• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.153-159
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• 2008

For $\mathbb{F}[e^{{\pm}x}]_{\{{\partial}\}}$, all the derivations of the evaluation algebra $\mathbb{F}[e^{{\pm}x}]_{\{{\partial}\}}$ is found in the paper (see [16]). For $M=\{{\partial}_1,\;{\partial}_1^2\},\;Der_{non}(\mathbb{F}[e^{{\pm}x}]_M))$ of the evaluation algebra $\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M$ is found in the paper (see [2]). For $M=({\partial}_1^2,\;{\partial}_2^2)$, we find $Der_{non}(\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M))$ of the evaluation algebra $\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M$ in this paper.

• The KIPS Transactions:PartA
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• v.12A no.2 s.92
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• pp.95-102
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal which is widely used for a floating point division, calculates the reciprocal by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the reciprocal of a floating point number F, the algorithm repeats the following operations: '$'X_{i+1}=X=X_i*(2-e_r-F*X_i),\;i\in\{0,\;1,\;2,...n-1\}'$ with the initial value $'X_0=\frac{1}{F}{\pm}e_0'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 27 for the single precision floating point, and 57 for the double precision floating point. Let $'X_i=\frac{1}{F}+e_i{'}$, these is $'X_{i+1}=\frac{1}{F}-e_{i+1},\;where\;{'}e_{i+1}, is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to $'\frac{1}{F}{'}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables $(X_0=\frac{1}{F}{\pm}e_0)$ with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal unit. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia scientific computing, etc.

• Biomolecules & Therapeutics
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• v.10 no.4
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• pp.293-302
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• 2002

The classical concept for iron uptake into mammalian cells has been the endocytosis of transferrin( $T_{f}$ )-bound F $e^{3+}$ via the $T_{f}$ - $T_{f}$ receptor cycle. In this case, we could not explain the uptake of F $e^{2＋}$ ion and the export of iron from endosome. Studies on iron transport revealed that other transport system exists in epithelial cells of the intestine. One of non- $T_{f}$ -receptor-mediated transport systems is Nramp2/DMT1/DCT1 which transports M $n^{＋＋}$, $Mg^{＋＋}$, Z $n^{＋＋}$, $Co^{＋＋}$, N $i^{＋＋}$ or C $u^{＋＋}$ ion as well as F $e^{+2}$ ion. DMT1 was cloned from intestines of iron-deficient rats and shown to be a hydrogen ion-coupled iron transporter and a protein regulated by absorbed dietary iron. DMT1 is founded in other cells such as cortical and hippocampal glial cells as well as endothelial cells in duodenum. Two F $e^{3+}$ ion bound to transferrin( $T_{f}$ ) are taken up via the $T_{f}$ - $T_{f}$ receptor cycle in the intestinal epithelial cell. F $e^{3+}$ in endosome was converted to F $e^{2＋}$ ion, and then exported to cytosol via DMT1. F $e^{2＋}$ ion is taken up into cytosol via DMT1. Several other transporters such as FET, FRE, CCC2, AFT1, SMF, FTR, ZER, ZIP, ZnT and CTR have been reported recently and dysfunction of the transporters are related with diseases containing Wilson's disease, Menkes disease and hemochromatosis. Evidences from several studies strongly suggest that DMT1 is the major transporter of iron in the intestine and functions critically in transport of other metal ions.

• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.413-420
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal square mot calculates it by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal square root algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the rediprocal square root of a floating point number F, the algorithm repeats the following operations: '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$' with the initial value is '$X_0=\frac{1}{\sqrt{F}}{\pm}e_0$'. The bits to the right of p fractional bits in intermediate multiplication results are truncated and this truncation error is less than '$e_r=2^{-p}$'. The value of p is 28 for the single precision floating point, and 58 for the double precision floating point. Let '$X_i=\frac{1}{\sqrt{F}}{\pm}e_i$, there is '$X_{i+1}=\frac{1}{\sqrt{F}}-e_{i+1}$, where '$e_{i+1}{<}\frac{3{\sqrt{F}}{{e_i}^2}}{2}{\mp}\frac{{Fe_i}^3}{2}+2e_r$'. If '$|\frac{\sqrt{3-e_r-{FX_i}^2}}{2}-1|<2^{\frac{\sqrt{-p}{2}}}$' is true, '$e_{i+1}<8e_r$' is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to '$\frac{1}{\sqrt{F}}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications Per an operation is derived from many reciprocal square root tables ($X_0=\frac{1}{\sqrt{F}}{\pm}e_0$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• 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.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.323-334
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• 2008

We define injective and projective representations of quivers with two vertices with n arrows. In the representation of quivers we denote n edges between two vertices as ${\Rightarrow}$ and n maps as $f_1{\sim}f_n$, and $E{\oplus}E{\oplus}{\cdots}{\oplus}E$ (n times) as ${\oplus}_nE$. We show that if E is an injective left R-module, then $${\oplus}_nE{\Longrightarrow[50]^{p_1{\sim}p_n}}E$$ is an injective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $p_i(a_1,a_2,{\cdots},a_n)=a_i,\;i{\in}\{1,2,{\cdots},n\}$. Dually we show that if $M_1{\Longrightarrow[50]^{f_1{\sim}f_n}}M_2$ is an injective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are injective left R-modules. We also show that if P is a projective left R-module, then $$P\Longrightarrow[50]^{i_1{\sim}i_n}{\oplus}_nP$$ is a projective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $i_k$ is the kth injection. And if $M_1\Longrightarrow[50]^{f_1{\sim}f_n}M_2$ is an projective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are projective left R-modules.

