• Bulletin of the Korean Chemical Society
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• v.27 no.5
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• pp.679-686
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• 2006

The positions of $PbI _2$ molecule synthesized into the molecular-dimensioned cavities of $\mid K_6 (Pb _4I_2)(PbI_2) _{0.67}-(H_2O)_2\mid [Si _{12}Al _{12}O _{48}]$-LTA have been determined. A single crystal of $\mid Pb _6\mid [Si _{12}Al _{12}O _{48}]$-LTA, prepared by the dynamic ion-exchange of $\mid Na _{12}\mid [Si _{12}Al _{12}O _{48}]$-LTA with aqueous 0.05 M $Pb _(NO _3)_2$ and washed with deionized water, was placed in a stream of flowing aqueous 0.05 M KI at 294 K for three days. The resulting crystal structure of the product $( \mid K_6 (Pb _4I_2)(PbI_2) _{0.67}(H_2O)_2\mid [Si _{12}Al _{12}O _{48}]$-LTA, a = 12.353(1) $\AA$) was determined at 294 K by single-crystal X-ray diffraction in the space group Pm3 m. It was refined with all measured reflections to the final error index $R_1$ = 0.062 for 623 reflections which $F_o$ > 4$\sigma$($F_o$). 4.67 $Pb ^{2+}$ and six $K^+$ ions per unit cell are found at three crystallographically distinct positions: 3.67 $Pb ^{2+}$ and three $K^+$ ions on the 3-fold axes opposite six-rings in the large cavity, three $K^+$ ions off the plane of the eight-rings, and the remaining one $Pb ^{2+}$ ion lies opposite four-ring in the large cavity. 0.67 $Pb ^{2+}$ ions and 1.34 $I^-$ ions per unit cell are found in the sodalite units, indicating the formation of a $PbI _2$ molecule in 67% of the sodalite units. Each $PbI _2$ (Pb-I = 3.392(7) $\AA$) is held in place by the coordination of its one $Pb ^{2+}$ ion to the zeolite framework (a $Pb ^{2+}$ cation is 0.74 $\AA$ from a six-ring oxygens) and by the coordination of its two $I^-$ ions to $K^+$ ions through six-rings (I-K = 3.63(4) $\AA$). Two additional $I^-$ ions per unit cell are found opposite a four-ring in the large cavity and form $Pb _2K_2I^{5+}$ and $Pb _2K_2I^{3+}$ moieties, respectively, and two water molecules per unit cell are also found on the 3-fold axes in the large cavity.

• Korean Journal of Food Science and Technology
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• v.51 no.4
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• pp.336-342
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• 2019

To elucidate structure-function relationship of polysaccharide from Angelica gigas, the AGE-2c-I was purified by two successive chromatography steps. AGE-2c-I showed a potent anti-complementary activity in a dose-dependent manner. AGE-2c-I with a molecular weight of 140 kDa comprised four monosaccharides and 13 glycosyl linkages, and strongly reacted with ${\beta}$-glucosyl Yariv reagent. For the fine structure analysis of AGE-2c-I, it was sequentially digested by exo-arabinofuranosidase and endo-galactanase. The results indicated that AGE-2c-I was a typical RG-I polysaccharide with side chains such as highly branched ${\alpha}$-arabinan, ${\beta}$-($1{\rightarrow}4$)-galactan and arabino-${\beta}$-3,6-galactan. To characterize the active moiety of AGE-2c-I, the anti-complementary activities of AGE-2c-I and its subfractions were assayed. It was observed that the anti-complementary activity of AGE-2c-I was due to the entire structure that resembled RG-I. In addition, arabino-${\beta}$-3,6-galactan side chain (GN-I) in AGE-2c-I probably plays a crucial role in the anti-complementary activity, whereas ${\alpha}$-arabinan side chain (AFN-I) consisting of 5-linked Araf and 3,5-branched Araf partially contributes to the activity.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.549-560
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• 1997

For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$$.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.153-161
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• 2011

Greg([Greg]) considered that $$N_k= \sum\limits_{i=1}^k(-1)^{i+1}P_{i,k}(p)N_1^i$$ where the $P_{i,k}$'s were polynomials with positive integer coefficients. In this paper, we will give the equations for $\sum\limits{P_{i,k}$ modulo 3. Using this, if we send a information for elliptic curve to sender, we can make a new checksum method for Manchester coding in IEEE 802.3 or IEEE 802.4.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.401-402
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• 2007

In this paper, we propose an automatic method to finding corresponding points. One 2D image can be changed 3D shape by 3D model. The main idea is using gabor wavelet values from 3D model. And Elastic Bunch Graph Matching algorithm is more stable in 3D model.

