• Korean Journal of Mathematics
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• v.22 no.3
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• pp.491-500
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• 2014

The base of a signed digraph S is the minimum number k such that for any vertices u, v of S, there is a pair of walks of length k from u to v with different signs. Let K be a signed complete graph of order n, which is a signed digraph obtained by assigning +1 or -1 to each arc of the n-th order complete graph $K_n$ considered as a digraph. In this paper we show that for $n{\geq}3$ the base of a primitive non-powerful signed complete graph K of order n is 2, 3 or 4.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.12
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• pp.20-26
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• 1994

Lossless system has been employed to design the perfect reconstruction filter banks and has particularly a close relation with the desing of orthogonal wavelet filter (OWF). With such a relation, we generalize 2-band OWF to the M-band OWF which has an improved performances. The improvement is achieved using the two techniques. One is that the wavelet low pass filter has (N-1)th order regularity with extra zeros while the existing filter has N-th order regularity. The other is that unitary matrix is designed by adding the zeros to the proper positions. As a result, M-band OWF designed by propose method has better performance than M-band OWF designed by exsiting method.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2237-2239
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• 2001

Backstepping procedures for output-feedback of nonlinear systems are considered. For these systems, a sliding mode cascade observer to estimate derivatives of the output is builded. In the 1st step of the observer, the output is estimated, and the 1st order derivative of the output is estimated via the 2nd step of the observer. Also, n-th order derivative of the output is estimated in the n+1th step of the observer. Observer errors and tracking errors converge to a residual set close to zero asymptotically.

• Proceedings of the KSAR Conference
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• 2003.06a
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• pp.75-75
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• 2003

Since the establishment of embryonic stem cell, pluripotency of the cells was known to allow differentiation of the cells into various cell types consisting whole body. Several protocols have been developed to induce expression of specific genes.. However, no precise protocol that will generate a single type of the cells from stem cells has been reported. In order to produce cells suitable for transplantion into brain of PD animal model, which arouse due to a progressive degeneration of dopaminergic neurons in midbrain, human embryonic stem cell (hESC, MB03) was transfected with cDNAs cording for tyrosine hydroxylase (TH). Successful transfection was confirmed by western immunoblotting. Newly transfected cell line (TH#2/MB03) was induced to differentiate by the two neurogenic factors retinoic acid (RA) and b-FGF. Exp. I) Upon differentiation using RA/ascorbic acid (AA), embryoid bodies (EB, for 4days) derived from hES cells were exposed to RA (10$^{-6}$ M)/AA (50 mM) for 4 days, and were allowed to differentiate in N2 medium for 7, 14, 21, or 28 days. Exp. II) When bFGF was used, neuronal precursor cells were selected for 8 days in N2 medium after EB formation. After selection, cells were expanded at the presence of bFGF (20 ng/ml) for another 6 days followed by a final differentiation in N2 medium for 7, 14, 21 or 28 days. By indirect immunocytochemical studies, proportion of cells expressing NF200 increased rapidly from 20% at 7 days to 70 % at 28 days in RA/AA-treated group, while those cells expressing NF160 decreased from 80% at 7 days to 10% at 28 days upon differentiation in N2 medium. However, in differentiation by RA/AA treatment system, there was a significant increase in proportion of neuron maturity (73%) at day 14 after N2 medium. TH#2/MB03 cells expressing TH are >90% when matured at the absence of either bDNF or TGF-$\alpha$. These results suggested that TH#2/MB03 cells could be differentiated in vitro into mature neurons by RA/AA.

• International Journal of Contents
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• v.11 no.2
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• pp.57-62
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• 2015

Relative entropy is a divergence measure between two probability density functions of a random variable. Assuming that the random variable has only two alphabets, the relative entropy becomes a cross-entropy error function that can accelerate training convergence of multi-layer perceptron neural networks. Also, the n-th order extension of cross-entropy (nCE) error function exhibits an improved performance in viewpoints of learning convergence and generalization capability. In this paper, we derive a new divergence measure between two probability density functions from the nCE error function. And the new divergence measure is compared with the relative entropy through the use of three-dimensional plots.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.519-530
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• 2001

A two commodity continuous review inventory system with independent Poisson processes for the demands is considered in this paper. The maximum inventory level for the i-th commodity fixed as $S_i$(i = 1,2). The net inventory level at time t for the i-th commodity is denoted by $I_i(t),\;i\;=\;1,2$. If the total net inventory level $I(t)\;=\;I_1(t)+I_2(t)$ drops to a prefixed level s $[{\leq}\;\frac{({S_1}-2}{2}\;or\;\frac{({S_2}-2}{2}]$, an order will be placed for $(S_{i}-s)$ units of i-th commodity(i=1,2). The probability distribution for inventory level and mean reorders and shortage rates in the steady state are computed. Numerical illustrations of the results are also provided.

• Journal of Power Electronics
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• v.15 no.4
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• pp.1085-1092
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• 2015

In this paper, the expressions of the estimated information of a single-phase enhanced phase-locked loop (EPLL), when input signal contains harmonics and a DC offset while the fundamental component takes step changes, are derived. The theoretical analysis results indicate that in the estimated information, the n^th-order harmonics cause n+1^th-order periodic ripples, and the DC offset causes a periodic ripple at the fundamental frequency. Step changes of the amplitude, phase angle and frequency of the fundamental component cause a transient periodic ripple at twice the frequency. These periodic ripples deteriorate the performance of the EPLL. A hybrid filter based EPLL (HF-EPLL) is proposed to eliminate these periodic ripples. A delay signal cancellation filter is set at the input of the EPLL to cancel the DC offset and even-order harmonics. A sliding Goertzel transform-based filter is introduced into the amplitude estimation loop and frequency estimation loop to eliminate the periodic ripples caused by the residual input odd-order harmonics and step change of the input fundamental component. The parameter design rules of the two filters are discussed in detail. Experimental waveforms of both the conventional EPLL and the proposed HF-EPLL are given and compared with each other to verify the theoretical analysis and advantages of the proposed HF-EPLL.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.283-296
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• 2009

Let f(x) = $x^n\;+\;a$ be a binomial polynomial in Z[x] and $f_m(x)$ be the m-th iterate of f(x). In this work we study a necessary condition to be the Galois group of $f_m(x)$ is isomorphic to a wreath product group $[C_n]^m$ where $C_n$ is a cyclic group of order n.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.229-243
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• 2019

We use the so-called pseudoinversion of degenerate metrics technique on foliated compact null hypersurface, $M^{n+1}$, in Lorentzian manifold ${\overline{M}}^{n+2}$, to derive an integral formula involving the r-th order mean curvatures of its foliations, ${\mathcal{F}}^n$. We apply our formula to minimal foliations, showing that, under certain geometric conditions, they are isomorphic to n-dimensional spheres. We also use the formula to deduce expressions for total mean curvatures of such foliations.

• Journal of Korea Multimedia Society
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• v.22 no.9
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• pp.1029-1035
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• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.