• 한국자기학회지
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• 제2권3호
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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.

• 대한수학회지
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• 제49권5호
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• pp.1017-1030
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• 2012

We consider forced second order differential equation with $p$-Laplacian and nonlinearities given by a Riemann-Stieltjes integrals in the form of $$(p(t){\phi}_{\gamma}(x^{\prime}(t)))^{\prime}+q_0(t){\phi}_{\gamma}(x(t))+{\int}^b_0q(t,s){\phi}_{{\alpha}(s)}(x(t))d{\zeta}(s)=e(t)$$, where ${\phi}_{\alpha}(u):={\mid}u{\mid}^{\alpha}\;sgn\;u$, ${\gamma}$, $b{\in}(0,{\infty})$, ${\alpha}{\in}C[0,b)$ is strictly increasing such that $0{\leq}{\alpha}(0)<{\gamma}<{\alpha}(b-)$, $p$, $q_0$, $e{\in}C([t_0,{\infty}),{\mathbb{R}})$ with $p(t)>0$ on $[t_0,{\infty})$, $q{\in}C([0,{\infty}){\times}[0,b))$, and ${\zeta}:[0,b){\rightarrow}{\mathbb{R}}$ is nondecreasing. Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. As special cases, our work generalizes, unifies, and improves many existing results in the literature.

• 열처리공학회지
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• 제15권2호
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• pp.76-81
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• 2002

The melt-spun amorphous $Fe_{77-X}P_{13}C_4B_4Al_2Mo_X$(x=4~10) and $Fe_{82-X}P_XC_4B_4Al_2Mo_8$(x=9~15) alloys were found to exhibit a large supercooled liquid region(${\Delta}T_x$) exceeding 40 K before crystallization. The largest ${\Delta}T_x$ for the glassy alloys containing Mo reaches as large as 65 K for the $Fe_{69}P_{13}C_4B_4Al_2Mo_8$ alloy. The corrosion behavior of the amorphous $Fe_{77-X}P_{13}C_4B_4Al_2Mo_X$(x=4~15) and $Fe_(82-X)P_XC_4B_4Al_2Mo_8$ (x=9~17) alloys were examined by electrochemical measurements in 9M $H_2SO_4$ solution at 303 K. The addition of Mo(or P) for replacing some portion of Fe is effective in improving the corrosion resistance of the investigated Fe-based glassy alloys. They are spontaneously passivated and have a wide passive region with low passive current density.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.49-57
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• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.

• 대한수학회보
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• 제22권1호
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• pp.11-15
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• 1985

Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is non-degenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$(V,R) induced by B is an isomorphism), and with a quadratic mapping .phi.: V.rarw.R such that B(x,y)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) and .phi.(rx) = $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U9R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$,.., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2 we reserve the notation [a $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.

• 대한수학회보
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• 제34권3호
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• pp.385-394
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• 1997

In this paper, we prove in p-uniforlmy convex space a fixed point theorem for a class of mappings T satsfying: for each x, y in the domain and for n = 1, 2, 3, $\cdots$, $$ \left\$\mid$ T^n x - T^n y \right\$\mid$ \leq a \cdot \left\$\mid$ x - y \right\$\mid$ + b(\left\$\mid$ x - T^n x \right\$\mid$ + \left\$\mid$ y - T^n y \right\$\mid$) + c(\left\$\mid$ c - T^n y \right\$\mid$ + \left\$\mid$ y - T^n x \right\$\mid$, $$ where a, b, c are nonnegative constants satisfying certain conditions. Further we establish some fixed point theorems for these mappings in a Hilbert space, in $L^p$ spaces, in Hardy spaces $H^p$ and in Sobolev spaces $H^{p,k}$ for 1 < p < $\infty$ and k $\leq$ 0. As a consequence of our main result, we also the results of Goebel and Kirk [7], Lim [8], Lifshitz [12], Xu [20] and others.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권12호
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• pp.6188-6204
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• 2017

Over the years, more password-based authentication key agreement schemes using chaotic maps were susceptible to attack by off-line password guess attack. This work approaches this problem by a new method--new theorem of chaotic maps: $T_{a+b}(X)+T_{a-b}(X)=2T_a(X)T_b(X)$,(a>b). In fact, this method can be used to design two-party, three-party, even in N-party intelligently. For the sake of brevity and readability, only a two-party instance: a novel Two-party Password-Authenticated Key Agreement Protocol is proposed for resisting password guess attack in this work. Compared with the related literatures recently, our proposed scheme can be not only own high efficiency and unique functionality, but is also robust to various attacks and achieves perfect forward secrecy. For capturing improved ratio of security and efficiency intuitively, the paper firstly proposes a new parameter called security/efficiency ratio(S/E Ratio). The higher the value of the S/E Ratio, the better it is. Finally, we give the security proof and the efficiency analysis of our proposed scheme.

