• 전기학회논문지
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• 제64권1호
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• pp.128-135
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• 2015

In this study, we develop the very short-term precipitation forecasting model as well as classifier based on polynomial radial basis function neural networks by using AWS(Automatic Weather Station) and KLAPS(Korea Local Analysis and Prediction System) meteorological data. The polynomial-based radial basis function neural networks is designed to realize precipitation forecasting model as well as classifier. The structure of the proposed RBFNNs consists of three modules such as condition, conclusion, and inference phase. The input space of the condition phase is divided by using Fuzzy C-means(FCM) and the local area of the conclusion phase is represented as four types of polynomial functions. The coefficients of connection weights are estimated by weighted least square estimation(WLSE) for modeling as well as least square estimation(LSE) method for classifier. The final output of the inference phase is obtained through fuzzy inference method. The essential parameters of the proposed model and classifier such ad input variable, polynomial order type, the number of rules, and fuzzification coefficient are optimized by means of Particle Swarm Optimization(PSO) and Differential Evolution(DE). The performance of the proposed precipitation forecasting system is evaluated by using KLAPS meteorological data.

• 대한수학회지
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• 제50권5호
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• 대한수학회지
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• 제55권3호
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• pp.705-717
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• 2018

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly determined, a Milnor fiber homotopy equivalent to a bouquet of circles, or an irreducible translated component in the characteristic variety of their complement. Monodromy eigenspaces in the first cohomology group of the corresponding Milnor fibers are also described in terms of explicit differential forms.

• 호남수학학술지
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• 제44권3호
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• pp.391-401
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• 2022

In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.

• 한국지능시스템학회논문지
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• 제23권5호
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• pp.473-478
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• 2013

본 논문에서는 KLAPS(Korea Local Analysis and Prediction System)의 재분석 자료를 이용하여 지능형 뉴로-퍼지 알고리즘 RBFNNs(Polynomial-based Radial Basis Function Neural Networks) 기반 호우특보 판별 모델을 개발한다. 기존의 호우예측 시스템들의 예측능력은 일반적으로 기상데이터의 가공 기법의 영향을 받는다. 본 연구에서는 이를 보완하기 위하여 기상데이터의 전처리를 통한 호우예측 방법을 소개한다. 기상 데이터 전처리 기법은 KLAPS 데이터를 기반으로 지점별 변환, 누적강수량 생성, 시계열 데이터 가공, 호우특보 추출 방식에 의하여 설계된다. 최종적으로, 향후 t(t=1,2,3) 시간 후 6시간 동안 누적강수량에 대해 예측하고 호우특보를 결정하기 위한 정보를 제공한다. 또한 다항식의 형태, 규칙의 개수, 퍼지화 계수와 같은 제안된 모델의 중요 파라미터는 최적화 기법인 차분 진화(Differential Evolution; DE)를 이용하여 최적화한다.

• 대한수학회논문집
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• 제12권3호
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• pp.603-617
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• 1997

Consider a Sobolev inner product on the space of polynomials such as $$ \phi(p,q) = \lambda p(c)q(c) + <\tau,p'(x)q'(x)> $$ where $\tau$ is a moment functional and c and $\lambda$ are real constants. We investigate properties of orthogonal polynomials relative to $\phi(\cdot,\cdot)$ and give necessary and sufficient conditions under which such Sobolev orthogonal polynomials satisfy a spectral type differential equation with polynomial coefficients.

• 대한수학회보
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• 제52권1호
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• pp.13-33
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• 2015

In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.

• Kyungpook Mathematical Journal
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• 제50권3호
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• pp.447-454
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• 2010

In this paper, we investigate the uniqueness problems of meromorphic functions that share a small function with its differential polynomials, and give a result which is related to a conjecture of R. Br$\"{u}$ck and improve the results of I. Lahiri and Q. C. Zhang.

• 대한수학회보
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• 제47권2호
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• pp.319-339
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• 2010

In this paper, we prove that if $f^nf'\;-\;P$ and $g^ng'\;-\;P$ share 0 CM, where f and g are two distinct transcendental meromorphic functions, $n\;{\geq}\;11$ is a positive integer, and P is a nonzero polynomial such that its degree ${\gamma}p\;{\leq}\;11$, then either $f\;=\;c_1e^{cQ}$ and $g\;=\;c_2e^{-cQ}$, where $c_1$, $c_2$ and c are three nonzero complex numbers satisfying $(c_1c_2)^{n+1}c^2\;=\;-1$, Q is a polynomial such that $Q\;=\;\int_o^z\;P(\eta)d{\eta}$, or f = tg for a complex number t such that $t^{n+1}\;=\;1$. The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Hua, and other authors.

• 대한수학회보
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• 제57권4호
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• pp.1061-1073
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• 2020

In this paper, the expressions of meromorphic solutions of the following nonlinear complex differential equation of the form $$f^n+Qd(z,f)=\sum\limits_{i=1}^{3}pi(z)e^{{\alpha}_i(z)}$$ are studied by using Nevanlinna theory, where n ≥ 5 is an integer, Q_d(z, f) is a differential polynomial in f of degree d ≤ n - 4 with rational functions as its coefficients, p₁(z), p₂(z), p₃(z) are non-vanishing rational functions, and α₁(z), α₂(z), α₃(z) are nonconstant polynomials such that α'₁(z), α'₂(z), α'₃(z) are distinct each other. Moreover, examples are given to illustrate the accuracy of the condition.