• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.5
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• pp.277-282
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• 2003

In this paper we propose Using Higher Order Neuron on the Supervised Learning Machine of the Kohonen Feature Map. The architecture of proposed model adopts the higher order neuron in the input layer of Kohonen Feature Map as a Supervised Learning Machine. It is able to estimate boundary on input pattern space because or the higher order neuron. However, it suffers from a problem that the number of neuron weight increases because of the higher order neuron in the input layer. In this time, we solved this problem by placing the second order neuron among the higher order neuron. The feature of the higher order neuron can be mapped similar inputs on the Kohonen Feature Map. It also is the network with topological mapping. We have simulated the proposed model in respect of the recognition rate by XOR problem, discrimination of 20 alphabet patterns, Mirror Symmetry problem, and numerical letters Pattern Problem.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.153-159
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• 2014

In this paper, we introduce a pair of higher-order symmetric dual models/problems. Weak, strong and converse duality theorems for this pair are established under the assumption of higher-order invexity. Moreover, self duality theorem is also discussed.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.87-99
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• 2017

To indicate the statistical complexity of dynamical systems, we introduce the notions of higher order irregular set and higher order maximal Birkhoff average oscillation in this paper. We prove that, in the setting of topologically mixing Markov chain, the set consisting of those points having maximal k-order Birkhoff average oscillation for all positive integers k is as large as the whole space from the topological point of view. As applications, we discuss the corresponding results on a repeller.

• ETRI Journal
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• v.23 no.1
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• pp.9-15
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• 2001

We suggest a generalized Lax pair on a Hermitian symmetric space to generate a new coupled higher-order nonlinear $Schr{\ddot{o}}dinger$ equation of a dual type which contains both bright and dark soliton equations depending on parameters in the Lax pair. Through the generalized ways of reduction and the scaling transformation for the coupled higher-order nonlinear $Schr{\ddot{o}}dinger$ equation, two integrable types of higher-order dark soliton equations and their extensions to vector equations are newly derived in addition to the corresponding equations of the known higher-order bright solitons. Analytical discussion on a general scalar solution of the higher-order dark soliton equation is then made in detail.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.105-112
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• 2006

The nonlinear damping force model is made to identify the properties of the ER (electro-rheological) fluid suspension damper. The instrumentation is carried out to measure the damping force of the ER damper. The higher order spectral analysis method is used to investigate the nonlinear frequency coupling phenomena with the damping force signal according to the sinusoidal excitation of the damper. The distinctive higher order nonlinear characteristics are observed. The nonlinear damping force model, which has the higher order velocity terms, is proposed with the result of higher order spectrum analysis. The higher order terms coefficients, which vary according to the strength of the electric field, are calculated using the least square method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.663-668
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• 2007

An enhanced first shear deformation theory for composite plate is developed. The detailed process is as follows. Firstly, the theory is formulated by modifying higher order zigzag theory. That is, the higher order theory is separated into the warping function representing the higher order terms and lower order terms. Secondly, the relationships between higher order zig-zag field and averaged first shear deformation field based on the Reissner-Mindlin's plate theory are derived. Lastly, the effective shear modulus is calculated by minimizing error between higher order energy and first order energy. Then the governing equation of FSDT is solved by substituting shear modulus into effective shear modulus. The recovery processing with the nodal unknown obtained from governing equation is performed. The accuracy of the present proposed theory is demonstrated through numerical examples. The proposed method will serve as a powerful tool in the prediction of laminated composite plate.

• East Asian mathematical journal
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• v.34 no.5
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• pp.601-614
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• 2018

In this paper, we introduce an extrapolated higher order characteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher order of convergence in the temporal and the spatial directions with respect to $L^2$ norm.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.135-142
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• 2000

We consider a multigrid algorithm for higher order finite difference scheme for the Poisson problem on rectangular domain. Several smoothers including Jacobi, Red-black Gauss-Seidel are tested and compared. Since higher order scheme gives much more accurate result then 5-point scheme, one may use small number of levels with higher order scheme and thus the overall cost is reduced quite a lot. The numerical experiment compares the two cases.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.695-708
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• 2022

In this paper, we present a new definition and generalization of the first and second kinds of Daehee numbers and polynomials with the higher order. Some new results for these polynomials and numbers are derived. Furthermore, some interesting special cases of the new generalized Daehee polynomials and numbers of higher order are deduced.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.173-179
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• 2011

The main aim of this paper is to give some relationships between q-Bernstein, higher order genocchi and Euler polynomials.