactured. The distributions of velocities, turbulence intensities, turbulence kinetic energy, turbulent correlation coefficients, spray angle, droplet mean diameters, volume flux, number density are quantitatively analyzed. It is possible to discern the effects of increasing air pressure. It indicates that the strong axial momentum in spite of more or less disparity between the velocity components means more reluctant to disperse radially, and that axial fluctuating velocities are substantially higher than those of radial and tangential ones, suggesting that the disintegration process is enhanced under higher air assist. The larger droplets are detected in the spray centerline at the near stations and smaller ones are generated due to further subsequent breakup at farther axial locations are attributed to the internal mixing type nozzle characteristics. Despite of the strong axial momentum, the poor atomization around the centre close to the nozzle exit is attributed to the lower rates of spherical particles which are not subject to instantaneous breakup. As it goes downstream, however, substantial increases in SMD(Sauter Mean Diameter) from the central part toward spray periphery are understandable because the droplet relative velocity is too low to bring about any subsequent disintegration.