• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.505-510
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• 2011

We give a constructive proof that a (partial) evaluation of a multivariate algebraic function with algebraic numbers is again an algebraic function. Especially, we obtain a bound on the degree of an evaluation with the degrees of the original algebraic function and the algebraic numbers evaluated. Furthermore, we show that our bound is sharp with an example.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.6
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• pp.105-110
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• 2005

The linearized polynomial fan be regarded as a generalization of the identity function so that the inverse of the linearized polynomial is a generalization of e inverse function. Since the inverse function has so many good cryptographic properties, the inverse of the linearized polynomial is also a candidate of good Boolean functions. In particular, a construction method of vector resilient functions with high algebraic degree was proposed at Crypto 2001. But the analysis about the algebraic degree of the inverse of the linearized Polynomial. Hence we correct the inexact result and give the exact maximal algebraic degree.

• The Mathematical Education
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• v.41 no.3
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• pp.341-360
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• 2002

The purpose of the study was to investigate the effectiveness of dynamic software in solving high school analytic geometry problems compared with traditional algebraic approach. Three high school students who have revealed high performance in mathematics were involved in this study. It was considered that they mastered the basic concepts of equations of plane figure and curves of secondary degree. The research questions for the study were the followings: 1) In what degree students understand relationship between geometric approach and algebraic approach in solving geometry problems? 2) What are the difficulties students encounter in the process of using the dynamic software? 3) In what degree the constructions of geometric figures help students to understand the mathematical concepts? 4) What are the effects of dynamic software in constructing analytic geometry concepts? 5) In what degree students have developed the images of algebraic concepts? According to the results of the study, it was revealed that mathematical connections between geometric approach and algebraic approach was complementary. And the students revealed more rely on the algebraic expression over geometric figures in the process of solving geometry problems. The conceptual images of algebraic expression were not developed fully, and they blamed it upon the current college entrance examination system.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1601-1606
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• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1259-1267
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• 2022

In this paper we present a full circle approximation method using parametric polynomial curves with algebraic coefficients which are curvature continuous at both endpoints. Our method yields the n-th degree parametric polynomial curves which have a total number of 2n contacts with the full circle at both endpoints and the midpoint. The parametric polynomial approximants have algebraic coefficients involving rational numbers and radicals for degree higher than four. We obtain the exact Hausdorff distances between the circle and the approximation curves.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.317-324
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• 2008

This paper shows the degree of simultaneous neural network approximation for a target function in $C^r$[-1, 1] and its first derivative. We use the Jackson's theorem for differentiable functions to get a degree of approximation to a target function by algebraic polynomials and trigonometric polynomials. We also make use of the de La Vall$\grave{e}$e Poussin sum to get an approximation order by algebraic polynomials to the derivative of a target function. By showing that the divided difference with a generalized translation network can be arbitrarily closed to algebraic polynomials on [-1, 1], we obtain the degree of simultaneous approximation.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.1
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• pp.71-77
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• 2004

It was proved that Hen is an algebraic ,elation of degree [n(l+1]/2] for an (n, 1)-combine. which consists of n LFSRs and l memory bits. For the summation generator with $2^k$ LFSRs which uses k memory bits, we show that there is a non-trivial relation of degree at most $2^k$ using k+1 consecutive outputs. In general, for the summation generator with n LFSRs, we can construct a non-trivial algebraic relation of degree at most 2$^{{2^{[${log}_2$}n]}}$ using [${log}_2$＋1 consecutive outputs.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.4
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• pp.325-336
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• 1994

A numerical simulation of velocity and temperature fields and Nusselt number distributions is performed by using the algebraic stress model (ASM) for the velocity profiles and low Reynolds number ${\kappa}-{\varepsilon}$ model and the algebraic heat flux model(AHFM) for turbulent heat transfer in a $180^{\circ}$ bend with a constant wall heat flux. In the low Reynolds number ${\kappa}-{\varepsilon}$ model, turbulent Prandtl number is modified by considering the streamline curvature effect and the non-equilibrium effect between turbulent kinetic energy production and dissipation rate. Every heat flux term presented in the transport equation of turbulent heat flux is reduced to algebraic expressions in a way similar to algebraic stress model. Also. in the wall region, low Reynods number algebraic heat flux model(AHFM) is applied.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.699-709
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• 2016

Our paper is devoted to the study of certain diophantine equations on the ring of polynomials over a finite field, which are intimately related to algebraic formal power series which have partial quotients of unbounded degree in their continued fraction expansion. In particular it is shown that there are Pisot formal power series with degree greater than 2, having infinitely many large partial quotients in their simple continued fraction expansions. This generalizes an earlier result of Baum and Sweet for algebraic formal power series.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.