• 대한수학회논문집
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• 제27권1호
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• pp.107-116
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• 2012

Here, by using the symbolical method introduced by Burchnall and Chaundy, we aim at constructing certain expansion formulas for the generalized hypergeometric function $_pF_q$. In addition, using our expansion formulas for $_pF_q$, we present formulas of an analytic continuation of the Clausen hypergeometric function $_3F_2$, which are much simpler than an earlier known result. We also give some integral representations for $_3F_2$.

• JSTS:Journal of Semiconductor Technology and Science
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• 제13권1호
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• pp.34-42
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• 2013

Human faces have been broadly studied in digital image and video processing fields. An appearance-based method, the adaptive boosting learning algorithm using integral image representations has been successfully employed for face detection, taking advantage of the feature extraction's low computational complexity. In this paper, we propose a face-detection postprocessing method that equalizes instantaneous facial regions in an efficient hardware architecture for use in real-time multimedia applications. The proposed system requires low hardware resources and exhibits robust performance in terms of the movements, zooming, and classification of faces. A series of experimental results obtained using video sequences collected under dynamic conditions are discussed.

• 호남수학학술지
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• 제38권4호
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• pp.739-752
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• 2016

The main aim of this paper is to introduce an extension of the generalized ${\tau}$-Gauss hypergeometric function $_rF^{\tau}_s(z)$ and investigate various properties of the new function such as integral representations, derivative formulas, Laplace transform, Mellin trans-form and fractional calculus operators. Some of the interesting special cases of our main results have been discussed.

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

• 호남수학학술지
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• 제46권2호
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• Structural Engineering and Mechanics
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• 제71권6호
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• pp.627-641
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• 2019

The paper focuses on bending analysis of the functionally graded (FG) plates with arbitrary shapes and boundary conditions. The material property of FG plates is modelled by using the power law distribution. Based on the first order shear deformation plate theory (FSDT), the governing equations as well as boundary conditions are formulated and obtained by using the principle of virtual work. The coupled Boundary Element-Radial Basis Function (BE-RBF) method is established to solve the complex FG plates. The proposed methodology is developed by applying the concept of the analog equation method (AEM). According to the AEM, the original governing differential equations are replaced by three Poisson equations with fictitious sources under the same boundary conditions. Then, the fictitious sources are established by the application of a technique based on the boundary element method and approximated by using the radial basis functions. The solution of the actual problem is attained from the known integral representations of the potential problem. Therefore, the kernels of the boundary integral equations are conveniently evaluated and readily determined, so that the complex FG plates can be easily computed. The reliability of the proposed method is evaluated by comparing the present results with those from analytical solutions. The effects of the power index, the length to thickness ratio and the modulus ratio on the bending responses are investigated. Finally, many interesting features and results obtained from the analysis of the FG plates with arbitrary shapes and boundary conditions are demonstrated.

• 대한수학회지
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• 제52권4호
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• pp.853-868
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• 2015

Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of $\lambda$ an integral weight and $\underline{w}$ a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of $\lambda$ and $\underline{w}$.

• 제어로봇시스템학회논문지
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• 제20권9호
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• pp.930-935
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• 2014

A Gabor filter is a linear filter used for edge detectionas frequency and orientation representations of Gabor filters are similar to those of the human visual system. In this thesis, we propose a pedestrian detection algorithm using a Gabor filter bank. In order to extract the features of the pedestrian, we use various image processing algorithms and data structure algorithms. First, color image segmentation is performed to consider the information of the RGB color space. Second, histogram equalization is performed to enhance the brightness of the input images. Third, convolution is performed between a Gabor filter bank and the enhanced images. Fourth, statistical values are calculated by using the integral image (summed area table) method. The calculated statistical values are used for the feature matrix of the pedestrian area. To evaluate the proposed algorithm, the INRIA pedestrian database and SVM (Support Vector Machine) are used, and we compare the proposed algorithm and the HOG (Histogram of Oriented Gradient) pedestrian detector, presentlyreferred to as the methodology of pedestrian detection algorithm. The experimental results show that the proposed algorithm is more accurate compared to the HOG pedestrian detector.

• 한국전자파학회논문지
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• 제9권5호
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• pp.640-647
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• 1998

다중 분해능 웨이블릿 해석법을 마이크로스트립 패치 안테나의 산란해석에 적용하였다. 다충구조에 대한 스펙 트럼 영역 그린 함수(spectral domain Green's dyad)의 특성올 공간-스펙트럼 영역 표현법을 이용하여 살펴보고, 스펙트럼 영역 웨이블릿을 주어진 문제에 적용하는 것이 유용함을 관찰하였다. 적분방정식에 모멘트법을 이 용하여 행렬방정식을 얻고, 그 풀이에 CG(conjugate gradient)법과 스펙트럼 영역 웨이블릿올 결합하여 효율 적으로 문제를 풀이할 수 있다. 단충구조 위에 놓인 정방형 패치에 대하여 기폰의 모멘트법 결과와 다충 분해능 웨이블릿 해석법올 적용한 결과를 비교하였다.