• Korean Journal of Mathematics
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• v.24 no.4
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• pp.613-626
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• 2016

In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator. We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, minimal, II-minimal and Weingarten surface. Moreover, the parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.621-633
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• 2002

This paper provides some functional equations and parametric expressions of f-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.387-390
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• 2006

Numerical study has been conducted in two dimensions about a NACA0012 airfoil with an oscillating microflap on the surface. We show that this microflap is effective in controlling the unsteady stall at high angles of attack. We solve the compressible Navier-Stokes equations for the Reynolds numbers with an extensible chimera grid fitted to the oscillatory microflap. For turbulent calculation, we adopt the SST $k-{\omega}$ model. We investigate the parametric effect of angle of attacks, Reynolds number, and the location where the microflap is installed.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1049-1054
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• 1990

We formulate optimal quadratic regulator problems with trajectory sensitivity terms as a optimization problem for a fixed controller structure. Using well-known techniques for parametric LQ problems, we give an algorithm to obtain suboptimal feedback gains by iterative solutions of two Lyapunov equations. A numerical example is given to illustrate the effectiveness of the proposed algorithm.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1309-1320
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• 2018

In this paper, we show that proper biharmonic spacelike curve ${\gamma}$ in Lorentzian Heisenberg space (${\mathbb{H}}_3$, g) is pseudo-helix with ${\kappa}^2-{\tau}^2=-1+4{\eta}(B)^2$. Moreover, ${\gamma}$ has the spacelike normal vector field and is a slant curve. Finally, we find the parametric equations of them.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.191-196
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• 2007

The main components in the generalized Mandelbrot sets are under a theoretical investigation for their parametric boundary equations. Using the boundary geometries, a fast construction algorithm is introduced for the generalized Mandelbrot set. This fast algorithm definitely reduces the construction CPU time in comparison with the naive algorithm. Its graphic implementation displays the mysterious and beautiful fractal sets.

• Steel and Composite Structures
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• v.27 no.4
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• pp.479-493
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• 2018

In this paper nonlocal free vibration analysis of a doubly curved piezoelectric nano shell is studied. First order shear deformation theory and nonlocal elasticity theory is employed to derive governing equations of motion based on Hamilton's principle. The doubly curved piezoelectric nano shell is resting on Pasternak's foundation. A parametric study is presented to investigate the influence of significant parameters such as nonlocal parameter, two radii of curvature, and ratio of radius to thickness on the fundamental frequency of doubly curved piezoelectric nano shell.

• Structural Engineering and Mechanics
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• v.77 no.5
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• pp.587-599
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• 2021

Based on Euler-Bernoulli beam theory and continuous element method, the free vibration of bi-dimensional functionally graded beams is investigated. It is assumed that the material properties vary exponentially along the beam thickness and length. The characteristic frequency equations of beams with different boundary conditions are obtained by transfer matrix method. The validity of the proposed method is assessed through comparison with available results. Parametric studies are carried out to analyze the influences of the gradient indexes and the beam slenderness ratio on the natural frequencies of bi-dimensional functionally graded beams.

• Transactions of the Korean hydrogen and new energy society
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• v.31 no.4
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• pp.387-394
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• 2020

A parametric study of a 2.5 kW class propeller type micro hydraulic turbine was performed. In order to analyze the internal flow characteristics in the hydraulic turbine, three dimensional Reynolds-averaged Navier-Stokes equations with shear stress transport turbulence model were used and the hexahedral grid system was used to construct computational domain. To secure the reliability of the numerical analysis, the grid dependency test was performed using the grid convergence index method based on the Richardson extrapolation, and the grid dependency was removed when about 1.7 million nodes were used. For the parametric study, the axial distance at shroud span (L) between the inlet guide vane and the runner, and the inlet and outlet blade angles (β₁, β₂) of the runner were selected as the geometric parameters. The inlet and outlet angles of the runner were defined in the 3 spans from the hub to tip, and a total of 7 geometric parameters were investigated. It was confirmed that the outlet angles of the runner had the most sensitive effect on the power and efficiency of the micro hydraulic turbine.

• Current Optics and Photonics
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• v.2 no.3
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• pp.261-268
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• 2018

Stimulated polariton scattering (SPS) from the $A_1$ transverse optical (TO) modes of $BaTiO_3$ bulk crystal generating a terahertz (THz) wave with the noncollinear phase-matching (NPM) condition is theoretically investigated. To our best knowledge, this is the first report on THz wave generation from $BaTiO_3$ bulk crystal via SPS. Phase-matching (PM) characteristics in the NPM configuration are analyzed. Effective parametric gain lengths for the Stokes and THz waves in the NPM configuration are calculated. The effective parametric gain coefficient and absorption coefficient of the THz wave in $BaTiO_3$ are theoretically simulated. The THz phonon flux densities generated via SPS in $BaTiO_3$ are theoretically calculated by solving the coupled wave equations under the NPM condition. The PM characteristics and THz-wave parametric gain characteristics in $BaTiO_3$ are compared to those in $MgO:LiNbO_3$. The results of the analysis indicate that $BaTiO_3$ is an attractive optical crystal for efficient THz wave generation via SPS.