• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.2
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• pp.315-323
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• 2015

Nowadays, it is expected that mobility loads such as electric railways and electric vehicles will be penetrated gradually and affect on the power system stability by their load characteristics. Various researches have been carried out about electric vehicles for the recent decade though the load of electric railway could be forecasted because of the specified path and timetable, is a field with a long historic background. Some precise 5th polynomial equations are required to analyze the power system stability considering mobility load to be increased in the immediate future while the electric railway dispatching simulator uses load models with constant power and constant impedance for the system analysis. In this paper, seasonal urban railway load models are established as the form of 5th polynomial equations and substation load modeling methods are proposed merging railway station load models and general load models. Additionally, load management effects by the load modeling are confirmed through the case studies, in which seasonal load models are developed for Seoul Subway Line No. 2, Gyeongui Line and Airport Railroad and the substation load change is analyzed according to the railway load change.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.254-259
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• 1998

A new design methology is proposed to identify the structure and parameters of fuzzy model using PNN and a fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and cubic besides the biquadratic polynomial used in the GMDH. The FPNN(Fuzzy Polynomial Neural Networks) algorithm uses PNN(Polynomial Neural networks) structure and a fuzzy inference method. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here a regression polynomial inference is based on consequence of fuzzy rules with a polynomial equations such as linear, quadratic and cubic equation. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture. In this paper, we will consider a model that combines the advantage of both FPNN and PNN. Also we use the training and testing data set to obtain a balance between the approximation and generalization of process model. Several numerical examples are used to evaluate the performance of the our proposed model.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1185-1196
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• 2016

We show a class of homogeneous polynomials of Fermat-Waring type such that for a polynomial P of this class, if $P(f_1,{\ldots},f_{N+1})=P(g_1,{\ldots},g_{N+1})$, where $f_1,{\ldots},f_{N+1}$; $g_1,{\ldots},g_{N+1}$ are two families of linearly independent entire functions, then $f_i=cg_i$, $i=1,2,{\ldots},N+1$, where c is a root of unity. As a consequence, we prove that if X is a hypersurface defined by a homogeneous polynomial in this class, then X is a unique range set for linearly non-degenerate non-Archimedean holomorphic curves.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.983-1002
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• 2021

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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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.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.268-273
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• 2002

In this paper, a new parallel multiplier circuit over $GF(2^m)$ has been proposed. The new multiplier is composed of polynomial multiplicative operation part and modular arithmetic operation part, irreducible polynomial operation part. And each operation has modular circuit block. For design the new proposed circuit, it develop generalized equations using frame each operation idea and show a example for $GF(2^m)$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.885-895
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• 2021

In this paper, we study a kind of self-inversive polynomials in bicomplex algebra. For a bicomplex polynomial, this is the study of a relation between a kind of symmetry of its coefficients and a kind of symmetry of zeros. For our deep study, we define several new levels of self-inversivity. We prove some functional equations for standard ones, a decomposition theorem for generalized ones and a comparison theorem. Although we focus the j-conjugation in our study, our argument can be applied for other conjugations.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.39-54
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• 2005

In Chinese Mathematics, Jia Xian(要憲) introduced Zeng cheng kai fang fa(增乘開方法) to get approximations of solutions of Polynomial equations which is a generalization of square roots and cube roots in Jiu zhang suan shu. The synthetic divisions in Zeng cheng kai fang fa give ise to two concepts of Fan il(飜積) and Yi il(益積) which were extensively used in Chosun Dynasty Mathematics. We first study their history in China and Chosun Dynasty and then investigate the historical fact that Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) obtained the sufficient conditions for Fan il and Yi il for quadratic equations and proved them in the middle of 19th century.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.675-677
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• 1998

In this paper, we propose the fuzzy inference algorithm with multi-layer structure. MFIS(Multi-layer Fuzzy Inference System) uses PNN(Polynomial Neural networks) structure and the fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Hendling), and uses several types of polynomials such as linear, quadratic and cubic, as well as the biquadratic polynomial used in the GMDH. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here, the regression polynomial inference is based on consequence of fuzzy rules with the polynomial equations such as linear, quadratic and cubic equation. Each node of the MFIS is defined as fuzzy rules and its structure is a kind of neuro-fuzzy structure. We use the training and testing data set to obtain a balance between the approximation and the generalization of process model. Several numerical examples are used to evaluate the performance of the our proposed model.

• Journal of Information Technology Services
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• v.19 no.1
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• pp.145-158
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• 2020

With the development and widespread application of online shopping, the number of online consumers has increased. With one click of a mouse, people can buy anything they want without going out and have it sent right to the doors. As consumers benefit from online shopping, people are becoming more concerned about protecting their privacy. In the group buying scenario described in our paper, online shopping was regarded as intra-group communication. To protect the sensitive information of consumers, the polynomial-based encryption key sharing method (Piao et al., 2013; Piao and Kim, 2018) can be applied to online shopping communication. In this paper, we analyze security problems by using a polynomial-based scheme in the following ways : First, in Kamal's attack, they said it does not provide perfect forward and backward secrecy when the members leave or join the group because the secret key can be broken in polynomial time. Second, for simultaneous equations, the leaving node will compute the new secret key if it can be confirmed that the updated new polynomial is recomputed. Third, using Newton's method, attackers can successively find better approximations to the roots of a function. Fourth, the Berlekamp Algorithm can factor polynomials over finite fields and solve the root of the polynomial. Fifth, for a brute-force attack, if the key size is small, brute force can be used to find the root of the polynomial, we need to make a key with appropriately large size to prevent brute force attacks. According to these analyses, we finally recommend the use of a relatively reasonable hash-based mechanism that solves all of the possible security problems and is the most suitable mechanism for our application. The study of adequate and suitable protective methods of consumer security will have academic significance and provide the practical implications.