• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.43-55
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• 1996

Explicit formulas for bi-Hermite polynomials are found and their combinatorial model is considered. This combinatorial model is a generalization of the combinatorial model of Hermite polynomials as matching polynomials.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.779-806
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• 2015

We construct a state model for the two-variable Kauman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in $\mathbb{R}^3$.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.7
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• pp.1315-1320
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• 2007

In this paper, we introduce a new fuzzy model called fuzzy combined polynomial neural networks, which are based on the representative fuzzy model named polynomial fuzzy model. In the design procedure of the proposed fuzzy model, the coefficients on consequent parts are estimated by using not general least square estimation algorithm that is a sort of global learning algorithm but weighted least square estimation algorithm, a sort of local learning algorithm. We are able to adopt various type of structures as the consequent part of fuzzy model when using a local learning algorithm. Among various structures, we select Polynomial Neural Networks which have nonlinear characteristic and the final result of which is a complex mathematical polynomial. The approximation ability of the proposed model can be improved using Polynomial Neural Networks as the consequent part.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.869-878
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• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

• Journal for History of Mathematics
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• v.36 no.1
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• pp.1-17
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• 2023

Paper folding is a versatile tool that can be used not only as a mathematical model for analyzing the geometric properties of plane and spatial figures but also as a visual method for finding the real roots of polynomial equations. The historical evolution of origami's geometric and algebraic techniques has led to the discovery of definitions and properties that can enhance one's cognitive understanding of mathematical concepts and generate mathematical interest and motivation on an emotional level. This paper aims to examine the history of origami geometry, the utilization of origami for solving polynomial equations, and the process of determining the real roots of quadratic, cubic, and quartic equations through origami techniques.

• Journal of the Korean Geotechnical Society
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• v.21 no.2
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• pp.145-150
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• 2005

It is useful to select an appropriate mathematical model to predict landslide. Through observation and analysis of real-time measured time series, a reasonable mathematic model is chosen to do prediction of landslide. Two theoretical models, such as polynomial function and growth model, are suggested for the description and analysis of measured defermation from an active landslides. These models are applied herein to describe the main characteristics of defermation process for two types of landslide, namely polynomial and growth models. The TRS (tensiof rotation and settlement) sensors are applied to adopt two models, and the data analysis of two field (Neurpjae and Buksil) resulted in good coincidence between measured data and models.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.1
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• pp.130-140
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• 1998

This paper presents a method to estimate subpixel accuracy motion vectors using a mathermatical model withoug interpolation. the proposed method decides the coefficients of mathematical model, which represents the motion vector which is achieved by full search. And then the proposed method estimates subpixel accuracy motion vector from achieved mathematical model. Step by step mathematical models such as type 1, type 2, type 3, modified bype 2, modified type 3, and Partial Interpolation type 3 are presented. In type 1, quadratic polynomial, which has 9 unknown coefficients and models the 3by 3 pixel plane, is used to get the subpixel accuracy motion vectors by inverse matrix solution. In type 2 and 3, each quadratic polynomial which is simplified from type 1 has 5 and 6 unknown coefficients and is used by least square solution. Modified type 2 and modified type 3 are enhanced models by weighting only 5 pixels out of 9. P.I. type 3 is more accurate method by partial interpolation around subpixel which isachieved by type 3. LThese simulation results show that the more delicate model has the better performance and modified models which are simplified have excellent performance with reduced computational complexity.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.767-779
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• 2003

We consider a model of population dynamics whose mortality function is unbounded. We approximate the solution of the model using a discontinuous Galerkin finite element for the age variable and a backward Euler for the time variable. We present several numerical examples. It is experimentally shown that the scheme converges at the rate of $h^{3/2}$ in the case of piecewise linear polynomial space.

• Geomechanics and Engineering
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• v.23 no.6
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• pp.547-560
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• 2020

This paper studies the dynamic foundation-soil-foundation interaction for two square rigid foundations embedded in a viscoelastic soil layer. The vibrations come from only one rigid foundation placed in the soil layer and subjected to harmonic loads of translation, rocking, and torsion. The required dynamic response of rigid surface foundations constitutes the solution of the wave equations obtained by taking account of the conditions of interaction. The solution is formulated using the frequency domain Boundary Element Method (BEM) in conjunction with the Kausel-Peek Green's function for a layered stratum, with the aid of the Thin Layer Method (TLM), to study the dynamic interaction between adjacent foundations. This approach allows the establishment of a mathematical model that enables us to determine the dynamic displacements amplitude of adjacent foundations according to their different separations, the depth of the substratum, foundations masss, foundations embedded, and the frequencies of excitation. This paper attempts to introduce an approach based on a polynomial mathematical tool conducted from several results of numerical methods (BEM-TLM) so that practicing civil engineers can evaluation the dynamic foundations displacements more easy.

• Korean Journal of Food Science and Technology
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• v.37 no.2
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• pp.194-198
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• 2005

Growth curves of Listeria monocytogenes in modified surimi-based imitation crab (MIC) broth were obtained by measuring cell concentration in MIC broth at different culture conditions [initial cell numbers, $1.0{\times}10^{2},\;1.0{\times}10^{3}\;and\;1.0{\times}10^{4}$, colony forming unit (CFU)/mL; temperature, 15, 20, 25, 37, and $40^{\circ}C$] and applied to Gompertz model to determine microbial growth indicators, maximum specific growth rate constant (k), lag time (LT), and generation time (GT). Maximum specific growth rate of L. monocytogenes increased rapidly with increasing temperature and reached maximum at $37^{\circ}C$, whereas LT and GT decreased with increasing temperature and reached minimum at $37^{\circ}C$. Initial cell number had no effect on k, LT, and GT (p > 0.05). Polynomial and square root models were developed to express combined effects of temperature and initial cell number using Gauss-Newton Algorism. Relative coefficients of experimental k and predicted k of polynomial and square root models were 0.92 and 0.95, respectively, based on response surface model. Results indicate L. monocytogenes growth was mainly affected by temperature and square root model was more effective than polynomial model for growth prediction.