• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.1100-1102
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• 2000

Most systems in tile real world are non-linear and can be represented by the non-linear autoregressive moving average (NARMA) model. The extension of fuzzy system for modeling the system that is represented by NARMA model will be proposed in this paper. Here, fuzzy basis function (FBF) is used as fuzzy NARMA(p,q) model. Then, an approach to Identify fuzzy NARMA models based on fuzzy basis functions is proposed. The efficacy of the proposed approach is shown from experimental results.

• Structural Engineering and Mechanics
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• v.81 no.5
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• pp.607-616
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• 2022

In this work, the free vibration problem of a rotating Rayleigh beam is solved using the meshless Petrov-Galerkin method which is a truly meshless method. The Rayleigh beam includes rotatory inertia in addition to Euler-Bernoulli beam theory. The radial basis functions, which satisfy the Kronecker delta property, are used for the interpolation. The essential boundary conditions can be easily applied with radial basis functions. The results are obtained using six nodes within a subdomain. The results accurately match with the published literature. Also, the results with Euler-Bernoulli are obtained to compare the change in higher natural frequencies with change in the slenderness ratio (${\sqrt{A_0R^2/I_0}}$). The mass and stiffness matrices are derived where we get two stiffness matrices for the node and boundary respectively. The non-dimensional form is discussed as well.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.767-788
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• 2004

The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.405-424
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• 2018

In this paper we study some comparative growth properties of composite entire functions on the basis of relative (p, q)-th order and relative (p, q)-th lower order of entire function with respect to another entire function where p and q are any two positive integers.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.619-635
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• 2017

In this paper we establish some newly developed results related to the growth rates of composite entire functions on the basis of their generalized relative orders and generalized relative lower orders.

• Journal of Ocean Engineering and Technology
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• v.23 no.5
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• pp.1-8
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• 2009

This paper is a continuation of the recent development on Hermite-based divergence free element method and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square enclosure with temperature difference across the two sides. The basis functions for the velocity field consist of the Hermite function and its curl while the basis functions for the temperature field consists of the Hermite function and its gradients. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x and y derivatives. This paper presents numerical results for Ra = 105, and compares with those from a stabilized finite element method developed by Illinca et al. (2000). The comparison has been done on 32 by 32 uniform elements and the degree of approximation of elements used for the stabilized finite element are linear (Deg. 1) and quadratic (Deg. 2). The numerical results from both methods show well agreements with those of De vahl Davi (1983).

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.6
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• pp.47-52
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• 2002

The wavelet functions are originated from scaling functions and can be used as activation function in the hidden node of the network by deciding two parameters such as scale and center. In this paper, we would like to propose the mixed structure. When we compose the WNN using wavelet functions, we propose to set a single scale function as a node function together. The properties of the proposed structure is that while one scale function approximates the target function roughly, the other wavelet functions approximate it finely. During the determination of the parameters, the wavelet functions can be determined by the global search algorithm such as genetic algorithm to be suitable for the suggested problem. Finally, we use the back-propagation algorithm in the learning of the weights.

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.2
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• pp.26-35
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• 1996

In this paper, some fundamental problems concerning RBF(radial-basis-function) networks and approximation of functions are addressed. First, a comprehensive introduction to RBF networks is given with typical RBF networks classified into three classes. Next, sharp conditions are given under which continuous functions of a finite number of real variables can be approximated arbitrarily well by a certain class of RBF networks. Finally, a related result is given concerning the representation of functions in the form of distributed RBF networks.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.615-625
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• 2018

In this paper, we discuss the connection between the 5-dimensional complex Lie algebra ${\mathcal{K}} _5$ and Special functions. We construct certain two variable models of the irreducible representations of ${\mathcal{K}}_5$. We also use an Euler type integral transformation to obtain the new transformed models, in which the basis function appears as $_2F_1$. Further, we utilize these models to get some generating functions and recurrence relations.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.629-663
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• 2018

Let us suppose that ${\mathbb{K}}$ be a complete ultrametric algebraically closed field and $\mathcal{A}$ (${\mathbb{K}}$) be the ${\mathbb{K}}$-algebra of entire functions on K. The main aim of this paper is to study some newly developed results related to the growth rates of iterated p-adic entire functions on the basis of their relative orders, relative type and relative weak type.