• Journal of KIISE:Computer Systems and Theory
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• v.35 no.9_10
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• pp.421-428
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• 2008

A. Ghafoor proposed Even networks as a class of fault-tolerant multiprocessor networks in [1] and analyzed so many useful properties include node disjoint paths. By introducing node disjoint paths in [1], fault diameter of Even networks is d+2(d=odd) and d+3(d=even). But the lengths of node disjoint paths proved in [1] are not the shortest. In this paper, we show that Even network Ed is node symmetric. We also propose the shortest lengths of node disjoint paths using cyclic permutation, and fault diameter of Even networks is d+1.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1037-1049
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• 2015

It is well-known that the spectrum of a $spin^{\mathbb{C}}$ Dirac operator on a closed Riemannian $spin^{\mathbb{C}}$ manifold $M^{2k}$ of dimension 2k for $k{\in}{\mathbb{N}}$ is symmetric. In this article, we prove that over an odd-dimensional Riemannian product $M^{2p}_1{\times}M^{2q+1}_2$ with a product $spin^{\mathbb{C}}$ structure for $p{\geq}1$, $q{\geq}0$, the spectrum of a $spin^{\mathbb{C}}$ Dirac operator given by a product connection is symmetric if and only if either the $spin^{\mathbb{C}}$ Dirac spectrum of $M^{2q+1}_2$ is symmetric or $(e^{{\frac{1}{2}}c_1(L_1)}{\hat{A}}(M_1))[M_1]=0$, where $L_1$ is the associated line bundle for the given $spin^{\mathbb{C}}$ structure of $M_1$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1467-1480
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• 2015

Generalized Fibonacci and Lucas sequences ($U_n$) and ($V_n$) are defined by the recurrence relations $U_{n+1}=PU_n+QU_{n-1}$ and $V_{n+1}=PV_n+QV_{n-1}$, $n{\geq}1$, with initial conditions $U_0=0$, $U_1=1$ and $V_0=2$, $V_1=P$. This paper deals with Fibonacci and Lucas numbers of the form $U_n$(P, Q) and $V_n$(P, Q) with the special consideration that $P{\geq}3$ is odd and Q = -1. Under these consideration, we solve the equations $V_n=5kx^2$, $V_n=7kx^2$, $V_n=5kx^2{\pm}1$, and $V_n=7kx^2{\pm}1$ when $k{\mid}P$ with k > 1. Moreover, we solve the equations $V_n=5x^2{\pm}1$ and $V_n=7x^2{\pm}1$.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.395-414
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• 2016

In this work, we study on subdivision schemes reproducing polynomials and build a symmetric subdivision scheme reproducing polynomials of a certain predetermined degree, which is a slight variant of the family of Deslauries-Dubic interpolatory ones. Related to polynomial reproduction, a necessary and sufficient condition for a subdivision scheme to reproduce polynomials of degree L was recently established under the assumption of non-singularity of subdivision schemes. In case of stepwise polynomial reproduction, we give a characterization for a subdivision scheme to reproduce stepwise all polynomials of degree ${\leq}L$ without the assumption of non-singularity. This characterization shows that we can investigate the polynomial reproduction property only by checking the odd and even masks of the subdivision scheme. The minimal-support condition being relaxed, we present explicitly a general formula for the mask of (2n + 4)-point symmetric subdivision scheme with two parameters that reproduces all polynomials of degree ${\leq}2n+1$. The uniqueness of such a symmetric subdivision scheme is proved, provided the two parameters are given arbitrarily. By varying the values of the parameters, this scheme is shown to become various other well known subdivision schemes, ranging from interpolatory to approximating.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.673-688
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• 2011

Let $n{\geq}2$ be an even integer. We investigate that if an odd mapping f : X ${\rightarrow}$ Y satisfies the following equation $2_{n-2}C_{\frac{n}{2}-1}rf\(\sum\limits^n_{j=1}{\frac{x_j}{r}}\)\;+\;{\sum\limits_{i_k{\in}\{0,1\} \atop {{\sum}^n_{k=1}\;i_k={\frac{n}{2}}}}\;rf\(\sum\limits^n_{i=1}(-1)^{i_k}{\frac{x_i}{r}}\)=2_{n-2}C_{{\frac{n}{2}}-1}\sum\limits^n_{i=1}f(x_i),$ then f : X ${\rightarrow}$ Y is additive, where $r{\in}R$. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C-algebras. As an application, we show that every almost linear bijection h : A ${\rightarrow}$ B of unital $C^*$-algebras A and B is a $C^*$-algebra isomorphism when $h(\frac{2^s}{r^s}uy)=h(\frac{2^s}{r^s}u)h(y)$ for all unitaries u ${\in}$ A, all y ${\in}$ A, and s = 0, 1, 2,....

