• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.1
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• pp.188-198
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• 2005

The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's 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 square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. 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 doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. 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 ($T=\frac{1}{\sqrt{F}}+e_i$) 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 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.

• Nuclear Engineering and Technology
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• v.14 no.1
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• pp.22-40
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• 1982

The nuclear LS-energy matrix elements have been calculated with the harmonic oscillator shell model wave functions for the configurations ( $l_{i}$ $l_{i+1}$｜ $l_{i}$ $l_{i+1}$) where 1$_1$= $l_{s}$ , $l_2$=lp, $l_3$=ld, 2s, $l_4$=1f, 2p, $l_{5}$ =1g, 2d, 3s. The resulting matrix elements are expressed in terms of both Talmi integrals $I_1$ and Slater integrals $F^{k}$ . In addition to this various sum rules are derived and applied to check the results of the calculations.ons.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.517-523
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• 2007

Let R/I be an Artinian algebra of codimension 3 with Hilbert function H such that $h_{d-1}>h_d=h_{d+1}$. Ahn and Shin showed that A cannot be level if ${\beta}_{1,d+2}(Gin(I))={\beta}_{2,d+2}(Gin(I))$ where Gin(I) is a generic initial ideal of I. We prove that some certain graded Artinian algebra R/I cannot be level if either ${\beta}_{1,d}(I^{lex})={\beta}_{2,d}(I^{lex})+1\;or\;{\beta}_{1,d+1}(I^{lex})={\beta}_{2,d+1}(I^{lex})\;where\;I^{lex}$ is a lex-segment ideal associated to I.

• Journal of Power Electronics
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• v.4 no.4
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• pp.217-227
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• 2004

A robust controller that combines the merits of the feed-back, feed-forward and model-following control for induction motor drives utilizing field orientation control is designed in this paper. The proposed controller is a two-degrees-of­freedom (2DOF) integral plus proportional & rate feedback (I-PD) speed controller combined with a model-following (2DOF I-PD MFC) speed controller. A systematic mathematical procedure is derived to find the parameters of the 2DOF I-PD MFC speed controller according to certain specifications for the drive system. Initially, we start with the I-PD feed­back controller design, then we add the feed-forward controller. These two controllers combine to form the 2DOF I-PD speed controller. To realize high dynamic performance for disturbance rejection and set point tracking characterisitics, a MFC controller is designed and added to the 2DOF I-PD controller. This combination is called a 2DOF I-PD MFC speed controller. We then study the effect of the 2DOF I-PD MFC speed controller on the performance of the drive system under different operating conditions. A computer simulation is also run to demonstrate the effectiveness of the proposed controller. The results verify that the proposed 2DOF I-PD MFC controller is more accurate and more reliable in the presence of load disturbance and motor parameter variations than a 2DOF I-PD controller without a MFC. Also, the proposed controller grants rapid and accurate responses to the reference model, regardless of whether a load disturbance is imposed or the induction machine parameters vary.

• The Korean Journal of Physiology and Pharmacology
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• v.4 no.5
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• pp.403-408
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• 2000

The outward currents elicited in hamster eggs by depolarizing pulses were studied. The currents appeared to comprise at least two components, a transient outward component $(I_{to})$ and a steady-state outward component $(I_{\infty}).\;I_{to}$ was transiently followed by the cessation of inward $Ca^{2+}$ current $(I_{Ca}),$ and its current-voltage (I-V) relation was a mirror image of that of $(I_{Ca}).$ Either blockade of $(I_{Ca})$ by $Co^{2+}$ or replacement of $Ca^{2+}$ with $Sr^{2+}$ abolished $I_{to}$ without change in $I_{\infty}.$ Intracellular EGTA (10 mM) inhibited $I_{to}$ but not $I_{\infty}.$ suggesting strongly that generation of $I_{to}$ requires intracellular $Ca^{2+}.$ Apamin (1 nM) abolished selectively $I_{to},$ indicatingthat $I_{to}$ is $Ca^{2+}-dependent\;K^+$ current. On the other hand, $I_{\infty}$ was $Ca^{2+}-independent.$ Both $I_{to}$ and $I_{\infty}$ were completely inhibited by internal $Cs^+$ and external TEA. The estimated reversal potential of $I_{to}$ was close to the theoretical $E_K.$ Taken together, both outward currents were carried by $K^+$ channels. From these results, $I_{to}$ is likely to be a current responsible for the hyperpolarizing responses seen in hamster eggs at fertilization.

