• Computational Structural Engineering
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• v.10 no.1
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• pp.159-171
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• 1997

This study investigates the stress distribution in a transversely isotropic medium containing a spheroidal cavity where the medium is under uniaxial tension in z-direction in one case and pure shear in the plane of isotropy in another case. The technical approach used in this study combines exact analytical and numerical methods. The exact analytical method is based upon three potential functions taken in terms of the Legendre associated functions of the first and second kind. The numerical method is based upon the finite difference approach. Numerical results concerning the two loading conditions with five anisotropic materials are presented.

• Journal of the Korean Magnetics Society
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• v.9 no.5
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• pp.227-233
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• 1999

The magnetic field in single-layer solenoid with multi-current is calculated using Elliptical function, Legendre polynomials and Biot-Savart law. The optimization conditions to a highly uniform magnetic field in the center of solenoid has been studied. The variation of magnetic field depending on radius difference was examined. The uniformity of magnetic field is compared with that obtained each multi-current method. The five-current method increases the working space within 0.02 ppm uniformity by eighty times that using single current method. And this method improves the magnetic field uniformity which is equivalent to the effect of 160 m long solenoid by using single current.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.169-183
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• 2019

The main aim of this paper is to establish a new class of integrals involving the generalized Galu$Galu{\grave{e}}$-type Struve function with the different type of polynomials such as Jacobi, Legendre, and Hermite. Also, we derive the integral formula involving Legendre, Wright generalized Bessel and generalized Hypergeometric functions. The results obtained here are general in nature and can deduce many known and new integral formulas involving the various type of polynomials.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.469-477
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• 2024

For a knot in the 3-sphere, the Upsilon invariant is a piecewise linear function defined on the interval [0, 2]. It is known that this invariant of an L-space knot is the Legendre-Fenchel transform (or, convex conjugate) of a certain gap function derived from the Alexander polynomial. To recover an information lost in the Upsilon invariant, Kim and Livingston introduced the secondary Upsilon invariant. In this note, we prove that the secondary Upsilon invariant of an L-space knot is a concave conjugate of a restricted gap function. Also, a similar argument gives an alternative proof of the above fact that the Upsilon invariant of an L-space knot is a convex conjugate of a gap function.

• Kyungpook Mathematical Journal
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• v.13 no.1
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• pp.21-25
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• 1973

• Kyungpook Mathematical Journal
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• v.12 no.1
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• pp.103-114
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• 1972

• Kyungpook Mathematical Journal
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• v.10 no.1
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• pp.53-57
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• 1970

• Kyungpook Mathematical Journal
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• v.10 no.2
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• pp.107-113
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• 1970

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.311-319
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• 1978

This paper deals with the evaluation of two definite integrals involving spheroidal wave function, H-function of two variables, and the generalized hypergeometric function. Also, an expansion formula for the product of generalized hypergeometric function and the H-function of two variables has been obtained. Since the H-function of two variables, spheroidal wave functions, and the generalized hypergeometric function may be transformed into a number of higher transcendental functions and polynomials, the results obtained in this paper include some known results as their particular cases. As an application of such results, a problem of heat conduction in a non-homogenous bar has been solved by using the generalized Legendre transform [9].

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.6
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• pp.1273-1278
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• 1997

Pseudonoise sequences of period 2$^{m}$ -1 with idel autocorrelation have been researched such as m-sequences, GMW sequences, Legendre sequences, and extended sequences. The m-sequences, the GMW sequences, the Legendre sequences, and the extended sequences are best described in terms of the trace function by previous works. Besides, there are Hall's sextic residue sequences and miscellaneous sequences with ideal autocorrelation, whose general constructions are not known so far. However, are are no explicit descripton of the Hall's sextic residue sequences and the miscellaneous sequences in terms of the trace function. In this paper, the Hall's sextic residue sequences and the miscellaneous sequences of period 2$^{m}$ -1 are expressed as a sum of trace functions. The miscellaneous sequences with ideal autocorrelation, which are newly found by computer search, are also expressed as a sum of trace functions.