• 대한수학회논문집
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• 제29권2호
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• pp.379-385
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• 2014

For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1986년도 하계학술대회논문집
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• pp.167-168
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• 1986

• 한국CDE학회논문집
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• 제5권3호
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• pp.276-284
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• 2000

Usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in a power form is done by either a knot refinement followed by basis conversions or applying a Taylor expansion on the B-spline curve for each knot span. Presented in this paper is a new algorithm, called a direct expansion algorithm, for the problem. The algorithm first locates the coefficients of all the linear terms that make up the basis functions in a knot span, and then the algorithm directly obtains the power form representation of basis functions by expanding the summation of products of appropriate linear terms. Then, a polynomial segment of a knot span can be easily obtained by the summation of products of the basis functions within the knot span with corresponding control points. Repeating this operation for each knot span, all of the polynomials of the B-spline curve can be transformed into a power form. The algorithm has been applied to both static and dynamic curves. It turns out that the proposed algorithm outperforms the existing algorithms for the conversion for both types of curves. Especially, the proposed algorithm shows significantly fast performance for the dynamic curves.

• Kyungpook Mathematical Journal
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• 제50권1호
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• pp.49-58
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• 2010

We show that the Links-Gould polynomial of a link has finite type coefficients in a multivariate series expansion, and express the leading coefficients in terms of the linking numbers of a link.

• 대한수학회지
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• 제49권5호
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• pp.993-1015
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• 2012

In this paper, we study the quantum sl($n$) representation category using the web space. Specially, we extend sl($n$) web space for $n{\geq}4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl($n$). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial ($n=0$) and Jones polynomial ($n=2$) and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.

• ETRI Journal
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• 제26권3호
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• pp.241-251
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• 2004

We propose two improved scalar multiplication methods on elliptic curves over $F_{{q}^{n}}$ $q= 2^{m}$ using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield $F_q$ can be sped up by Frobenius expansion. Previous methods are restricted to the case of a small m. However, when m is small, it is hard to find curves having good cryptographic properties. Our methods are suitable for curves defined over medium-sized fields, that is, $10{\leq}m{\leq}20$. These methods are variants of the conventional multiple-base binary (MBB) method combined with the window method. One of our methods is for a polynomial basis representation with software implementation, and the other is for a normal basis representation with hardware implementation. Our software experiment shows that it is about 10% faster than the MBB method, which also uses Frobenius expansion, and about 20% faster than the Montgomery method, which is the fastest general method in polynomial basis implementation.

• 대한수학회보
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• 제49권1호
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• pp.127-133
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• 2012

It is well known that if the ${\beta}$-expansion of any nonnegative integer is finite, then ${\beta}$ is a Pisot or Salem number. We prove here that $\mathbb{F}_q((x^{-1}))$, the ${\beta}$-expansion of the polynomial part of ${\beta}$ is finite if and only if ${\beta}$ is a Pisot series. Consequently we give an other proof of Scheiche theorem about finiteness property in $\mathbb{F}_q((x^{-1}))$. Finally we show that if the base ${\beta}$ is a Pisot series, then there is a bound of the length of the fractional part of ${\beta}$-expansion of any polynomial P in $\mathbb{F}_q[x]$.

• Nuclear Engineering and Technology
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• 제56권3호
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• pp.772-784
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• 2024

The hexagonal nodal code RENUS has been enhanced to handle irregularly deformed hexagonal assemblies. The underlying RENUS methods involving triangle-based polynomial expansion nodal (T-PEN) and corner point balance (CPB) were extended in a way to use line and surface integrals of polynomials in a deformed hexagonal geometry. The nodal calculation is accelerated by the coarse mesh finite difference (CMFD) formulation extended to unstructured geometry. The accuracy of the unstructured nodal solution was evaluated for a group of 2D SFR core problems in which the assembly corner points are arbitrarily displaced. The RENUS results for the change in nuclear characteristics resulting from fuel deformation were compared with those of the reference McCARD Monte Carlo code. It turned out that the two solutions agree within 18 pcm in reactivity change and 0.46% in assembly power distribution change. These results demonstrate that the proposed unstructured nodal method can accurately model heterogeneous thermal expansion in hexagonal fueled cores.

• 대한수학회보
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• 제46권1호
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• pp.183-198
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• 2009

In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function $\phi$. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p - 1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p - 1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p - 1. We derive an algorithm for computing the polynomial of degree p - 1.

• 대한수학회보
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• 제46권2호
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• pp.229-234
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• 2009

We find congruences for the t-expansion coefficients of a Drinfeld modular form for ${\Gamma}^+_0$(Q), where Q is a monic irreducible polynomial. As an application we obtain new congruence relations for the t-expansion coefficients of Drinfeld modular forms for ${GL_2}(\mathbb{F}_q[T])$.