• Korean Journal of Crystallography
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• v.11 no.1
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• pp.10-15
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• 2000

Compound trans-[FeH(NCS(i-Pr)-S)(dppe)₂](1) reacted with isopropyl iodide (i-PrI) to give an Fe(II)-organic isothiocyanide complex, trans-[FeH(NCS(i-Pr)-S)(dppe)₂]I (2). Compound 2 was structurally characterized, in which the hydride ligand appears to be involved in the "dihydrogen" bonding, M-H…H-C. Crystallographic data for 2: monoclinic space group P2₁/n, a=13.490(2)Å, b=17.269(3)Å, c=21.384(3)Å, β=90.682(7)°, Z=4, R(wR₂)=0.0348(0.0894).

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.231-244
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• 2005

We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space H. $$Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,$$ $where\;Lu^i=\;\frac{\partial u^i}{\partial t}\;-\;Au^{i}$, A is a linear closed operator on Hand M(t, x) is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\beta^1\leq\beta^2\;then\;u^1{\leq}u^2$ under some conditions.

• Journal of the Korean Ceramic Society
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• v.31 no.8
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• pp.861-868
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• 1994

CaO-Al2O3 glass is a good candidate as optical fiber amplifier and laser. In this study, optical properties for 4I13/2longrightarrow4I15/2 transition of Er3+ ions doped in CaO-Al2O3 glasses were investigated. Optical absorptions, radiative transition probabilities and lifetimes for 4I13/2 level were evaluated by using Judd-Ofelt theory. Also, induced- emmision cross-sections of 4I13/2longrightarrow4I15/2 transition were calculated. Radiative transition probability and lifetime of 4I13/2 level were 144.6s-1, 690$mutextrm{s}$ respectively for 60CaO.40Al2O3 glass(FS0) and 152.6s-1, 660 $mutextrm{s}$ for 54 CaO.36Al2O3.10SiO2 glass (FS10). Each induced-emission cross sections for FS0 and FS10 was 0.749$\times$10-20 $\textrm{cm}^2$, 0.892$\times$10-20 $\textrm{cm}^2$. Obtained values were comparable with those of ZBLA glass studied as optical fiber amplifier and laser material.

• Korean Journal of Animal Reproduction
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• v.22 no.1
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• pp.89-94
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• 1998

A study was made to investigate the effects of concerning factors with IGF-I recovery on the final IGF-I concentration in the effluent and to establish recovery conditions of IGF-I using liquid emulsion membranes(LEM). D2EHPA was best carrier among Amberlite LA2, Aliquit 336 and D2EHPA for recovery rate of IGF-I. Recovery rate of IGF-I by D2EHPA volume in the oil phase was increased as increasing D2EHPA volume, and optimal volume of D2EHPA was 5% in this experiment. The recovery rate of IGF-I by D2EHPA was increased by the decreasing from pH 7 to pH 4 of external phase. Therefore, optimal pH value was 4.0. Optimal concentrations of sulfuric acid in internal phase, paraffin oil in oil phase and Span 80 for recovery rate of IGF-I were 0.1M, 2.0% and 5%, respectively, and optimal W/O rate was 2. These results suggested that optimal conditions for recovery of IGF-I were D2EHPA(5%) as carrier, pH 4.0, 0.1M sulfuric acid, 2% paraffin oil, 2.0 W/O rate and 5.0% Span 80.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.573-580
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• 2006

In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation $$x_{n+1}-x_n+\sum_{i=1}^{m}p_ix_{n-k_i}+qx_{n-z}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$ and $z{\in}\{-1,0\}$. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation $${\Delta}^rx_n+\sum_{i=1}^{m}p_ix_{n-k_i}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$. The results are given terms of the $p_i$ and the $k_i$ for each $i=1,2,{\cdots},m$.