• The Journal of the Korea Contents Association
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• v.15 no.1
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• pp.475-481
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• 2015

We use polynomial regression instead of linear regression if there is a nonlinear relation between a dependent variable and independent variables in a regression analysis. The performance of polynomial regression, however, may deteriorate because of the correlation caused by the power terms of independent variables. We present a polynomial regression model for the numerical inversion of PGF and show that polynomial regression results in the deterioration of the estimation of the coefficients. We apply principal components regression to the polynomial regression model and show that principal components regression dramatically improves the performance of the parameter estimation.

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.514-518
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• 2004

This paper presents an algorithm generating inverse element over finite fields $GF(3^{m})$, and constructing method of inverse element generator based on inverse element generating algorithm. A method computing inverse of an element over $GF(3^{m})$ which corresponds to a polynomial over $GF(3^{m})$ with order less than equal to m-l. Here, the computation is based on multiplication, square and cube method derived from the mathematics properties over finite fields.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.768-771
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• 2008

This paper presents an algorithm for generating inverse element over finite fields $GF(3^m)$, and constructing method of inverse element generator based on inverse element generating algorithm. The method need to compute inverse of an element eve. $GF(3^m)$ which corresponds to a polynomial eve. $GF(3^m)$ with order less than equal to m-1. Here, the computation is based on multiplication, square and cube method derived from the mathematics properties over finite fields.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.05a
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• pp.433-436
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• 2009

Many researchers had made a diversity of attempts for generating pseudorandom sequences such as the method of using LFSR whose characteristic polynomial is a primitive polynomial, of using Cellular Automata and of using quadratic functions. In this paper, we can analyze and characterize the methods for generating maximal period pseudorandom sequences constructed by quadratic functions.

• Journal of the Korean Mathematical Society
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• v.8 no.1
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.533-546
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• 2020

Since Sheffer introduced the so-called Sheffer polynomials in 1939, the polynomials have been extensively investigated, applied and classified. In this paper, by using matrix algebra, specifically, some properties of Pascal and Wronskian matrices, we aim to present certain interesting identities involving the 2-variable truncated exponential based Sheffer polynomial sequences. Also, we use the main results to give some interesting identities involving so-called 2-variable truncated exponential based Miller-Lee type polynomials. Further, we remark that a number of different identities involving the above polynomial sequences can be derived by applying the method here to other combined generating functions.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.1
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• pp.133-140
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• 2018

In this paper we discover the generation principle of a sequence when the characteristic polynomial of the sequence is a power of a primitive polynomial. With the generation principle, we can rearrange a sequence. Also we get the linear complexity and the required term of the sequence efficiently.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.443-462
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• 2014

Using a simple recurrence relation, we give a new method to compute the Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for the Jones polynomials. The method is used to estimate the degree of the Jones polynomials for some families of braids and to obtain general qualitative results.

• The Transactions of the Korea Information Processing Society
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• v.6 no.9
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• pp.2431-2441
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• 1999

Equations are widely used in representing information. One of the basic questions about equations is to determine whether a given equation follows logically from the set of equations. Rewrite systems are one of the method to answer many instances of this problem. A rewrite system simplifies a given term by applying rewrite rules successively. Hence it is important that the process of simplification does not go on indefinitely. One of the methods to check whether a rewrite system terminates (that is, the rewrite system does not go on indefinitely) is polynomial orderings. A polynomial ordering assigns an appropriate polynomial to each function symbol. However, how to assign polynomials to function symbols is not known. We propose an automatic way of generating polynomial orderings using genetic algorithms.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.473-486
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• 2021

We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper.