• Journal of the Korean Magnetics Society
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• v.10 no.5
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• pp.220-224
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• 2000

Ultra-fine $Co_{1+x}$F $e_{2-}$2x/ $Ti_{x}$ $O_4$ferrite powders have been prepared by the sol-gel method. The crystallographic and magnetic properties of the sample have been investigated by means of x-ray diffraction, Mossbauer spetroscopy and vibrating sample magnetometry. The formation of nano crystallized particles is confirmed. The x-ray diffractions of all samples with various compositions clearly indicate the presence of spinel structure. The Mossbauer spectra could be fitted as the superposition of two sextets due to F $e^{3+}$ A-site and B-site. The IS and QS values nearly constant with substituted Co-Ti contents, whereas $H_{hf}$ of B-site decreases with increasing Co-Ti substitution in $Co_{1+x}$F $e_{2-}$2x/ $Ti_{x}$ $O_4$. The magnetic behaviour of powders shows that the saturation magnetization and the coercivity decrease with increasing x in $Co_{1+x}$F $e_{2-}$2x/ $Ti_{x}$ $O_4$.$.X>.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.907-913
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• 2010

Let D be an integrally closed domain with quotient field K, * be a star operation on D, X, Y be indeterminates over D, $N_*\;=\;\{f\;{\in}\;D[X]|\;(c_D(f))^*\;=\;D\}$ and $R\;=\;D[X]_{N_*}$. Let b be the b-operation on R, and let $*_c$ be the star operation on D defined by $I^{*_c}\;=\;(ID[X]_{N_*})^b\;{\cap}\;K$. Finally, let Kr(R, b) (resp., Kr(D, $*_c$)) be the Kronecker function ring of R (resp., D) with respect to Y (resp., X, Y). In this paper, we show that Kr(R, b) $\subseteq$ Kr(D, $*_c$) and Kr(R, b) is a kfr with respect to K(Y) and X in the notion of [2]. We also prove that Kr(R, b) = Kr(D, $*_c$) if and only if D is a $P{\ast}MD$. As a corollary, we have that if D is not a $P{\ast}MD$, then Kr(R, b) is an example of a kfr with respect to K(Y) and X but not a Kronecker function ring with respect to K(Y) and X.

• Journal of Magnetics
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• v.1 no.1
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• pp.31-36
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• 1996

An externally applied magnetic field during heat treating the $Nd_2Fe_{14}B/Fe_3B$ based spring magnet was found to enhance the exchange coupling between the hard and soft magnetic grains. More than 30% increase in $M_r/M_s$ values for melt-spun $Nd_2Fe_{73.5}Co_3$$(Hf_{1-x}Ga_x)B_{18.5}$ (x=0, 0.5, 1) alloys was resulted from a uniform distribution of $Fe_3B, \alpha-Fe$ and $Nd_2Fe_{14}B$ phases, and also from a reduced grain size of those phases by 20%. The externally applied magnetic field induced a uniform distribution of fine grains. A study of Mossbauer effect also report that the enhancement of total magnetization of nanocomposite $Nd_2Fe_{14}B/Fe_3B$ alloys is attributed to an increased formation of $Fe_3$B after magnetic annealing.

• Magazine of the Korean Society of Agricultural Engineers
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• v.15 no.4
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• pp.3160-3169
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• 1973

Rainfall, evaporation, and permeability of water are the most important factors in determining the demand of water. The Daegu area has only a meteorologi observatory and there is not sufficient data for adapting the advanced method for derivation of the estimated of evaporation in the Daegu area. However, by using available data, the writer devoted his great effort in deriving the most reasonable formula applicable to the Daegu area and it is adaptable for various purposes such as industry and estimation of groundwater etc. The data used in this study was the monthly amount of evaporation of the Daegu area for the past 13 years(1960 to 1970). A year can be divided into two groups by relative degrees of evaporation in this area: the first group (less evaporation) is January, February, March, October, November, and December, and the second (more evaporation) is April, May, June, July, August, and September. The amount of evaporation of the two groups were statistically treated by the theory of probability for derivation of estimated formula of evaporation. The formula derved is believed to fully consider. The characteristic hydrological environment of this area as the following shows: log(x＋3)=0.8963＋0.1125$\xi$..........(4, 5, 6, 7, 8, 9 month) log(x-0.7)=0.2051＋0.3023$\xi$..........(1, 2, 3, 10, 11, 12 month) This study obtained the above formula of probability of the monthly evaporation of this area by using the relation: $F_(x)=\frac{1}{{\surd}{\pi}}\int\limits_{-\infty}^{\xi}e^{-\xi2}d{\xi}\;{\xi}=alog_{\alpha}({\frac{x_0+b'}{x_0+b})\;(-b<x<{\infty})$ $$log(x_0＋b)=0.80961$ $$\frac{1}{a}=\sqrt{\frac{2N}{N-1}}\;Sx=0.1125$$ $$b=\frac{1}{m}\sum\limits_{i-I}^{m}b_s=3.14$$ $$S_x=\sqrt{\frac{1}{N}\sum\limits_{i-I}^{N}\{log(x_i+b)\}^2-\{log(x_i+b)\}^2}=0.0791$$ (4, 5, 6, 7, 8, 9 month) This formula may be advantageously applied to estimation of evaporation in the Daegu area. Notation for general terms has been denoted by following: $W_(x)$: probability of occurance. $$W_(x)=\int_x^{\infty}f(x)dx$$ P : probability $$P=\frac{N!}{t!(N-t)}{F_i^{N-{\pi}}(1-F_i)^l$$ $$F_{\eta}:\; Thomas\;plot\;F_{\eta}=(1-\frac{n}{N+1})$$ $X_l\;X_i$: maximun, minimum value of total number of sample size(other notation for general terms was used as needed)

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.875-883
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• 2012

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.11-21
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• 2003

In this paper, we solve the following functional equation $$af\(\frac{x+y+z}{b}\)+af\(\frac{x-y+z}{b}\)+af\(\frac{x+y-z}{b}\)+af\(\frac{-x+y+z}{b}\)=cf(x)+cf(y)+cf(z)$$, and prove the Hyers-Ulam-Rassias stability of the functional equation as given above.

• Journal of Korean Ophthalmic Optics Society
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• v.6 no.2
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• pp.65-70
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• 2001

We obtained the sum of two curvature ($C_x+C_y$) in toric lens which two toroidal surface is the right angle each other. $$C_x+C_y=\frac{x^2+y^2}{2r_1}+\frac{x^2}{2}(\frac{1}{r_2}-\frac{1}{r_1})$$ and the sum of two curvature ($C_a+C_b$) in toric lens about the cross angle. $$(C_a+C_b)=\frac{x^2cos^2{\alpha}_1}{2r_1}+\frac{x^2cos^2{\alpha}_2}{2r_2}+\frac{y^2sin^2{\alpha}_1}{2r_1}+\frac{y^2sin^2{\alpha}_2}{2r_2}$$ and claculated the parameter S, C, ${\theta}$ of a combination power in toric lens of the cross angle including surface curvature ($C_x$, $C_y$) values. $$S=(n-1)\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]-\frac{C}{2},\;C=-\frac{2(n-1)}{sin2{\theta}}\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]$$ $${\theta}=\frac{1}{2}tan^{-1}\[-\frac{{C_xy^2sin2{\theta}_1}+{C_yx^2sin2{\theta}_2}}{{C_xy^2cos2{\theta}_1}+{C_yx^2cos2{\theta}_2}}\]$$.

• Korean Journal of Plant Taxonomy
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• v.42 no.4
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• pp.307-315
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• 2012

Somatic chromosome numbers for 10 taxa and karyotypes analysis for 6 taxa of Korean Vicia were investigated. Somatic chromosome numbers of treated taxa were 2n = 12, 14 or 24 and therefore they proved to be diploid or tetraploid with basic chromosome numbers of x = 6 or 7. The chromosome number of V. hirticalycina (2n = 2x = 12) was reported for the first time in this study. The chromosome numbers of nine taxa were the same as in previous studies; V. angustifolia (2n = 2x = 12), V. cracca (2n = 4x = 24), V. hirsuta (2n = 2x = 14), V. tetrasperma (2n = 2x = 14 + 2B), V. amurensis (2n = 2x = 12), V. chosenensis (2n = 2x = 12, 12 + 2B), V. unijuga (2n = 4x = 24), V. unijuga f. minor (2n = 4x = 24), V. venosa var. cuspidata (2n = 4x = 24). The karyotypes of V. cracca, V. amurensis, V. hirticalycina, V. unijuga, V. unijuga f. minor, V. venosa var. cuspidata were observed as 2 m + 8 sm + 2 st, 2 m + 2 sm + 2 st, 3 m + 1 sm + 2 st, 4 m + 6 sm + 2 st, 4 m + 6 sm + 2 st, 4 m + 8 sm, respectively.

• Journal of the Korean Ceramic Society
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• v.40 no.5
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• pp.455-459
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• 2003

Tunneling spectra of B $i_2$S $r_2$Ca(C $u_{1-x}$ N $i_{x}$ )$_2$ $O_{8+}$$\delta$/ film by LPE method have been measured using break junctions. The energy gap 2$\Delta$ and 2$\Delta$/ $k_{B}$ $T_{c}$ $^{zero}$ increased with increase of ft. We obtained the energy gap Parameter 2$\Delta$(4.2 K) = 54.4~64 meV, and corresponding1y $\Delta$/ $k_{B}$ $T_{c}$ $^{zero}$=7.36~10.14, larger than the BCS value. The lattice constant c and critical temperature $T_{c}$ $^{zero}$ decrease with increase of $\chi$$_{L}$.