• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.555-563
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• 2002

This paper discusses cubic equations in general saddlepoint approximations. Exact roots are found for various cases by trigonometric identities, the root which is appropriate for the general saddlepoint approximations is selected and discussed, and the defective cases in which the general saddlepoint approximations cannot be used are found.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1406-1409
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• 2004

The Resolver usually used in industry is the absolute angle analog sensor that must be in order to driving BLDC (brushless DC) motor, and it needs RDC(Resolver-to-Digital converter) for changing the output signal to digital to be applied to the SVPWM(Space Vector Pulse Width Modulation) algorithm. Commonly used S/W RDC needs trigonometric function. What it takes a lot of calculation time of processor is gotten at weak point. In this paper, S/W RDC is realized except trigonometric functions as a result of feedback resolver outputs after filtering using FIR filter. thus, processing time is reduced. So, One-chip DSP Controller operating the Vector Control, RDC, and SVPWM can be designed.

• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.87-97
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• 2004

In gradient-dependent plasticity theory, the yield strength depends on the Laplacian of an equivalent plastic strain measure (hardening parameter), and the consistency condition results in a differential equation with respect to the plastic multiplier. The plastic multiplier is then discretized in addition to the usual discretization of the displacements, and the consistency condition is solved simultaneously with the equilibrium equations. The disadvantage is that the plastic multiplier requires a Hermitian interpolation that has four degrees of freedom at each node. Instead of using a Hermitian interpolation, in this article, a 3-node incompatible (trigonometric) interpolation is proposed for the plastic multiplier. This incompatible interpolation uses only the function values of each node, but it is continuous across element boundaries and its second-order derivatives exist within the elements. It greatly reduces the degrees of freedom for a problem, and is shown through a numerical example on localization to yield good results.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.797-805
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• 2012

Many circular distributions are known to be not only asymmetric but also bimodal. Hidden truncation method of generating asymmetric distribution is applied to a bivariate circular distribution to generate an asymmetric circular distribution. While many other existing asymmetric circular distributions can only model an asymmetric data, this new circular model has great flexibility in terms of asymmetry and bi-modality. Some properties of the new model, such as the trigonometric moment generating function, and asymptotic inference about the truncation parameter are presented. Simulation and real data examples are provided at the end to demonstrate the utility of the novel distribution.

• Journal of Power Electronics
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• v.9 no.3
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• pp.499-506
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• 2009

In this paper, the initial pole-position estimation of a surface (non-salient) permanent magnet synchronous motor is mathematically analyzed and surveyed on the basis of simulation analysis, and developed for accurate servo motor drive. This algorithm is well carried out under the full closed-loop position control without any pole sensors and is completely insensitive to any motor parameters. This estimation is based on the principle that the initial pole-position is simply calculated by the reverse trigonometric function using the two feedback currents in the full closed-loop position control. The proposed algorithm consists of the predefined reference position profile, the information of feedback currents, speed, and relative position, and the reverse trigonometric function for the initial-pole position estimation. Comparing with the existing researches, the mathematical analysis is introduced to get a more accurate initial pole-position of the surface permanent magnet motor under the closed-loop position control. It is found that the proposed algorithm can be easily applied in servo drive applications because it satisfies the following user's specifications; accuracy and moving distance.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• East Asian mathematical journal
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• v.32 no.1
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• pp.43-46
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• 2016

The Clausen function $Cl_2$(x) arises in several applications. A large number of indefinite integrals of logarithmic or trigonometric functions can be expressed in closed form in terms of $Cl_2$(x). Very recently, Choi and Srivatava [3] and Choi [1] investigated certain integral formulas associated with $Cl_2$(x). In this sequel, we present an interesting new definite integral formula for the Clausen function $Cl_2$(x) by using a known relationship between the Clausen function $Cl_2$(x) and the generalized Zeta function ${\zeta}$(s, a). Also an interesting integral representation for the Catalan constant G is considered as one of two special cases of our main result.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.393-419
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• 2020

Trigonometry allows us to recognize the usefulness of mathematics through connection with real life and other disciplines, and lays the foundation for the concept of higher mathematics through connection with trigonometric functions. Since international comparisons on the trigonometry area of textbooks can give implications to trigonometry teaching and learning in Korea, this study attempted to compare trigonometry in textbooks in Korea, Australia and Finland. In this study, through the horizontal and vertical analysis presented by Charalambous et al.(2010), the objectives of the curriculum, content system, achievement standards, learning timing of trigonometry content, learning paths, and context of problems were analyzed. The order of learning in which the three countries expanded size of angle was similar, and there was a difference in the introduction of trigonometric functions and the continuity of grades dealing with trigonometry. In the learning path of textbooks on the definition method of trigonometric ratios, the unit circle method was developed from the triangle method to the trigonometric function. However, in Korea, after the explanation using the quadrant in middle school, the general angle and trigonometric functions were studied without expanding the angle. As a result of analyzing the context of the problem, the proportion of problems without context was the highest in all three countries, and the rate of camouflage context problem was twice as high in Korea as in Australia or Finland. Through this, the author suggest to include the unit circle method in the learning path in Korea, to present a problem that can emphasize the real-life context, to utilize technological tools, and to reconsider the ways and areas of the curriculum that deal with trigonometry.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.667-677
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• 2013

A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind $J_{\nu}(z)$. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.

• Journal of The Korean Astronomical Society
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• v.26 no.2
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• pp.141-152
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• 1993

The sample of sub dwarfs are selected from LHS catalogue on the bases of the reduced proper motion diagram utilizing Chui criteria, and confirmed with the available photometric and/or kinematic data. Among them, 20 sub dwarfs have trigonometric parallaxes with accuracy better than $20\%$. The color­absolute magnitude relation is derived with them. By adopting this color-magnitude relation and $V/V_m$ method, we have derived the sub dwarf luminosity function over the absolute magnitude range of $M_v$= 4.5 and 9.5. This halo luminosity function is consistent with that of Eggen(1987). By adopting the available mass-luminosity relations for halo stars, we have found that the halo IMF is steeper than disk IMFs of Scalo(1986) and Salpter(1955) in this small mass region.