• Nuclear Engineering and Technology
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• v.4 no.3
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• pp.214-222
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• 1972

In the optic,11 grade LiF crystal, the electron traps corresponding to the thermoluminescence(abbreviated to TL) glow peak develop as irradiation dose is increased. Originally the electron trap of the crystal has two levels but as the dose reaches to the order of 10$^4$rontgen, it attains five levels as observed in the TL glow curves. The five trap depths are determined from the glow peak temperatures for two different heating rates, $\theta$=6.6$^{\circ}C$/sec and 3.4$^{\circ}C$/sec. The electron trap depths have the following values E$_1$=0.79 eV, E$_2$=0.93 eV, E$_3$=1.02 eV, E$_4$=1.35 eV, E$_{5}$=1.69eV. The special feature of thermoluminescence of optical grade LiF is that the traps, except E$_1$and E$_2$corresponding to 12$0^{\circ}C$ glow peak and 15$0^{\circ}C$ glow peak for $\theta$=6.6$^{\circ}C$/sec, have severe thermal instability, namely E$_3$, E$_4$and E$_{5}$ levels disappear during bleaching process. These defects in the optical grade LiF crystal seem annealed out during the course of TL measurement. The fresh or long time unused LiF(Mg) crystal shows only two glow peaks at 17$0^{\circ}C$ and 23$0^{\circ}C$ for $\theta$=6.6$^{\circ}C$/sec, but upon sensitization with r-ray irradiation, it converts to the six glow peak state. The four electron traps, E$_1$, E$_2$, E$_3$, and E$_{6}$ created by r-ray irradiation and corresponding to the glow peaks at T=10$0^{\circ}C$ 13$0^{\circ}C$, 15$0^{\circ}C$ and 29$0^{\circ}C$ are stable and not easily annealed out thermally, The sensitization essentially required to LiF(Mg) dosimeter is to give the crystal the stable six levels in the electron trap. In optical grade LiF, the plot between logarithm of total TL output versus logarithm of r-ray dose gives more supra-linear feature than that of LiF(Mg). However, if one takes the height of 12$0^{\circ}C$ glow peak(S=6.6$^{\circ}C$/sec), instead of the total TL output, the curve becomes close to that of LiF(Mg).

• Archives of Pharmacal Research
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• v.21 no.6
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• pp.640-644
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• 1998

AT cells exhibit defective cell cycle regulation following DNA damage. Previous studies have shown that induction of p53 and p2i proteins are delayed in response to ionizing rad iation, resulting in the failure of G1/S checkpoint in AT cells. In this study, further investigation of the molecular mechanisms underlying G1/S phase progression in AT cells was conducted. Exponentially growing normal and AT cells were exposed to 2 Gly of ionizing radiation and the expression levels and functional activities of Rb and E2F-1 proteins were determined. We observed overexpression of hyperphosphorylated Rb and E2F-1 proteins in AT cells, which was unaffected post-irradiation. Furthermore, gel shift assays showed that E2F-1-DNA binding was constitutive in AT cells, whereas it was inhibited in control cells following exposure to ionizing radiation. The data suggests that abnormalities in the function of Rb and E2F-1 proteins may also be responsible for the failure of AT cells to arrest in the G1/S checkpoint in response to DNA damage.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.187-204
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• 2011

B. C. Carlson [Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232-242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some earlier results. Here, by simply splitting Srivastava's hypergeometric function $H_B$ into eight parts, we show how some useful and generalized relations between Srivastava's hypergeometric functions $H_B$ and $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ${\Psi}_2$ function and $Kamp\acute{e}$ de $F\acute{e}riet$ function, and between the product of exponential and Bessel functions with $Kamp\acute{e}$ de $F\acute{e}riet$ functions.

• MALSORI
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• no.63
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• pp.47-66
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• 2007

This study aims at exploring the degree of phonetic similarity between Korean and Japanese vowels in terms of acoustic features by performing the speech production test on Korean speakers and Japanese speakers. For this purpose, the speech of 16 Japanese speakers for Japanese speech data, and the speech of 16 Korean speakers for Korean speech data were utilized. The findings in assessing the degree of the similarity of the 7 nearest equivalents of the Korean and Japanese vowels are as follows: First, Korean /i/ and /e/ turned out to display no significant differences in terms of F1 and F2 with their counterparts, Japanese /i/ and /e/, and the distribution of F1 and F2 of Korean /i/ and /e/ in the distributional map completely overlapped with Japanese /i/ and /e/. Accordingly, Korean /i/ and /e/ were believed to be "identical." Second, Korean /a/, /o/, and /i/ displayed a significant difference in either F1 or F2, but showed a great similarity in distribution of F1 and F2 with Japanese /a/, /o/, and /m/ respectively. Korean /a/ /o/, and /i/, therefore, were categorized as very similar to Japanese vowels. Third, Korean /u/, which has the counterpart /m/ in Japanese, showed a significant difference in both F1 and F2, and only half of the distribution overlapped. Thus, Korean /u/ was analyzed as being a moderately similar vowel to Japanese vowels. Fourth, Korean /${\wedge}$/ did not have a close counterpart in Japanese, and was classified as "the least similar vowel."