• ETRI Journal
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• v.23 no.4
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• pp.151-157
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• 2001

Spectroscopic and thermal analysis indicates that tellurite glasses doped with $B_2O_3$ and $GeO_2$ are promising candidate host materials for wide-band erbium doped fiber amplifier (EDFA) with a high 980 nm pump efficiency. In this study, we measured the thermal stabilities and the emission cross-sections for $Er^{3+}:^{4}I_{13/2}\;{\to}\;^{4}I_{15/2}$ transition in this tellurite glass system. We also determined the Judd-Ofelt parameters and calculated the radiative transition rates and the multiphonon relaxation rates in this glass system. The 15 mol% substitution of $B_2O_3$ for $TeO_2$ in the $Er^{3+}-doped\;75TeO_2-20ZnO-5K_2O$ glass raised the multiphonon relaxation rate for $^4I_{11/2}\;{\to}\;^4I_{13/2}$ transition from 4960 $s^{-1}$ to 24700 $s^{-1}$, but shortened the lifetime of the $^4I_{13/2}$ level by 14 % and reduced the emission cross-section for the $^4I_{13/2}\;{\to}\;^4I_{15/2}$ transition by 11%. The 15 mol% $GeO_2$ substitution in the same glass system also reduced the emission cross-section but increased the lifetime by 7%. However, the multiphonon relaxation rate for $^4I_{11/2}{\to}^4I_{13/2}$ transition was raised merely by 1000 $s^{-1}$. Therefore, a mixed substitution of $B_2O_3$ and $GeO_2$ for $TeO_2$ was concluded to be suitable for the 980 nm pump efficiency and the fluorescence efficiency of $^4I_{13/2}{\to}^4I_{15/2}$ transition in $Er^{3+}-doped$ tellurite glasses.

• Journal of the Korean Chemical Society
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• v.37 no.1
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• pp.76-82
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• 1993

Two crystal structures of fully dehydrated Ca(II) and Tl(I) exchanged zeolite A, $Ca_{5.6}Tl_{0.8}-A (a = 12.242(2){\AA})\;and\;Ca_{1.4}Tl_{9.2}-A (a = 12.191(1){\AA})$, have been determined by single-crystal X-ray diffraction methods in the cubic space group Pm3m at 21(1)$^{\circ}C$. All crystals were ion exchanged in flowing streams of mixed $Ca(NO_3)_2\;and\;TINO_3$ aqueous solution with total concentration of 0.05M. All crystals were dehydrated at 360$^{\circ}C$ under $2{\times}10^{-6}\;torr$ for two days. The structures of the dehydrated $Ca_{5.6}Tl_{0.8}-A$ and $Ca_{1.4}Tl_{9.2}-A$ were refined to the final error indicies, $R_1$ = 0.072 and $R_2$ = 0.076 with 179 reflections for I > 3$\sigma$(I), and $R_1$ = 0.048 and $R_2$ = 0.043 with 226 reflections for I > 3$\sigma$(I), respectively. In each structure, Ca(II) ions are located on threefold axes associated with three 6-ring oxygens. $Ca^{2+}$ ions prefer to 6-ring sites and $Tl^+$ ions prefer to 8-ring sites when total number of exchanged cations per unit cell is more than 8.

• Tunnel and Underground Space
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• v.12 no.4
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• pp.268-276
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• 2002

In this study, a 3D coordinate measurement system equipped with a laser displacement meter for digitizing rock joint surface was established and the digitized data were used to calculate several roughness parameters. The parameters used in this study were micro avenge inclination $angle(i_{ave})$, average slope of joint $asperity(SL_{ ave})$, root mean square of $i-angle(i_{rms})$, standard deviation of height(SDH), standard deviation of $i-angle(SD_i)$, roughness profile $index(R_P)$, and fractal dimension(D). The relationships between the roughness parameters based on the digitzation of the surface profile were analyzed. Since the measured value varied according to the degree of reflection and the variation of colors at the measuring point, rock joint surface was painted in white to minimize the influence of the surface conditions. The comparison of the measured values and roughness parameters before and after painting revealed the better consequence from measurement on the painted surfaces. Also, effect of measuring interval was studied. As measured interval was increased, roughness parameters were exponentially decreased. The incremental sequence of degree of decrease was $SDH\; i_{ave},\; i_{rms},\; SD_i,\;and\; R_ p-1$. As a result of comparison of parameters from pin-type measurement system and laser type measurement system, all value of parameters were higher when laser-type measurement system was used, except SDH.

• 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.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.595-613
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• 2022

Let R be a commutative ring with identity and let I be a proper ideal of R. In this paper, we study the ideal based extended zero-divisor graph 𝚪'_I (R) and prove that 𝚪'_I (R) is connected with diameter at most two and if 𝚪'_I (R) contains a cycle, then girth is at most four girth at most four. Furthermore, we study affinity the connection between the ideal based extended zero-divisor graph 𝚪'_I (R) and the ideal-based zero-divisor graph 𝚪_I (R) associated with the ideal I of R. Among the other things, for a radical ideal of a ring R, we show that the ideal-based extended zero-divisor graph 𝚪'_I (R) is identical to the ideal-based zero-divisor graph 𝚪_I (R) if and only if R has exactly two minimal prime-ideals which contain I.