• Journal of the Korean Operations Research and Management Science Society
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• v.42 no.1
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• pp.19-28
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• 2017

Moments of stationary intervals and those of the counting process can be used for moment fittings of the point processes. As for the Markovian arrival processes, the moments of stationary intervals are given as a polynomial function of parameters whereas the moments of the counting process involve exponential terms. Therefore, moment fittings are more complicated with the counting process than with stationary intervals. However, in queueing network analysis, cross-correlation between point processes can be modeled more conveniently with counting processes than with stationary intervals. A Laplace-Stieltjies transform of the stationary intervals of MAP (3)s is recently proposed in minimal number of parameters. We extend the results and present the Laplace transform of the counting process of MAP (3)s. We also show how moments of the counting process such as index of dispersions for counts, IDC, and limiting IDC can be used for moment fittings. Examples of exact MAP (3) moment fittings are also presented on the basis of moments of stationary intervals and those of the counting process.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.157-165
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• 2010

Let (M,p) be a germ of a $C^{\infty}$ CR manifold of CR dimension n and CR codimension d. Suppose (M,p) admits a $C^{\infty}$ contraction at p. In this paper, we show that (M,p) is CR equivalent to a generic submanifold in $\mathbb{C}^{n+d}$ defined by a vector valued weighted homogeneous polynomial.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.83-86
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• 2007

We determine the largest integer i such that $0 and the coefficient of $t^{i}$ is odd in the polynomial $(1+t+t^{2}+{\cdots}+t^{n})^{n+1}$. We apply this to prove that the co-index of the tangent bundle over $FP^{n}$ is stable if $2^{r}{\leq}n<2^{r}+\frac{1}{3}(2^{r}-2)$ for some integer r.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.163-172
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• 2003

In this paper we study the property of harmonic vector fields. We call a vector fields ${\xi}$ harmonic if it is a harmonic map from the manifold into its tangent bundle with the Sasaki metric. We show that the characteristic polynomial of operator $A={\nabla}{\xi}\;in\;S^{2n+1}\;is\;(x^2+1)^n$.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.34 no.12
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• pp.472-484
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• 1985

A design of robust voltage controller for high speed excitation of synchronous machine was carried out by pole assignment techniques. An affine map from characteristic polynomial coefficients to feedback parameters is formulated in order to place the system eigen values in the desired region. The feedback parameters determined from linearized model are tested on nonlinear model subjecting it to small disturbances and system faults to show the effectiveness of the controller designed by the proposed technique. The results obtained indicate that the controller presented improves the dynamic stability and system performances of conventionally controlled synchronous machine significantly.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.485-494
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• 2023

Let Y be the quintic del Pezzo 4-fold defined by the linear section of Gr(2, 5) by ℙ⁷. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in Y. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree 2 in Y. We also compute the intersection Poincaré polynomial of the stable map space.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1171-1187
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• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.47-52
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• 2018

Let ${\delta}$ be a derivation in a noetherian integral domain A. It is shown that a natural map induces a homeomorphism between the spectrum of $A[z;{\delta}]$ and the Poisson spectrum of $A[z;{\delta}]_p$ such that its restriction to the primitive spectrum of $A[z;{\delta}]$ is also a homeomorphism onto the Poisson primitive spectrum of $A[z;{\delta}]_p$.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1431-1443
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• 2016

Let k be a global field of characteristic unequal to two. Let $C:y^2=f(x)$ be a nonsingular projective curve over k, where f(x) is a quartic polynomial over k with nonzero discriminant, and K = k(C) be the function field of C. For each prime spot p on k, let ${\hat{k}}_p$ denote the corresponding completion of k and ${\hat{k}}_p(C)$ the function field of $C{\times}_k{\hat{k}}_p$. Consider the map $$h:Br(K){\rightarrow}{\prod\limits_{\mathfrak{p}}}Br({\hat{k}}_p(C))$$, where p ranges over all the prime spots of k. In this paper, we explicitly describe all the constant classes (coming from Br(k)) lying in the kernel of the map h, which is an obstruction to the Hasse principle for the Brauer groups of the curve. The kernel of h can be expressed in terms of quaternion algebras with their prime spots. We also provide specific examples over ${\mathbb{Q}}$, the rationals, for this kernel.

• Journal of Mechanical Science and Technology
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• v.19 no.3
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• pp.792-801
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• 2005

This paper discusses a dc motor equipped electric power steering (EPS) system and demonstrates its advantages over a typical hydraulic power steering (HPS) system. The tire-road interaction torque at the steering tires is calculated using the 2 d.o.f. bicycle model, in other words by using a single-track model, which was verified with the J-turn test of a real vehicle. Because the detail parameters of a steering system are not easily acquired, a simple system is modeled here. In previous EPS systems, the assisting torque for the measured driving torque is developed as a boost curve similar to that of the HPS system. To improve steering stiffness and return-ability of the steering system, a third-order polynomial as a torque map is introduced and modified within the preferred driving torques researched by Bertollini. Using the torque map modification sufficiently improves the EPS system.