• International Journal of Knowledge Content Development & Technology
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• 제3권2호
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• pp.43-65
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• 2013

In this work, we first introduce two main approaches to writing requirements and then propose a method based on Natural Language Processing to improve requirement authoring and the overall coherence, cohesion and organization of requirement documents. We investigate the structure of requirement kernels, and then the discourse structure associated with those kernels. This will then enable the system to accurately extract requirements and their related contexts from texts (called requirement mining). Finally, we relate a first experimentation on requirement mining based on texts from seven companies. An evaluation that compares those results with manually annotated corpora of documents is given to conclude.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.347-354
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• 2010

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

• 한국식품영양학회지
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• 제7권4호
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• pp.267-273
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• 1994

To provide the effective application scheme and basic information of buckwheat (Fagopyrum esculentum Moench), buckwheat was germinated at 10$^{\circ}C$ for 7 days and 100 kernels weight, germination rate, root length, chemical composition and mineral contents were examined at 24 hour Intervals. During the germination period, the 100 kernels weight increased approximately 0.3g per day. The germination rate increased sharply after 2 days and the root length increased greatly after 4 days. The crude protein contents increased with germination time, whereas the carbohydrate contents decreased. The crude ash and fat contents did not differ significantly during the germination period. The Ca contents Increased for the 4th day of gemination, but gradually decreased afterwords. The Na contents increased in the initial stage of germination, but then gradually decreased. However, there were no significant change In the Mg, K. Fe. Mn and Zn contents.

• 대한수학회논문집
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• 제27권2호
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.465-480
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• 2019

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators $(K^{\varphi}_wf)_{w>0}$. First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the first order of modulus of continuity. Further, we study the order of approximation in $C({\mathbb{R}})$, the set of all uniformly continuous and bounded functions on ${\mathbb{R}}$ for the family $(K^{\varphi}_wf)_{w>0}$. Finally, we give some examples of kernels such as B-spline kernels and the Blackman-Harris kernel to which the theory can be applied.

• 대한수학회보
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• 제58권4호
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• pp.1003-1019
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• 2021

In this paper, we introduce a class of maximal functions along twisted surfaces in ℝⁿ×ℝ^m of the form {(𝜙(|v|)u, 𝜑(|u|)v) : (u, v) ∈ ℝⁿ×ℝ^m}. We prove L^p bounds when the kernels lie in the space L^q (𝕊^n-1×𝕊^m-1). As a consequence, we establish the L^p boundedness for such class of operators provided that the kernels are in L log L(𝕊^n-1×𝕊^m-1) or in the Block spaces B^0,0_q (𝕊^n-1×𝕊^m-1) (q > 1).

• East Asian mathematical journal
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• 제37권3호
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• pp.333-354
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• 2021

A support vector machine (SVM) is a state-of-the-art machine learning model rooted in structural risk minimization. SVM is underestimated with regards to its application to real world problems because of the difficulties associated with its use. We aim at showing that the performance of SVM highly depends on which kernel function to use. To achieve these, after providing a summary of support vector machines and kernel function, we constructed experiments with various benchmark datasets to compare the performance of various kernel functions. For evaluating the performance of SVM, the F1-score and its Standard Deviation with 10-cross validation was used. Furthermore, we used taylor diagrams to reveal the difference between kernels. Finally, we provided Python codes for all our experiments to enable re-implementation of the experiments.

• Communications for Statistical Applications and Methods
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• 제29권1호
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• pp.127-150
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• 2022

We discuss multiple change-point estimation as edge detection in piecewise smooth functions with finitely many jump discontinuities. In this paper we propose change-point estimators using concentration kernels with Fourier coefficients. The change-points can be located via the signal based on Fourier transformation system. This method yields location and amplitude of the change-points with refinement via concentration kernels. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of change-points with an almost optimal rate. In a simulation study the proposed change-point estimators are compared and discussed. Applications of the proposed methods are provided with Nile flow data and daily won-dollar exchange rate data.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송∙미디어공학회 2020년도 추계학술대회
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• pp.25-28
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• 2020

Automatic segmentation of brain tissues such as WM, GM, and CSF from brain MRI scans is helpful for the diagnosis of many neurological disorders. Accurate segmentation of these brain structures is a very challenging task due to low tissue contrast, bias filed, and partial volume effects. With the aim to improve brain MRI segmentation accuracy, we propose an end-to-end convolutional based U-SegNet architecture designed with multi-scale kernels, which includes cascaded dilated convolutions for the task of brain MRI segmentation. The multi-scale convolution kernels are designed to extract abundant semantic features and capture context information at different scales. Further, the cascaded dilated convolution scheme helps to alleviate the vanishing gradient problem in the proposed model. Experimental outcomes indicate that the proposed architecture is superior to the traditional deep-learning methods such as Segnet, U-net, and U-Segnet and achieves high performance with an average DSC of 93% and 86% of JI value for brain MRI segmentation.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.363-379
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• 2022

In this paper, we carried out a new numerical approach for solving integral algebraic equations with weakly singular kernels. The novel method is based on the construction of B-spline tight framelets using the unitary and oblique extension principles. Some numerical examples are given to provide further explanation and validation of our method. The result of this study introduces a new technique for solving weakly singular integral algebraic equation and thus in turn will contribute to providing new insight into approximation solutions for integral algebraic equation (IAE).