• Kyungpook Mathematical Journal
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• v.54 no.1
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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.

• Korean Journal of Computational Design and Engineering
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• v.6 no.4
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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.

• Proceedings of the KIEE Conference
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• 2006.10c
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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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• v.14 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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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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• v.13 no.4
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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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• v.50 no.2
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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.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.41 no.1
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• pp.77-85
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• 1996

To obtain basic information for characteristics of naked barley cultivars, awn length and weight, kernel weight along spikelet positions of some cultivars bred in Korea were investigated. Awn length and weight of third to fifth spikelet, and kernel weight of second to fourth spikelet from spike tip were not different from each mean value for total of spike. From the spike base, awn of third to fourth spikelet was longest and heaviest, and kernel weight of fifth to sixth spikelet was heaviest. Value for awn length, awn weight, and kernel weight of lateral row florets was lower 13 to 26％, 26 to 41％, and 18 to 25％, respectively than one for those of central row floret. Difference for awn length and weight between central and lateral row in nami type cultivars compared to uzu type cultivars was small. In the ratio of weight/length of awn, awn of uzu type cultivars was thicker than that of nami type cultivars, and awn of central row was thicker than those of lateral rows. Kernel weight was linearly related to awn weight. When one spike was divided into three parts, awn length and weight of low part were not different from those of central part, but were longer and heavier than those of upper part. The order of kernel weight was central$\geq$low>upper part.

• Korean Journal of Mathematics
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• v.31 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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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.