• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.1-9
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• 2014

We build new Hilbert-type integral inequalities in the whole plane with the non-homogeneous kernel involving some parameters and the best constant factors. We also consider their reverse.

• 한국CDE학회논문집
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• 제6권4호
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• pp.271-276
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• 2001

A geometric kernel is the library of core mathematical functions that defines and stores 3D shapes in response to users'commands. We developed a light geometric kernel suitable to develop CAD/CAM application systems. The kernel contains geometric objects, such as points, curves and surfaces and a minimal set of functions for each type but does not contain lots of modeling and handling functions that are useful to create and maintain complex shapes from an idea sketch. The kernel was developed on MS-Windows NT using C++ with STL(Standard Template Library) but it is compatible with UNIX environments. This paper describes the structure of the kernel including several components: base, math, point sequence curve, geometry, translators. The base kernel gives portability to applications and the math kernel contains basic arithmetic and their classes, such as vector and matrix. The geometry kernel contains points, parametric curves, and parametric surfaces. A neutral fie format and programming and document styles are also presented in this paper.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년 학술대회 논문집 정보 및 제어부문
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• pp.211-213
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• 2006

In this study, plasma etching process was modeled by using support vector machine (SVM). The data used in modeling were collected from the etching of silica thin films in inductively coupled plasma. For training and testing neural network, 9 and 6 experiments were used respectively. The performance of SVM was evaluated as a function of kernel type and function type. For the kernel type, Epsilon-SVR and Nu-SVR were included. For the function type, linear, polynomial, and radial basis function (RBF) were included. The performance of SVM was optimized first in terms of kernel type, then as a function of function type. Five film characteristics were modeled by using SVM and the optimized models were compared to statistical regression models. The comparison revealed that statistical regression models yielded better predictions than SVM.

• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.929-937
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• 2003

Kernel type estimations of discontinuity point at an unknown location in regression function or its derivatives have been developed. It is known that the discontinuity point estimator based on $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a zero value at the point 0 makes a poor asymptotic behavior. Further, the asymptotic variance of $Gasser-M\ddot{u}ller$ regression estimator in the random design case is 1.5 times larger that the one in the corresponding fixed design case, while those two are identical for the local polynomial regression estimator. Although $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a non-zero value at the point 0 for the modification is used, computer simulation show that this phenomenon is also appeared in the discontinuity point estimation.

• 대한수학회지
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• 제39권3호
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• pp.425-437
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• 2002

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^{n}$ and let $z^{0}$ $\in$b$\Omega$ a point of finite type. We also assume that the Levi form of b$\Omega$ is comparable in a neighborhood of $z^{0}$ . Then we get precise estimates of the Bergman kernel function, $K_{\Omega}$(z, w), and its derivatives in a neighborhood of $z^{0}$ . .

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권4호
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• pp.254-268
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• 2013

For real-world clustering tasks, the input data is typically not easily separable due to the highly complex data structure or when clusters vary in size, density and shape. Kernel-based clustering has proven to be an effective approach to partition such data. In this paper, we provide an overview of several fuzzy kernel clustering algorithms. We focus on methods that optimize an fuzzy C-mean-type objective function. We highlight the advantages and disadvantages of each method. In addition to the completely unsupervised algorithms, we also provide an overview of some semi-supervised fuzzy kernel clustering algorithms. These algorithms use partial supervision information to guide the optimization process and avoid local minima. We also provide an overview of the different approaches that have been used to extend kernel clustering to handle very large data sets.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.307-314
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• 2010

By introducing a homogeneous kernel of 0-degree with an independent parameter and estimating the weight coefficient, a bilateral form of the Hilbert-type series inequality with a best constant factor is established.

• 한국작물학회지
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• 제41권1호
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• pp.77-85
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• 1996

쌀보리의 이삭에 관한 기초자료를 얻고자 우리나라에서 육성한 쌀보리의 품종을 공시하여 소수위치에 따른 망의 길이와 무게, 입중 등을 조사한 바 그 결과를 요약하면 다음과 같다. 1. 이삭의 정단부로부터 3∼5번째 소수가 망장 및 망중의 평균치와, 2∼4번째 소수가 입중의 평균치와 각각 일치하였다. 2. 이삭의 기부로부터 3∼4번째 소수의 망이 가장 길고 무거웠으며 5∼6번째 소수의 입중이 가장 무거웠다. 3. 측열 소수는 중앙열 소수에 비하여 망장은 13∼26%, 망중은 26∼41%, 입중은 18∼25% 적은 값을 보였다. nami형 품종은 uzu형 품종에 비하여 중앙열과 측열간 망장, 망중 차이가 적었다. 4. 망중/망장 비로 볼 때 uzu형 품종은 nami형 품종보다, 그리고 중앙열은 측열보다 망이 더 굵었다. 5. 이삭을 3등분하였을 때 망장, 망중은 하부와 중앙부 차이가 없었으나 상부보다는 길고 무거웠다. 입중은 상부가 항상 가벼웠고 중앙부는 하부보다 무겁거나 같았다. 6. 망중이 무거운 소술일수록 입중이 무거웠다.

• Korean Journal of Mathematics
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• 제31권2호
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• pp.189-201
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• 2023

In this article, we establish Hilbert-type integral inequalities with the help of a non-homogeneous kernel of hyperbolic function with best constant factor. We also study the obtained inequalities's equivalent form. Additionaly, several specific Hilbert's type inequalities with constant factors in the term of the rational fraction expansion of higher order derivatives of cotangent and cosine functions are presented.

• 대한수학회논문집
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• 제35권1호
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• pp.125-136
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• 2020

In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's H-function kernel. We employ a known differentiation formula of Fox's H-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.