• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.427-446
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• 1995

Let S be a set and B be a $\sigma$-field on S. We consider $(\Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $\Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = \cdots, X_-1, X_0, X_1, \cdots$ the coordinate maps on $\Omega$. From our assumptions it follows that ${X_i}_{i \in Z}$ is a stationary and ergodic process.

• Journal of Magnetics
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• v.18 no.4
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• pp.395-399
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• 2013

The metallic glass ribbons of $[(Fe_xCo_{1-x})_{0.75}B_{0.2}Si_{0.05}]_{96}Mo_4$ (x = 0, 0.3, 0.6, 0.9 at.%) and $[(Fe_xCo_{1-x})_{0.75}B_{0.2}Si_{0.05}]_{96}Nb_4$ (x = 0, 0.3, 0.6, 0.9 at.%) were obtained by melt spinning with 25-30 ${\mu}m$ thickness. The thermal stability, mechanical properties and magnetic properties of Fe-Co-B-Si based systems were investigated. The values of thermal stability were measured using differential scanning calorimetry (DSC), including glass transition temperature ($T_g$), crystallization temperature ($T_x$) and supercooled liquid region (${\Delta}T_x=T_x-T_g$). These amorphous ribbons were identified as fully amorphous, using X-ray diffraction (XRD). The mechanical properties of Febased samples were measured by nano-indentation. Magnetic properties of the amorphous ribbons were measured by a vibrating sample magnetometer (VSM). The amorphous ribbons of $[(Fe_xCo_{1-x})_{0.75}B_{0.2}Si_{0.05}]_{96}Mo_4$ (x = 0, 0.3, 0.6, 0.9 at.%) and $[(Fe_xCo_{1-x})_{0.75}B_{0.2}Si_{0.05}]_{96}Nb_4$ (x = 0, 0.3, 0.6, 0.9 at.%) exhibited soft magnetic properties with low coercive force ($H_c$) and high saturation magnetization (Ms).

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.807-816
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• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

• Journal of the Korean Magnetics Society
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• v.2 no.3
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• pp.216-221
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• 1992

Annealing effects on the permeability aftereffect(disaccommodation) of liquid quenched single strip $Fe_{73.5}Cu_1Nb_3Si_{16}B_{6.5}$ alloys were investigated with pulse method. The initial susceptibility X, $B_{10},$ (the flux density at 10 Oe) and disaccommodation intensity D (D = [X(1 s)-X(64 s)]/X(1 s), where X(1 s) and X(64 s) are the susceptibility of 1 and 64 s of rest time after A. C. demagnetization) were about 800, 0.8 T and 16 %, respectively. The soft magnetic properties were improved with isothermal annealing for 1 hour at $300{\sim}600^{\circ}C.$ X, $B_{10},$ and D at $570^{\circ}C$ of optimum annealing temperature were 15000, 1.2 T and 1.1 %, respectively. The origin of the change of characteristics were examined with fine crystalline structure and magnetostriction.

• Journal of the Korean Magnetics Society
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• v.4 no.2
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• pp.126-129
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• 1994

In order to invetigate the effect of Pr additive on the magnetostriction of amorphous Fe-B alloys, amorphous $Fe_{86-x}B_{14}Pr_{x}(2{\leq}x{\leq}8\;at.%)$ alloys were prepared by a rapid solidification process. As the Pr content increased in the as-prepared amorphous $Fe_{84}B_{14}Pr_{2}$ alloy annealed at $300^{\circ}C$ for 2 hr increased to 70 ppm. Ac power loss and permeability$(f=50\;kHz,\;B_{m}=0.1\;T)$ of the annealed amorphous $Fe_{84}B_{14}Pr_{2}$ alloy were 15 W/kg and $5.5{\times}10^{3}$, respectively.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.115-119
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• 1991

In this paper we obtain the asymptotic behavior of solutions of the perturbed system x' = (A(t) + B(t))x of x' = A(t)x by using the Floquet theorem.

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.427-431
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• 1995

The influence of Nd and B contents on the magnetic properties and structures of ${\alpha}-Fe$ based Nd-(Fe,Co)-B-Mo-Cu alloys was investigated. $Nd_{4}{(Fe_{0.9}Co_{0.1})}_{92-x}B_{x}Mo_{3}Cu_{1}$ and $Nd_{x}{(Fe_{0.9}Co_{0.1})}_{86-x}B_{10}Mo_{3}Cu_{1}$ amorphous alloys prepared by rapid solidification process were crystallized to form nanocrystalline structure. The increase of B content in $Nd_{4}{(Fe_{0.9}Co_{0.1})}_{92-x}B_{x}Mo_{3}Cu_{1}$ nanocrystalline resulted in the change of stucture of soft phase in the sequence of ${\alpha}-Fe$->${\alpha}-Fe+Fe_{3}B$->$Fe_{3}B$. The coercivitis of the alloys were increased with increasing B content and was 263 kA/m at x=18. On the contrary, the remanence has shown an opposite trends. The increase of Nd content in $Nd_{x}{(Fe_{0.9}Co_{0.1})}_{86-x}B_{10}Mo_{3}Cu_{1}$ nanocrystalline containing ${\alpha}-Fe$ as main phase had no effect on the structure and improved coercivity up to 256 kA/m. However, the remanence was decreased from 1.4 T to 1.15 T according to the increase of Nd content.

• Journal of the Korean Magnetics Society
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• v.3 no.3
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• pp.185-189
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• 1993

급속응고법으로 제작된 비정질 $Fe_{85-x}Co_{x}Zr_{7}B_{7}Cu_{1}$ 합금의 열처리에 따른 구조 및 자기특성이 조사되었다. 비정질 $Fe_{85-x}Co_{x}Zr_{7}B_{7}Cu_{1}$ 합금은 $600^{\circ}C$이하의 열처리온도에서 약 10 nm의 초미세결정립이 형성된다. $600^{\circ}C$이상의 열처리 조건에서는 결정립크기가 급격히 증가하여 자기특성을 열화시킨다. $Fe_{85-x}Co_{x}Zr_{7}B_{7}Cu_{1}$ 합금의 최적열처리온도는 Fe-Zr-B초미세결정립합금에 비하여 낮으며, 결정립크기 또한 감소한다. 이는 Cu의 첨가에 기인하는 것으로 판단된다. 최적열처리조건에서 $Fe_{80}Co_{5}Zr_{7}B_{7}Cu_{1}$ 초미세결정립합금의 포화자화 및 f=50 kHz, $B_{m}=0.2\;T$에서 측정한 투자율 및 철손은 각각 157.3 emu/g(1.5 T), $1.8{\times}10^{4}$ 및 13 W/kg으로 자기특성이 가장 우수하다.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.243-256
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• 2010

This paper is concerned with the neutral impulsive functional differential equations $$\{{x'(t)\;+\;a(t)x(t)\;=\;f(t,\;x(t\;-\;\tau(t),\;x'(t\;-\;\delta(t))),\;a.e.\;t\;{\in}\;R, \atop {\Delta}x(t_k)\;=\;b_kx(t_k),\;k\;{\in}\;Z.$$ Sufficient conditions for the existence of at least three positive T-periodic solution are established. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results.