• 대한수학회논문집
• /
• 제33권2호
• /
• pp.549-560
• /
• 2018

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

• Nuclear Engineering and Technology
• /
• 제2권4호
• /
• pp.263-268
• /
• 1970

시간과 에너지에 종속된 중성자 전도 방정식에 나타나는 연속 에너지 전도 연산자의 스펙트럼(Spectrum)을 분석했다. 스펙트럼에 관한 4가지 정리를 증명하고 일반화된 Mellin 에너지변화의 Convolution 정리를 얻었다. 또한 최종해에 필요한 완전성정리를 증명하고 점근적으로 가장 우세한 시간붕괴상수 1 - c를 발견하였다.

• 대한수학회보
• /
• 제53권5호
• /
• pp.1497-1530
• /
• 2016

External barrier options are two-asset options with stochastic variables where the payoff depends on one underlying asset and the barrier depends on another state variable. The barrier state variable determines whether the option is knocked in or out when the value of the variable is above or below some prescribed barrier level. This paper derives the explicit analytic solution of the chained option with an external single or double barrier by utilizing the probabilistic methods - the reflection principle and the change of measure. Before we do this, we examine the closed-form solution of the external barrier option with a single or double-curved barrier using the methods of image and double Mellin transforms. The exact solution of the external barrier option price enables us to obtain the pricing formula of the chained option with the external barrier more easily.

• Kyungpook Mathematical Journal
• /
• 제57권3호
• /
• pp.393-400
• /
• 2017

Very recently, Srivastava et al. [8] introduced an extension of the Pochhammer symbol and used it to define a generalization of the generalized hypergeometric functions. In this paper, by using the generalized Pochhammer symbol, we extend the generalized Hurwitz-Lerch Zeta function by Goyal and Laddha [6] and investigate some interesting properties which include various integral representations, Mellin transforms, differential formula and generating function. Some interesting special cases of our main results are also considered.

• 대한토목학회논문집
• /
• 제34권5호
• /
• pp.1639-1644
• /
• 2014

SAR 센서는 마이크로파를 이용한 능동센서로 기상조건에 상관없이 영상을 취득할 수 있다는 장점이 있어, 국토관리 및 재해 모니터링 등에 활발히 활용되고 있다. 주기적으로 취득되는 SAR 영상을 효과적으로 활용하기 위해서는 자동화된 영상 정합기법이 필요하지만 영상의 촬영 시간 및 기하에 따라 다른 양상의 기하조건을 가진 취득됨에 따라 충분한 정합 정확도를 기대하기 어렵다. 이에 본 연구에서는 기울기 속성을 추가한 MI (Mutual Information) 기법과 FMT (Fourier-Mellin Transform)기법, SIFT (Scale-Invariant Feature Transform) 기법을 임의의 변위와 회전 공차를 적용하고, 해상도를 변화시킨 TerraSAR-X 영상에 적용하여 그 결과를 비교하였다. 비교 결과, MI 기법의 경우엔 서로 상이한 기하에서 촬영된 영상에 적용하였을 때에도 일정 크기의 영상소가 다수 분포할 경우 0~2 픽셀 수준의 정확도를 지닐 수 있는 반면, FMT 기법의 경우에는 같은 사물에 대해서도 그 영상소 값이 서로 상이하여 정합 오차가 수십에서 수백 픽셀로 나타났다. 또한 SIFT 기법의 경우에도 영상 정합을 위한 공액점의 정확도가 0~17 % 수준으로 매우 낮아 서로 상이한 기하조건으로 취득된 SAR 영상에 적용이 어려울 것으로 나타났다.

• 대한수학회논문집
• /
• 제33권2호
• /
• pp.515-525
• /
• 2018

In this paper, we investigate a modified $G^2$ transform on a class of Boehmians. We prove the axioms which are necessary for establishing the $G^2$ class of Boehmians. Addition, scalar multiplication, convolution, differentiation and convergence in the derived spaces have been defined. The extended $G^2$ transform of a Boehmian is given as a one-to-one onto mapping that is continuous with respect to certain convergence in the defined spaces. The inverse problem is also discussed.

• Structural Engineering and Mechanics
• /
• 제48권2호
• /
• pp.241-255
• /
• 2013

The receding contact problem for two elastic layers whose elastic constants and heights are different supported by two elastic quarter planes is considered. The lower layer is supported by two elastic quarter planes and the upper elastic layer is subjected to symmetrical distributed load whose heights are 2a on its top surface. It is assumed that the contact between all surfaces is frictionless and the effect of gravity force is neglected. The problem is formulated and solved by using Theory of Elasticity and Integral Transform Technique. The problem is reduced to a system of singular integral equations in which contact pressures are the unknown functions by using integral transform technique and boundary conditions of the problem. Stresses and displacements are expressed depending on the contact pressures using Fourier and Mellin formula technique. The singular integral equation is solved numerically by using Gauss-Jacobi integration formulation. Numerical results are obtained for various dimensionless quantities for the contact pressures and the contact areas are presented in graphics and tables.

• 호남수학학술지
• /
• 제41권1호
• /
• pp.163-174
• /
• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

• 대한수학회논문집
• /
• 제32권2호
• /
• pp.321-332
• /
• 2017

In this paper, we generalize the extended Appell's and Lauricella's hypergeometric functions which have recently been introduced by Liu [9] and Khan [7]. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell's and Lauricella's hypergeometric functions.

• Kyungpook Mathematical Journal
• /
• 제45권1호
• /
• pp.1-11
• /
• 2005

Making use of the multidimensional fractional calculus operators introduced in [20], this paper gives the images under these operators of the celebrated Fox's H-function. Special cases are briefly point out, and some of the results are also studied on general spaces of functions $M_{\lambda}(R_{+}^n)$.