• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.223-238
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• 1994

A random vector $\b{X} = (X_1,\cdots,X_n)$ is weakly associated if and only if for every pair of partitions $\b{X}_1 = (X_{\pi(1)},\cdots,X_{\pi(k)}), \b{X}_2 = (X_{\pi(k+1),\cdots,X_{\pi(n)})$ of $\b{X}, P(\b{X}_1 \in A, \b{X}_2 \in B) \geq P(\b{X}_1 \in A)\b{P}(\b{X}_2 \in B)$ whenever A and B are open upper sets and $\pi$ is a permutation of ${1,\cdots,n}$. In this paper, we develop notions of weak positive dependence, which are weaker than a positive version of negative association (weak association) but stronger than positive orthant dependence by arguments similar to those of Shaked. We also illustrate some concepts of a particular interest. Various properties and interrelationships are derived.

• 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 Korean Magnetics Society
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• v.8 no.5
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• pp.271-274
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• 1998

Spin reorientation and magnetocrystalline anisotropy of magnetically aligned $(Nd_{1-x}R_x)_2Fe_{14}B$ (R=Y, Pr) power were studied. The spin reorientation temperature $(T_{SR})$ of $(Nd_{1-x}R_x)_2Fe_{14}B$ decreases linearly by increasing Pr-substitution with the ratio of ${\Delta}T_{SR}=-1.35$ K/Pr at.% in composition range of 0$\leq$x$\leq$0.75. The spin reorientation temperature of $(Nd_{1-x}R_x)_2Fe_{14}B$ decreases by increasing Pr-substitution to 118 K (x=0.5) then increases to 122 K (x=0.75). The spin reorientation angle at 4.2 K decreases by increasing rare earth substitution with the ratio of $\Delta$SRA=-0.073$^{\circ}$/Y at.% and $\Delta$SRA=-0.258$^{\circ}$/Pr at.% in composition range of 0$\leq$x$\leq$0.5. The spin reorientation is expected to disappear at x$\geq$0.9 in case of $(Nd_{1-x}R_x)_2Fe_{14}B$ and at x$\geq$0.8 in case of $(Nd_{1-x}R_x)_2Fe_{14}B$.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.307-314
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• 2005

In this paper we consider positive solutions of the following difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}},{\frac{B}{x_{n-2}}}],\;A,B\;>\;0$$. We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}x_{n-1}{\cdots}x_{n-k}},{\frac{B}{x_{n-(k+2)}{\cdots}x_{n-(2k+2)}}],\;A,B\;>\;0$$.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.1-6
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• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.

• Journal of the Korean Society for Heat Treatment
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• v.15 no.2
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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.

• Journal of the Korean Magnetics Society
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• v.7 no.6
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• pp.293-298
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• 1997

$Fe_5Si_Xb_{5-x}$ (x=0, 1, 2, 3) powders were prepared by mechanical alloying, and their phases and magnetic properties were investigated by using XRD, TEM, Mossbauer spectroscopy and VSM. Starting elements are incorporated into $\alpha$-Fe in the early stage of mechanical alloying, and the stable phases are formed as the milling proceeds. After the annealing at 80$0^{\circ}C$ for 2 hours, it is found that the FeB and $Fe_2B$ phases coexist for the $Fe_5B_5$(x=0) composition. By substituting Si for B, the formation of $Fe_2B$ phase is restricted and the $Fe_5SiB_2$, $Fe_2Si_{0.4}B_{0.6}$ and paramagnetic phase begin to appear. The FeB phase has wide range of hyperfine magnetic field because it is not fully crystallized on the annealing at 800 $^{\circ}C$. On the contrary, others have good crystalline phases and show well-defined hyperfine magnetic field. Magnetic saturation is highest for the $Fe_5B_5$ composition where the amount of the $Fe_2B$ phase in large.

• Korean Journal of Materials Research
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• v.8 no.2
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• pp.141-146
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• 1998

Ball mill을 이용하여 Ar 분위기에서 기계적 합금법으로 $Fe_{ 5}$$Si_{x}$ $B_{5-x}$ 분말을 제조하고, 제조된 분말을 연속 진공 열처리 시킨 후 Si첨가에 따른 결정구조 및 자기적성질을 조사하였다. 250시간 볼밀처리한 Fe$_{5}$ $B_{5}$ 합금에서 전체적으로 비정질 구조가 형성되었으나 일부분에 결정질이 존재하고 있었으며, $800^{\circ}C$에서 2시간 열처리하면 FeB와 $Fe_{2}$B 상이 혼재된 구조를 얻었다. 250시간 볼밀처리한 $Fe_{5}$ $Si_{2}$$B_{3}$합금에서 전체적으로 비정질 구조를 얻을 수 있었고, 이 시료를 2시간, $800^{\circ}C$로 열처리 하였을 때 $Fe_{2}$B상은 사라지고, 대부분 FeB의 균질한 상을 나타내었다. $Fe_{5}$ $B_{5}$ /조성에서는 분말 입자크기가 약 $1\mu\textrm{m}$이었으나, Si이 첨가되면 분말 입자크기가 약 $10\mu\textrm{m}$로 커졌다. Si의 첨가에 의해서 비정질상의 형성을 촉진시켜 단일 FeB상의 합성시간을 단축시킬 수 있었다.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1157-1163
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• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.

• Journal of Environmental Health Sciences
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• v.36 no.4
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• pp.313-322
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• 2010

The aim of this research was to apply experimental design methodology to optimization of conditions of electrochemical oxidation of Rhodamine B (RhB) and N, N-Dimethyl-4-nitrosoaniline (RNO, indicative of the OH radical). The reactions of electrochemical oxidation of RhB degradation were mathematically described as a function of the parameters of current ($X_1$), NaCl dosage ($X_2$) and pH ($X_3$) and modeled by the use of the central composite design. The application of response surface methodology (RSM) yielded the following regression equation, which is an empirical relationship between the removal efficiency of RhB and RNO and test variables in a coded unit: RhB removal efficiency (%) = $94.21+7.02X_1+10.94X_2-16.06X_3+3.70X_1X_3+9.05X_2X_3-{3.46X_1}^2-{4.67X_2}^2-{7.09X_3}^2$; RNO removal efficiency (%) = $54.78+13.33X_1+14.93X_2- 16.90X_3$. The model predictions agreed well with the experimentally observed result. Graphical response surface and contour plots were used to locate the optimum point. The estimated ridge of maximum response and optimal conditions for the RhB degradation using canonical analysis was 100.0%(current, 0.80 A; NaCl dosage, 2.97% and pH 6.37).