• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.171-182
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• 2009

In this paper, we consider the parameter space of the rational plane curves with uni-branched singularity. We show that such a parameter space is decomposable into irreducible components which are rational varieties. Rational parametrizations of the irreducible components are given in a constructive way, by a repeated use of Abhyankar-Moh Epimorphism Theorem. We compute an enumerative invariant of this parameter space, and include explicit computational examples to recover some classically-known invariants.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.309-322
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• 2022

In this paper, we introduce the notion of a new generalized type of rational F-contraction mapping. Further, the concept is used to obtain fixed points in a complete b-metric space. We also prove another unique fixed point theorem in the context of b-metric space. Our results are verified with example.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.259-267
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• 2022

We use L_∞ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion i_n,k : ℂPⁿ ↪ ℂP^n+k between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping aut₁ ℂPⁿ → map(ℂPⁿ, ℂP^n+k; i_n,k) and the resulting G-sequence.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.750-752
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• 2003

The objective of this investigation is to compare the geometric precision of Rigorous Sensor Model and Rational Function Model for QuickBird images. In rigorous sensor model, we use the on-board data and ground control points to fit an orbit; then, a least squares filtering technique is applied to collocate the orbit. In rational function model, we first use the rational polynomial coefficients provided by the satellite company. Then the systematic bias of the coefficients is compensated by an affine transformation using ground control points. Experimental results indicate that, the RFM provides a good approximation in the position accuracy.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.345-358
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• 1998

Let (p/q,n) denote the orbifold with its underlying space $S^3$ and a rational knot or link p/q as its singular set with a cyclic isotropy group of order n. In this paper we shall show the geometrical realization for the case (7/3,n) for all $n \geq 3$.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.405-413
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• 2004

Rational parameterization of curves and surfaces is one of the main topics in computer-aided geometric design because of their computational advantages. Pythagorean hodograph (PH) curves and Minkowski Pythagorean hodograph (MPH) curves have attracted many researcher's interest because they provide for rational representation of their offset curves in Euclidean space and Minkowski space, respectively. In [10], Kim presented the characterization of the PH curves in the Euclidean space and analyzed the relation between the class of PH curves and the class of rational curves. In this paper, we extend the characterization of PH curves in [10] into that of MPH curves in the general Minkowski space and consider some generalized MPH curves satisfying this characterization.

• East Asian mathematical journal
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• v.26 no.1
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• pp.69-73
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• 2010

We invoke the characterization of Pythagorean-hodograph polynomial curves and prove that it is impossible to parameterize any real curves, other than a straight line, by rational functions of its arc length.

• International Journal of Control, Automation, and Systems
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• v.5 no.4
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• pp.471-478
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• 2007

In this paper, an optimal Wiener-Hopf decoupling controller formula is obtained which is expressed in terms of rational matrices, thereby readily allowing the use of state-space algorithms. To this end, the characterization formula for the class of all realizable decoupling controller is formulated in terms of rational functions. The class of all stabilizing and decoupling controllers is parametrized via the free diagonal matrices and the optimal decoupling controller is determined from these free matrices.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.377-386
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• 2011

For a smooth algebraic curve C of genus g $\geq$ 4, let $SU_C$(r, d) be the moduli space of semistable bundles of rank r $\geq$ 2 over C with fixed determinant of degree d. When (r,d) = 1, it is known that $SU_C$(r, d) is a smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree $\geq$ r with respect to the ampl generator of Pic($SU_C$(r, d)). In this paper, we study the locus swept out by the rational curves on $SU_C$(r, d) of degree < r. As a by-product, we present another proof of Torelli theorem on $SU_C$(r, d).

• 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.