• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.4
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• pp.133-139
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• 2011

In this paper, we propose a hybrid filter for noise reduction. The proposed method adjusts rational filtering direction according to an edge in the image using median filtered data. Rational filter modulates the coefficients of a linear lowpass filter to limit its action in presence of image details. By the ratio of polynomials in the input variables, rational filter reduces noise adaptively. Median filter is widely used to reduce impulse noise, but removes some details for highly corrupted images. Also, desirable details are removed when the window size is large. Our proposed algorithm combines rational filter and median filter. Thus, proposed method not only preserves edge, but also reduces noise in uniform region. Experimental results show that our proposed method has better quality than those by existing median and rational filtering methods.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1309-1320
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• 2023

Let f : X → Y be a map between simply connected CW-complexes of finite type with X finite. In this paper, we prove that the rational cohomology of mapping spaces map(X, Y ; f) contains a polynomial algebra over a generator of degree N, where N = max{i, π_i(Y)⊗ℚ ≠ 0} is an even number. Moreover, we are interested in determining the rational homotopy type of map(𝕊ⁿ, ℂP^m; f) and we deduce its rational cohomology as a consequence. The paper ends with a brief discussion about the realization problem of mapping spaces.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.103-108
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• 2002

Applications of a column-reduced orthogonal rational matrix function to McMillan degrees and Wiener-Hopf factorizations are considered.

• Journal of the Korean Home Economics Association
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• v.33 no.5
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• pp.75-88
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• 1995

The objectives of this study were to classify the contents of clothing shopping orientation, to group women into shopper types, and to examine the differences in clothing purchase criteria according to the shopper types. Samples were 335 women(20-49 years of age) in Seoul, Korea. The data were analyzed using factor analysis, cluster analysis, one-way ANOVA, Duncan's multiple range test, X2 test, paired t-test, multiple regression analysis. The results of the study were the followings. 1. Five factors of clothing shopping orientation derived by factor analysis : F.1 'impulsive shopping' ; F.2 'rational shopping' ; F.3 'independent shopping' ; F.4 'economic shopping' ; F.5 'convenient shopping'. Three shopper types were classified by cluster analysis of the 5 factors : T.1 'convenient shopper' ; T.2 'impulsive shopper' ; T.3 'rational shopper'. 2. Significant differences were found among the 3 shopper types in all clothing purchase criteria. Rational shopper perceived all purchase criteria as more important than did the other 2 types. Impulsive shopper perceived 'fashion', 'attractiveness', 'style', and 'bland' as more important than did convenient shopper. 3. Married women and unemployed women were more distributed in rational shopper, while the unmarried and the employed more in impulsive shopper. Impulsive shopper used more credit care, purchased suits and blouses at department store and brand specialty store more than did rational shopper. Rational shopper purchased at discount store and wholesale store more than did impulsive shopper. 4. Women assessed 'color and fabric design' as most important in suit and blouse purchase criteria. 'Care' was perceived more important in blouses than in suits, and the other 9 purchase criteria(fashion, attractiveness, style, color and fabric design, fabric, durability, costruction, comfort, and brand) were perceived more important in suits than in blouses. 5. Rational and economic shopping orientation scores were higher in suit purchase than in blouse, while impulsive, independent, and convenient shopping orientation scores were higher in blouse purchase. 6. Post-purchase suit satisfaction was influenced by rational shopping orientation, educational level, style, income, and comfort. The explanatory power of the 5 variables was 17.2%. Post-purchase blouse satisfaction was influenced by style, care, rational shopping orientation, and independent shopping orientation. The explanatory power of the 4 variables was 10.2%.

• Korea-Australia Rheology Journal
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• v.15 no.3
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• pp.131-150
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• 2003

A new numerical algorithm of finite element methods is presented to solve high Deborah number flow problems with geometric singularities. The steady inertialess planar 4 : 1 contraction flow is chosen for its test. As a viscoelastic constitutive equation, we have applied the globally stable (dissipative and Hadamard stable) Leonov model that can also properly accommodate important nonlinear viscoelastic phenomena. The streamline upwinding method with discrete elastic-viscous stress splitting is incorporated. New interpolation functions classified as rational interpolation, an alternative formalism to enhance numerical convergence at high Deborah number, are implemented not for the whole set of finite elements but for a few elements attached to the entrance comer, where stress singularity seems to exist. The rational interpolation scheme contains one arbitrary parameter b that controls the singular behavior of the rational functions, and its value is specified to yield the best stabilization effect. The new interpolation method raises the limit of Deborah number by 2∼5 times. Therefore on average, we can obtain convergent solution up to the Deborah number of 200 for which the comer vortex size reaches 1.6 times of the half width of the upstream reservoir. Examining spatial violation of the positive definiteness of the elastic strain tensor, we conjecture that the stabilization effect results from the peculiar behavior of rational functions identified as steep gradient on one domain boundary and linear slope on the other. Whereas the rational interpolation of both elastic strain and velocity distorts solutions significantly, it is shown that the variation of solutions incurred by rational interpolation only of the elastic strain is almost negligible. It is also verified that the rational interpolation deteriorates speed of convergence with respect to mesh refinement.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.13-29
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• 2007

In this paper, we first present a method for finding the implicit equation of the curve given by rational parametric equations. The method is based on the computation of $Gr\"{o}bner$ bases. Then, another method for implicitization of curve and surface is given. In the case of rational curves, the method proceeds via giving the implicit polynomial f with indeterminate coefficients, substituting the rational expressions for the given curve and surface into the implicit polynomial to yield a rational expression $\frac{g}{h}$ in the parameters. Equating coefficients of g in terms of parameters to 0 to get a system of linear equations in the indeterminate coefficients of polynomial f, and finally solving the linear system, we get all the coefficients of f, and thus we obtain the corresponding implicit equation. In the case of polynomial surfaces, we can similarly as in the case of rational curves obtain its implicit equation. This method is based on characteristic set theory. Some examples will show that our methods are efficient.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.163-191
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• 2002

We introduce Clapp-Puppe type generalized Lusternik-Schnirelmann (co)category in a Quillen model category. We establish some of their basic properties and give various characterizations of them. As the first application of these characterizations, we show that our generalized (co)category is invariant under Quillen modelization equivalences. In particular, generalized (co)category is invariant under Quillen modelization equivalences. In particular, generalized (co)category of spaces and simplicial sets coincide. Another application of these characterizations is to define and study rational cocategory. Various other applications are also given.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.209-224
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• 2013

The problem of finding rational or integral points of an elliptic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polynomial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for $y^2=x^3+b$.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.807-814
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• 1996

Let $G = Z_2$. Let X be any compact connected orientable nonsingular real algebraic variety of dim X = k = odd with the trivial G action, and let Y be the unit sphere $S^{2n-k}$ with the antipodal action of G. Then we prove that any G invariant entire rational map $f : x \times Y \to S^{2n}$ is G homotopically trivial. We apply this result to prove that any entire rational map $g : X \times RP^{2n-k} \to S^{2n}$ is homotopically trivial.

• East Asian mathematical journal
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• v.28 no.2
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.