• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.275-285
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• 2013

In this paper a nonlinear matrix equation is considered which has the form $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_{m-1}X+A_m=0$$ where X is an $n{\times}n$ unknown real matrix and $A_m$, $A_{m-1}$, ${\cdots}$, $A_0$ are $n{\times}n$ matrices with real elements. Newtons method is applied to find the skew-symmetric solvent of the matrix polynomial P(X). We also suggest an algorithm which converges the skew-symmetric solvent even if the Fr$\acute{e}$echet derivative of P(X) is singular.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.837-847
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• 2011

For an integer $m{\geq}3$, every integer of the form $p_m(x)$ = $\frac{(m-2)x^2(m-4)x}{2}$ with x ${\in}$ $\mathbb{Z}$ is said to be a generalized m-gonal number. Let $a{\leq}b{\leq}c$ and k be positive integers. The quadruple (k, a, b, c) is said to be universal if for every nonnegative integer n there exist integers x, y, z such that n = $ap_k(x)+bp_k(y)+cp_k(z)$. Sun proved in [16] that, when k = 5 or $k{\geq}7$, there are only 20 candidates for universal quadruples, which h listed explicitly and which all involve only the case of pentagonal numbers (k = 5). He veri ed that six of the candidates are in fact universal and conjectured that the remaining ones are as well. In a subsequent paper [3], Ge and Sun established universality for all but seven of the remaining candidates, leaving only (5, 1, 1, t) for t = 6, 8, 9, 10, (5, 1, 2, 8) and (5, 1, 3, s) for s = 7, 8 as candidates. In this article, we prove that the remaining seven quadruples given above are, in fact, universal.

• Journal of the Korean Magnetics Society
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• v.2 no.3
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• pp.211-215
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• 1992

The temperature-dependent saturation magnetization curves of amorphous $Fe_{80-x}Co_xB_{20}$ (8 ${\le}$ x ${\le}$ 40, the step of x is 8) alloys were measured using a vibrating sample magnetometer from 77 K up to 1000 K. Curie temperature and the Bloch coefficient were estimated from the saturation magnetization curves. The low temperature dependence of magnetization is in good agreement with Bloch relation, $M_s(T)$=$M_s(O)$ (1-$BT^{3/2}$ - ${\cdots}.$). The spin wave stiffness constant, tne range of the exchange interaction, and the probable atomic spin were calculated from the saturation magnetization values.

• Journal of Navigation and Port Research
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• v.47 no.6
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• pp.419-429
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• 2023

The pinnacle of rapidly changing and advancing maritime transportation technology is expected to be the Maritime Autonomous Surface Ship (MASS). The implementation of various services within the MASS is likely to be feasible through the ship-centric network known as the S2X communication system. However, existing communication systems face issues such as service traffic saturation and failure to meet demanded functionalities, necessitating the proactive introduction of additional communication technologies. In this study, the concept of S2X communication for the MASS was redefined, deriving required functionalities and ultimately selecting frequencies suitable for utilization. Candidate frequency groups suitable for the derived communication requirements were identified, and communication frequencies prioritized for the initial application were chosen through expert consensus. It is anticipated that through further research, including experimentation to validate these frequencies, they could be utilized in implementing services for autonomous ship navigation in the future.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• Journal of the Korean Magnetics Society
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• v.23 no.2
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• pp.43-48
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• 2013

The Jahn-Teller distortion of chalcogenide $Fe_{0.9}M_{0.1}Cr_2S_4$ (M=Co, Ni, Zn) have been investigated by M$\ddot{o}$ssbauer spectroscopy. The crystal structures of $Fe_{0.9}M_{0.1}Cr_2S_4$ (M=Co, Ni, Zn) are cubic spinel at room temperature. Magnetoresistance measurements indicate these system is conducting-semiconducting transistion around $T_C$. Below $T_C$, the asymmetric line broadening is observed and considered to be dynamic Jahn-Teller distortion. Isomer shift value of the samples at room temperature was about 0.5 mm/s, which means that charge state of Fe ions is ferrous in character. The Ni substitutions for Fe occur to increase the Jahn-Teller relaxation. CMR properties could be explained with magnetic polaron due to Jahn-Teller effect, which is different from both the double exchange interactions of manganite system and the triple exchange interactions of chalcogenide $Cu_xFe_{1-x}Cr_2S_4$.

• JSTS:Journal of Semiconductor Technology and Science
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• v.9 no.2
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• pp.117-123
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• 2009

$Pb_{x}Cd_{1-x}S$ films are prepared in the composition range of 0.05${\leq}x{\leq}$0.25, using a chemical bath deposition growth technique under optimum conditions amide at realizing good photo response. The x-ray diffraction results show that the films are of PbS-CdS composite with individual CdS and PbS planes. The films exhibit two direct band gaps, 2.4 eV attributed to CdS, while the other varies continuously from 2.4 eV to 1.3 eV. The films surface morphology is smooth with crystallite, whose grain size increases with increasing mole fraction (x). The decrease in band gap with increase in lead concentration suggests inter-metallic compound of PbS (Eg=0.41 eV) with CdS (Eg=2.4 eV)

• Journal of the Korean Magnetics Society
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• v.15 no.2
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• pp.137-141
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• 2005

The CMR properties and magnetic properties of sulphospinels $Zn_xFe_{1-x}Cr_2S_4$ have been explored by X-ray diffraction, magnetoresistance measurement, and $M\ddot{o}ssbauer$ spectroscopy. The crystal structures in the range of x=0.05, 0.1, 0.2 are cubic at room temperature. Magnetoresistance measurement indicates that these system is semiconducting below about 160 K. The temperature of maximum magnetoresistance is almost consistent with Curie temperature. The Zn substitutions for Fe occur to increase the Jahn-Teller relaxation and the electric quadrupole shift. CMR properties could be explained with Jahn-Teller effect, and half-metallic electronic structure, which is different from both the double exchange interactions of manganite La-Ca-Mn-O system and the triple exchange interactions of chalcogenide $Cu_xFe_{1-x}Cr_2S_4$.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.155-171
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• 1997

Let $M^n$ be a connected subminifold of a Euclidean space $E^m$, equipped with the induced metric. Denoty by $\Delta$ the Laplacian operator of $M^n$ and by x the position vector. A well-known T. Takahashi's theorem [13] says that $\delta x = \lambda x$ for some constant $\lambda$ if and only if $M^n$ is either minimal subminifold of $E^m$ or minimal submanifold in a hypersphere of $E^m$. In [9], O. Garay studied the hypersurfaces $M^n$ in $E^{n+1}$ satisfying $\delta x = Dx$, where D is a diagonal matrix, and he classified such hypersurfaces. Garay's condition can be seen as a generalization of T.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.113-124
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• 2010

We consider matrix polynomial which has the form $P_1(X)=A_oX^m+A_1X^{m-1}+...+A_m=0$ where X and $A_i$ are $n{\times}n$ matrices with real elements. In this paper, we propose an iterative method for the symmetric and generalized centro-symmetric solution to the Newton step for solving the equation $P_1(X)$. Then we show that a symmetric and generalized centro-symmetric solvent of the matrix polynomial can be obtained by our Newton's method. Finally, we give some numerical experiments that confirm the theoretical results.