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.19 no.2
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• pp.169-175
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• 2006

This study investigated variation leakage current maximum value and waveform considering applied voltage phase angel by simulating three environmental conditions, such as fog, salt fog, and kaolin contamination .As the result of applied voltage phase angel characteristics, leakage currents presented almost in phases in the early stage regardless of environmental conditions just after applying the voltage, and the phase of leakage currents certain phase lags for the discharge of the applied voltage when surface discharges occurred due to the continuous environmental contamination. In addition, the difference in phase significantly increased according to the intensity of discharges. The change in distortion rates according to the environmental contamination presented a nearly same level just after applying the voltage. The distortion rate of third harmonic for the fundamental wave presented by the order of fog>salt fog>kaolin when surface discharges occurred due to the applied voltage for certain continued periods. In the case of the fog and salt fog, the scale of spectrums decreased according to the increase in frequencies from the results of the analysis of high frequencies. In addition, the even number frequency presented a relatively large level compared to the odd number frequency under the kaolin contamination.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.501-508
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• 2009

In this paper, we prove that folded hyper-star network FHS(2n,n) is node-symmetric and a bipartite network. We show that FHS(2n,n) can be embedded into odd network On+1 with dilation 2, congestion 1 and Od can be embedded into FHS(2n,n) with dilation 2 and congestion 1. Also, we show that $2n{\time}n$ torus can be embedded into FHS(2n,n) with dilation 2 and congestion 2.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.8
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• pp.655-664
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• 2002

The disturbance observer (DOB) has been widely utilized for high precision/speed motion control applications. However, it still lacks the analysis for the robustness and performance brought by using DOB. This paper proposes the robustness measure of DOB and reveals the relationships between the disturbance rejection performance and the order/time constant of a Q filter in DOB. Additionally, we propose six guidelines for the design of Q filter and show their validity through the experiments for DVD systems.

• JSTS:Journal of Semiconductor Technology and Science
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• v.16 no.5
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• pp.564-581
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• 2016

We present an efficient hardware prime generator that generates a prime p by combining trial division and Fermat test in parallel. Since the execution time of this parallel combination is greatly influenced by the number k of the smallest odd primes used in the trial division, it is important to determine the optimal k to create the fastest parallel combination. We present probabilistic analysis to determine the optimal k and to estimate the expected running time for the parallel combination. Our analysis is conducted in two stages. First, we roughly narrow the range of optimal k by using the expected values for the random variables used in the analysis. Second, we precisely determine the optimal k by using the exact probability distribution of the random variables. Our experiments show that the optimal k and the expected running time determined by our analysis are precise and accurate. Furthermore, we generalize our analysis and propose a guideline for a designer of a hardware prime generator to determine the optimal k by simply calculating the ratio of M to D, where M and D are the measured running times of a modular multiplication and an integer division, respectively.

• Journal of the Korea Fashion and Costume Design Association
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• v.15 no.4
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• pp.113-128
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• 2013

Those records indicate that Jik-geum Hyoong-bae fabric was imported from China and its period was during the fourteen and fifteen century. Gold threads used in three Jik-geum Hyoong-bae artifacts were all wrapped gold thread and gold thread of Danryeong from Young-dukdong, Yong-in, did not have a base, but instead the gold foil itself was attached to the silk cord. Such form of artifact had never been discovered before in Korea. Wrapped gold thread of Seoknamdong's basis was presumably bamboo paper. Three Jik-geum Hyoong-bae have the same weave structure. The ground is woven in a warp-faced 5-end satin weave. The pattern is brocaded with supplementary gold wefts. Supplementary gold wefts are composed of 1/4 twill binding by the odd number pairs of warps within every group of 10 pairs of warps. All of the Jik-geum Hyoong-bae textile were designed and weaved according to the overlapped collared costume's structure. This is also known as 'Jik-seong-pil-ryo'. One symmetric collared jacket excavated in Seok-namdong, Incheon, only has the right half of Hyoong-bae in the front. This is because symmetric collared jacket was made from overlapped collared costume. Tiger and peacock are the main patterns of Jik-geum Hyoong-bae which have realistic and free screen composition and this shows a huge difference to the later generation's standardized Hyoong-bae pattern.