• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.343-358
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• 2017

Let {$X_i$} be a sequence of stationary ${\alpha}-mixing$ random variables with probability density function f(x). The recursive kernel estimators of f(x) are defined by $$\hat{f}_n(x)={\frac{1}{n\sqrt{b_n}}{\sum_{j=1}^{n}}b_j{^{-\frac{1}{2}}K(\frac{x-X_j}{b_j})\;and\;{\tilde{f}}_n(x)={\frac{1}{n}}{\sum_{j=1}^{n}}{\frac{1}{b_j}}K(\frac{x-X_j}{b_j})$$, where 0 < $b_n{\rightarrow}0$ is bandwith and K is some kernel function. Under appropriate conditions, we establish the Berry-Esseen bounds for these estimators of f(x), which show the convergence rates of asymptotic normality of the estimators.

• 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 Magnetics
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• v.7 no.4
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• pp.143-146
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• 2002

Mechanical milling technique is considered to be a useful way of processing the fine Nd-Fe-B-type powder with high coercivity. In the present study, phase evolution of the $Nd_{15}(Fe_{1-x}Co_{x})_{77}B_{8}$ (x=0-0.6) alloys during the high energy mechanical milling and annealing was investigated. The effect of Co-substitution on the crystallization of the mechanically milled $Nd_{15}(Fe_{1-x}Co_{x})_{77}B_{8}$ amorphous material was examined. The Nd-Fe-B-type alloys can be amorphized completely by a high-energy mechanical milling. On annealing of the amorphous material, fine $\alpha$-Fe crystallites form first from the amorphous. These fine $\alpha$-Fe crystallites reacts with the remaining amorphous afterwards, leading to crystallization to $Nd_2Fe_{14}$B phase. The Co-substitution for Fe in $Nd_{15}(Fe_{1-x}Co_{x})_{77}B_{8}$ ($\mu$x=0∼0.6) alloys lower significantly the crystallization temperature of the amorphous phase to the $Nd_2Fe_{14}$B phase. The mechanically milled and annealed $Nd_{15}Fe_{77}B_8$ alloy without Co-substitution exhibits consistently better magnetic properties with respect to the alloys with Co-substitution.

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.880-894
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• 1995

Magnetic properties of $Nd_{x}{(Fe_{0.9}Co_{0.1})}_{90-x}B_{6}Nb_{3}Cu_{1}(x=\;3,\;4,\;5)$ rrelt-spun alloys with 6 at% B content were studied aiming for finding out a new $\alpha$-Fe based Nd-Fe-B nanocrystalline alloy with good hard magnetic properties. $Nd_{x}{(Fe_{0.9}Co_{0.1})}_{90-x}B_{6}Nb_{3}Cu_{1}$ melt-spun alloys prepared by RSP crystallized to nanocrystalline phase. An optimally annealed $Nd_{3}{(Fe_{0.9}Co_{0.1})}_{87}B_{6}Nb_{3}Cu_{1}$ melt-spun alloys had larger volume ratio of $\alpha$-Fe(Co) than that of higher Nd content alloy and showed high remanence of about 1.6 T. On the contrary, the increase of Nd content in $Nd_{x}{(Fe_{0.9}Co_{0.1})}_{90-x}B_{6}Nb_{3}Cu_{1}$ alloys gave rise to gradual increase of an amount of $Nd_{2}{(Fe,\;Co)}_{14}B$ phase and improved coercivity. An optimally annealed $Nd_{5}{(Fe_{0.9}Co_{0.1})}_{85}B_{6}Nb_{3}Cu_{1}$ alloy showed the most improved hard mag¬netic properties. The remanence, coercivityand energy product of the alloy were 1.35 T, 219 kA/m (2.75 kOe), and $129\;kJ/m^{3}$ (16.2 MGOe), respectively.

• Bulletin of the Korean Chemical Society
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• v.6 no.6
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• pp.344-347
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• 1985

Perovskite type oxides of $SrTiO_3,SrZrO_3,and\;SrTi_{1-x}Zr_xO_3$ have been systematically synthesized at $1250^{\circ}C$and $1550^{\circ}C$ with specimens containing additions of up to x=0.9 of zirconium by solid state reactions and characterized by X-ray diffraction. X-ray diffraction studies showed that the compound $SrTi_{1-x}Zr_xO_3$ has cubic structure. The lattice paramters of $SrTi_{1-x}Zr_xO_3$ solid solutions obey the Vegard's law and fairly large increase in volume can acompany the formation of this solution with increasing Zr content(X). Assuming the lattice constants of perovskite type compounds $A(B_{1-x}B'_x)O_3$where $B_{1-x}B'_x$ is $Ti_{1-x}Zr_x$, to be a linear function of the ionic radii of B and B' ions, the disordered ion pair of $Ti^{4+}$and $Zr^{4+}$ was verified from the lattice constants of a series compounds varying x=0,0.05, 0.25, 0.5, 0.75, 0.9, and 1.0 with known isovalent pairs.

• Journal of Magnetics
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• v.7 no.4
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• pp.127-131
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• 2002

HDDR characteristics and magnetic properties of $Nd_{15}{(Fe_{1-x}Co_{x})}_{77}B_{8}$(x=0-0.6) alloys were investigated. The effect of applying magnetic field during the recombination step on the anisotropic nature of the HDDR-treated material was also examined. The $Nd_{15}{(Fe_{1-x}Co_{x})}_{77}B_{8}$ phase in the Nd-Fe-B alloys with high Co-substitution alloy had remarkably enhanced phase stability. The $Nd_{15}{(Fe_{1-x}Co_{x})}_{77}B_{8}$(x=0-0.6) alloys with high Co-substitution could be HDDR-treated successfully by only using high pressure hydrogen. However, these alloys had no appreciable coercivity. The poor coercivity of the HDDR-treated $Nd_{15}{(Fe_{1-x}Co_{x})}_{77}B_{8}$(x=0-0.6) alloys with high Co-substitution was attributed to the $Nd{(Fe,Co)}_2$ phase in the alloys. The magnetic filed applied during the recombination step had little effect on the anisotropic nature of the HDDR-treated powder.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.123-131
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• 2014

The purpose of this paper is to study the perturbation analysis of the matrix equation $X=I-A^*X^{-1}A+B^*X^{-1}B$. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.

• Journal of IKEEE
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• v.28 no.1
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• pp.33-37
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• 2024

In this paper, we report the design and the measurement of a X-band low noise amplifier (LNA) monolithic microwave integrated circuit (MMIC) using a 0.25 ㎛ gate length microstrip GaN-on-SiC high electron mobility transistor (HEMT) technology. The developed X-band GaN-based LNA MMIC achieves small signal gain of 22.75 dB ~ 25.14 dB and noise figure of 1.84 dB ~ 1.94 dB in the desired band of 9 GHz to 10 GHz. Input and output return loss values are -11.36 dB ~ -24.49 dB and -11.11 dB ~ -17.68 dB, respectively. The LNA MMIC can withstand 40 dBm (10 W) input power without performance degradation. The chip dimensions are 3.67 mm × 1.15 mm. The developed GaN-based LNA MMIC is applicable to various X-band applications.