• 대한수학회지
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• 제35권3호
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• pp.583-611
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• 1998

We consider a general class of real-valued Levy processes {X(t), $t\geq0$}, and obtain suitable large deviation results for the empiricals L(t, A) defined by $t^{-1}{\int^t}_01_A$(X(s)ds for t > 0 and a Borel subset A of R. These results are used to obtain the asymptotic behavior of P{Z(t) < a}, where Z(t) = $sup_{u\leqt}\midx(u)\mid$ as $t\longrightarrow\infty$, in terms of the rate function in the large deviation principle. A subclass of these processes is the Feller class: there exist nonrandom functions b(t) and a(t) > 0 such that {(X(t) - b(t))/a(t) : t > 0} is stochastically compact, i.e., each sequence has a weakly convergent subsequence with a nondegenerate limit. The stable processes are in this class, but it is much larger. We consider processes in this class for which b(t) may be taken to be zero. For any t > 0, we consider the renormalized process ${X(u\psi(t))/a(\psi(t)),u\geq0}$, where $\psi$(t) = $t(log log t)^{-1}$, and obtain large deviation probability estimates for $L_{t}(A)$ := $(log log t)^{-1}$${\int_{0}}^{loglogt}1_A$$(X(u\psi(t))/a(\psi(t)))dv$. It turns out that the upper and lower bounds are sharp and depend on the entire compact set of limit laws of {X(t)/a(t)}. The results extend to random walks in the Feller class as well. Earlier results of this nature were obtained by Donsker and Varadhan for symmetric stable processes and by Jain for random walks in the domain of attraction of a stable law.

• 한국자기학회지
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• 제6권4호
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• pp.218-224
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• 1996

새로운 고성능 자심용 연자성 합금을 개발하기 위해, 급냉응고 방식에 의해 제조된 $Fe_{83-x}Al_{x}Nb_{5}B_{12}(X=1~5at%)$ 합금의 결정화거동 및 자기적 특성을 조사하였다. 3at% Al의 $Fe_{80}Al_{3}Nb_{5}B_{12}$ 합금이 조사된 Fe-Al-Nb-B계 합금중에서 가장 우수한 연자기 특성을 가지며, 이때 미세한 $\alpha-Fe$상 결정립 조직을 가지는 것으로 판명되었다. 또, 이 조성의 합금에 1 at%의 Cu를 첨가하면, 약 6~7 nm정도의 크기를 가지는 극히 미세한 결정립의 $\alpha-Fe$ 상조직이 얻어졌으며 이에 따라 대단히 현저한 연자기 특성의 향상이 실현되었다. 이때 초미세 결정구조 $Fe_{79}Al_{3}Nb_{5}B_{12}Cu_{1}$ 합금의 자기적 특성은 다음과 같다 : ${\mu}_{eff}(1\;kHz)=26,000,\;B_{10}=1.45\;T,\;H_{c}=25\;mOe,\;P_{c}(100\;kHz,\;0.2\;T)=55\;W/kg$.

• 아시안잔디학회지
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• 제10권1호
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• pp.41-47
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• 1996

The theory of slope erosion is developed along similar lines to the theory of heat flow in solid added to the correcting factor. if slope erosion in the forest and grassland proceeds according to the hypothesis, it is $\delta$y $\delta^2$y = k $\delta^2$y $\delta$$X^2$+f(s b. t) where 5 is internal properties of slope soil and b is biota on slope. When the variables of the equation of slope erosion are x = -λ the initial elevation=-f(λ), x=λ, x==a, the steady value of the initial elevation=y, and dy dx x=0> =O(t>o), respectively, the houndary condition due to the solution of the equation of slope erosion is y= 2 √$\pi$kt [∫a o λe $(X-λ)^2$4kt dλ- ∫ao- $(x+λ)^2$4kt dλ] + ∫∫∫ f (s.b. t)dtdbds