• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1007-1014
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• 2012

We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point 1/2.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2095-2105
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• 2015

Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.245-250
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• 2008

For simulation of a wing unfolding motion for the various aerodynamic conditions, equation governing unfolding motion and moments applying to the unfolding wing were modelled. Aerodynamic roll moment consists of the static roll moment and the damping moment, which were obtained through wind tunnel tests and numerical analyses respectively. Panel method was used to compute the roll damping coefficient with twisted wing, whose deflection angle was equivalent to angle of attack due to the deployment motion. Roll damping coefficient is a function of angle of attack, sideslip angle, and deployment angle but not of angular velocity of deployment. Simulation with aerodynamic damping model gave more similar deployment time compared to wing deployment test results.

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.245-250
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• 2008

For simulation of a wing unfolding motion for the various aerodynamic conditions, equation governing unfolding motion and moments applying to the unfolding wing were modelled. Aerodynamic roll moment consists of the static roll moment and the damping moment, which were obtained through wind tunnel tests and numerical analyses respectively. Panel method was used to compute the roll damping coefficient with twisted wing, whose deflection angle was equivalent to angle of attack due to the deployment motion. Roll damping coefficient is a function of angle of attack, sideslip angle, and deployment angle but not of angular velocity of deployment. Simulation with aerodynamic damping model gave more similar deployment time compared to wing deployment test results.

• The korean journal of orthodontics
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• v.31 no.3 s.86
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• pp.335-346
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• 2001

The purpose of this study was to investigate the ideal clinical torque(In the SWA rectangular wire, the torque by the angle between the plane part and twisted part to move the tooth) of the orthodontic rectangular wire which produce the proper labiolingual movement of the single tooth during finishing stage of the orthodontic treatment. The clinical torque is the sum of the play and the active torque which generates the moment at the bracket. The play is calculated by the formula and the active torque is calculated by the computer aided three-dimensional finite element method. The finite element model was consist of the three brackets which formed a row and 3 kinds of orthodontic rectangular wire(stainless steel, TMA, NiTi) which inserted in brackets. Both sides of the model were twisted and the moment generated in the center bracket was calculated. The sizes of seven wires which were used commonly were .016'X.022', .017'X.022', .017'X.025', .018'X.025', .019'X.025', .020'X.025', .021'X.025'. In 018' bracket, 016'X.022', .017'X.022', .017'X.025' wires were inserted and in 022' bracket, all the sizes of wires except .016'X.022' were inserted and tested. The following conclusions could be drawn from this study. 1. The moments generated on the same size of the wires by the same active torque were equal regardless of the bracket slot size. 2. The moments were increased with the size of the wires. The moment generated on the .021'X.025' wire was about 1.75 times as large as that on the .016'X.022' wire regardless of the material. 3. The moments were increased in the order of the NiTi, TMA stainless steel. The moment of the TMA wire was 0.35 times as small as that of the stainless steel wire and the moment of the NiTi was0.16 times as small as that of the stainless steel wire. 4. The moment was decreased as the interbracket distance was increased. 5. To get a desired moment with the specific size and material of the wire on the specific bracket slot, the formula and the results were displayed.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.1
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• pp.30-45
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• 2013

The present work focuses on the unsteady aerodynamics and aeroelastic properties of a small-medium sized wind-turbine blade operating under ideal conditions. A tapered/twisted blade representative of commercial blades used in an experiment setup at the National Renewable Energy Laboratory is considered. The aerodynamic loads are computed using Computational Fluid Dynamics (CFD) techniques. For this purpose, FLUENT$^{(R)}$, a commercial finite-volume code that solves the Navier-Stokes and the Reynolds-Averaged Navier-Stokes (RANS) equations, is used. Turbulence effects in the 2D simulations are modeled using the Wilcox k-w model for validation of the CFD approach. For the 3D aerodynamic simulations, in a first approximation, and considering that the intent is to present a methodology and workflow philosophy more than highly accurate turbulent simulations, the unsteady laminar Navier-Stokes equations were used to determine the unsteady loads acting on the blades. Five different blade pitch angles were considered and their aerodynamic performance compared. The structural dynamics of the flexible wind-turbine blade undergoing significant elastic displacements has been described by a nonlinear flap-lag-torsion slender-beam differential model. The aerodynamic quasi-steady forcing terms needed for the aeroelastic governing equations have been predicted through a strip-theory based on a simple 2D model, and the pertinent aerodynamic coefficients and the distribution over the blade span of the induced velocity derived using CFD. The resulting unsteady hub loads are achieved by a first space integration of the aeroelastic equations by applying the Galerkin's approach and by a time integration using a harmonic balance scheme. Comparison among two- and three- dimensional computations for the unsteady aerodynamic load, the flap, lag and torsional deflections, forces and moments are presented in the paper. Results, discussions and pertinent conclusions are outlined.