• 한국전자파학회논문지
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• 제17권8호
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• pp.788-794
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• 2006

본 논문에서는 임피던스 반 평면 문제에서 나오는 Sommerfeld 적분의 closed-form을 계산한다. 우선 주어진 Sommerfeld 적분을 두 개의 급수 형태로 표현한다. 급수 중 하나는 exponential integral로 알려진 초월 함수로, 다른 것은 Lommel 함수로 표현이 된다. Lommel 함수 표현으로부터 주어진 Sommerfeld 적분의 closed-form을 incomplete Weber integral로 표현한다. incomplete Weber integral은 여러 분야에서 사용되고 있고 많은 성질들이 알려져 있다. 또 exponential integral 함수 표현으로부터 Sommerfeld 적분을 incomplete Gamma 함수로 근사화한다. 구한 모든 식들은 수칙 적분 결과와 비교하여 validation을 한다.

• 대한수학회논문집
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• 제34권2호
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• pp.383-390
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• 2019

In this paper, we discuss special polynomials involving exponential distribution, which is related to life testing. We derive some identities of special polynomials such as the symmetric property, recurrence formula and so on. In addition, we investigate explicit properties of special polynomials by using their derivative and integral.

• 호남수학학술지
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• 제39권1호
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• pp.49-59
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• 2017

In this paper, a generalization of the exponential integral is given. As a consequence, several inequalities involving the generalized function are derived. Among other analytical techniques, the procedure utilizes the $H{\ddot{o}}lder^{\prime}s$ and Minkowskis inequalities for integrals.

• 한국재료학회지
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• 제4권5호
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• pp.574-580
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• 1994

본연구는 DSC (dynamic run)의 Barrett method Integral mdthod DGEBA/MDA/MN(malononitrile) DSC DSC pre exponential factor, kinetic parameter 들을 구할 수 있었다.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.349-369
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• 2013

The present paper envisages the $q$-analogue of the exponential operators, determined by G. Dattoli and his collaborators for translation and diffusive operators which were utilized to establish analytical solutions of difference and integral equations. The generalization of their technique is expected to cover wide range of such utilization.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권2호
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• pp.141-145
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• 2014

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi}^{\prime}(t)$ on (0, ${\infty}$).

• 전기학회논문지
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• 제59권6호
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• pp.1173-1178
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• 2010

In this note, a systematic design of a new robust nonlinear integral variable structure controller based on state dependent nonlinear form is presented for the control of uncertain more affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear integral variable structure controller is presented. To be linear in the closed loop resultant dynamics and remove the reaching phase problems, the linear integral sliding surface is suggested. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear integral sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 I
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• pp.629-632
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• 2003

This paper has been studied analysis and design of microstrip Rotman lens operating over wide band and wide steering angle by the contour integral method along with the segmentation method. All mutual coupling, internal reflections between ports with exponential taper are taken into account. Equally spaced ports are designed and realized which gives less amplitude ripple at array ports. The measured results of 12 input and 12 output lens show $\pm$1.8 dB insertion loss deviation over 6~18GHz wide frequency range and beam steering accuracy less than 1$^{\circ}$ over $\pm$53$^{\circ}$ angle and agrees well with the analysis results.

• 한국수학사학회지
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• 제27권6호
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• pp.409-419
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• 2014

In school mathematics, the logarithmic function is defined as the inverse function of an exponential function. And the natural logarithm is defined by the integral of the fractional function 1/x. But historically, Napier had already used the concept of logarithm in 1614 before the use of exponential function or integral. The calculation of the logarithm was a hard work. So mathematicians with arithmetic ability made the tables of values of logarithms and people used the tables for the estimation of data. In this paper, we first take a look at the mathematicians and mathematical principles related to the appearance and the developments of the logarithmic tables. And then we deal with the confusions between mathematicians, raised by the estimation data which were known as proportional parts or mean differences in common logarithmic tables.

• Structural Engineering and Mechanics
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• 제66권3호
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• pp.329-341
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• 2018

This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.