• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.281-292
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• 2005

In this paper a nonlinear alternative of Leray-Schauder type is proved in a Banach algebra involving three operators and it is further applied to a functional nonlinear integral equation of mixed type $$x(t)=k(t,x({\mu}(t)))+[f(t,x({\theta}(t)))]\(q(t)+{\int}_0{^{\sigma}^{(t)}}v(t,s)g(s,x({\eta}\(s)))ds\)$$ for proving the existence results in Banach algebras under generalized Lipschitz and $Carath{\acute{e}}odory$ conditions.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.101-113
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• 2005

We define and study a concept of $T_A$-space which is closely related to the generalized Gottlieb group. We know that X is a $T_A$-space if and only if there is a map $r:L(A,\;X){\rightarrow}L_0(A,\;X)$ called a $T_A$-structure such that $ri{\sim}1_{L_0(A,\;X)}$. The concepts of $T_{{\Sigma}B}$-spaces are preserved by retraction and product. We also introduce and study a dual concept of $T_A$-space.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.163-179
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• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.161-166
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• 1995

Let (${\Omega}$, ${\Sigma}$, ${\mu}$) be a finite perfect measure space, and let $f:{\Omega}{\rightarrow}X$ be strongly measurable. f is Pettis integrable if and only if there is a sequence ($f_n$) of Pettis integrable functions from ${\Omega}$ into X such that (a) there is a positive increasing function ${\phi}$ defined on [0, ${\infty}$) such that ${\lim}_{t{\rightarrow}{\infty}}\frac{{\phi}(t)}{t}={\infty}$ and sup $f_{\Omega}{\phi}({\mid}x^*f_n{\mid})d{\mu}$ < ${\infty}$ for each $x^*{\in}B_{X*}$,$n{\in}N$, and (b) for each $x^*{\in}X^*$, $lim_{n{\rightarrow}{\infty}}x^*f_n=x^*fa.e.$.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.4
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• pp.29-34
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• 2008

Generally, for conventional 3-D Hall sensor it is general that the sensitivity for $B_z$ is about 1/10 compared with those for $B_x$ or $B_y$. Therefore, in this work, we proposed 3-D Hall sensor with new structures. We have increased the sensitivity about 6 times to form the trench using anisotropic etching. And we have increased the sensitivity for the $B_z$ by 80 % compared with those of $B_x$ and $B_y$ using deposition of the ferromagnetic thin films on the bottom surface of the wafer to concentrate the magnetic fluxes. Sensitivities of the fabricated sensor with Ni/Fe film for $B_x,\;B_y$, and $B_z$ were measured as 361mV/T, 335mV/T, and 286mV/T, respectively. It has also showed sine wave of Hall voltages over a $360^{\circ}$ rotation. A packaged sensing part was $1.2{\times}1.2mm^2$. The measured linearity of the sensor was within ${\pm}3%$ of error. Resolution of the fabricated sensor was measured by $1{\times}10^{-5}T$.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.281-286
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• 2008

In this note we prove that if A and $B^*$ are subnormal operators and is a bounded linear operator such that AX - XB is a Hilbert-Schmidt operator, then f(A)X - Xf(B) is also a Hilbert-Schmidt operator and $${\parallel}f(A)X\;-\;Xf(B){\parallel}_2\;\leq\;L{\parallel}AX\;-\;XB{\parallel}_2$$, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and $X\;{\in}\;\cal{L}(\cal{H})$ is such that SX - XT belongs to a norm ideal (J, ${\parallel}\;{\cdot}\;{\parallel}_J$) and prove that f(S)X - Xf(T) $\in$ J and ${\parallel}f(S)X\;-\;Xf(T){\parallel}_J\;\leq\;C{\parallel}SX\;-\;XT{\parallel}_J$, for f in a certain class of functions.

• East Asian mathematical journal
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• v.25 no.2
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• Bulletin of the Korean Chemical Society
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• v.7 no.1
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• pp.29-35
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• 1986

An empirical formula for semiconductive metal oxides is proposed relating nonstoichiometric value x to a temperature or an oxygen partial pressure such that experimental data can be represented more accurately by the formula than by the well-known Arrhenius-type equation. The proposed empirical formula is log x = A + $B{\cdot}1000/T\;+\;C{\cdot}$exp$(-D{\cdot}1000/T)$ for a temperature dependence and $log\;{\times}\;=a\;+b{\cdot}log\;Po_2\;+\;c{\cdot}$exp$(-d{\cdot}log\;Po_2)$ for an oxygen partial pressure dependence. The A, B, C, D and a, b, c, d are parameters which are evaluated by means of a best-fitting method to experimental data. Subsequently, this empirical formula has been applied to the n-type metal oxides of $Zn_{1+x}O,\; Cd_{1+x}O,\;and\;PrO_{1.8003-x}$, and the p-type metal oxides of $CoO_{1+x},\; FeO_{1+x},\;and\;Cu_2O_{1+x}$. It gives a very good agreement with the experimental data through the best-fitted parameters within 6% of relative error. It is also possible to explain approximately qualitative characters of the parameters A, B, C, D and a, b, c, d from theoretical bases.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.2
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• pp.172-182
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• 2014

In this paper, is is presented the result of design and fabrication for X band T/R module using in active array radar. The high power RF circuit was fabricated using GaN element, so that high power and high efficiency was fulfilled comparing with the previous T/R module that have under 50 W output power for X band. Designed X band T/R module demonstrated 200 W(53 dBm) peak power, 20 us pulse width with 0.4 dB pulse droop and 20 % duty cycle. And it has characteristics of 26 dB receive gain and 4.5 dB noise figure. The structure was applied to prevent serious damage of receive path and GaN HPA by transmitting power during trasmit time of a pulse radar.

• Journal of the Korean Magnetics Society
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• v.7 no.3
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• pp.140-145
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• 1997

The amorphous state of $NdFe_{10.7}TiB_{0.3}$ and its nanocrystallization have been studied by X-ray diffraction, 모스바우어 spectroscopy, and a vibrating sample magnetometer (VSM), $NdFe_{10.7}TiB_{0.3}$ amorphous ribbons were fabricated by a sigle-roll melt-spinning method. The average hyperfine field $H_{hf}$(T) of the amorphous state shows a temperature dependence of $[H_{hf}(T)-H_{hf}(0)]/H_{hf}(0)=-0.46(T/T_c)^{3/2}-0.34(T/T_c)^{5/2}$ for $T/T_c<0.7$ indicative of spin wave excitation. The quadrupole splitting just above the Curie temperature $T_c$ is 0.46 mm/s, whereas the average quadrupole shift below $T_c$ is zero. The Curie and crystallization temperatures are determined to be $T_c$=380K and $T_x=490K$, respectively, for a heating rate of 5 K/min. The occupied area of nanocrystalline phase at around 770K is about 65%. Above the Curie temperature, VSM data show magnetic moments increases again. The formation of $\alpha$-Fe is the main reason for the increasing moment as conformed with the 모스바우어 measurements.