• East Asian mathematical journal
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• v.18 no.2
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• JSTS:Journal of Semiconductor Technology and Science
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• v.9 no.4
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• pp.233-239
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• 2009

A mixed CT/DT 2-1 cascaded ${\Sigma\Delta}M$ which includes a first stage CT ${\Sigma\Delta}M$ and a second stage mismatch insensitive two-channel time-interleaved DT ${\Sigma\Delta}M$ is proposed. With this approach, the advantages of both CT and DT ${\Sigma\Delta}Ms$ including high speed operation, inherent anti-aliasing filter, and good coefficient matching can be achieved. The two-channel time-interleaved ${\Sigma\Delta}M$ used in the second stage alleviates the speed constraints of the DT ${\Sigma\Delta}M$, whereas enables better matching between the analog and digital filter coefficients compared to CT ${\Sigma\Delta}Ms$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.1C
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• pp.14-23
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• 2003

This thesis proposes a sigma-delta modulator architecture with 2 Ms/s data rate and 12 bit resolution. A sigma-delta modulate has the features of oversampling and noise shaping. With these features, it can be connected with low resolution A/D converter to achieve higher resolution A/D converter. Most previous researches have been concentrated on high resolution but low data rate applications, e.g. audio applications. But, in order to be applied to various applications such as wireless data communication, researches on sigma-delta modulator architecture for higher data rate are required. The proposed sigma-delta modulator architecture has the sampling rate of 16 times Nyquist rate to achieve high data rate, and consists of a cascade of two 2nd order sigma-delta modulator to get relatively high resolution. The experimental result shows that the proposed architecture achieves 12-bit resolution at 2 Ms/s data rate.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.6
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• pp.24-33
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• 2000

This paper investigates the relationship between J-integral and crack tip opening displacement, ${\delta}_t$ using Gordens results of numerical analysis. Estimation were carried out for several strength levels such as ultimate, flow, yield, ultimate-flow, flow-yield stress to determine the influence of strain hardening and the ratio of crack length to width on the $J-{\delta}_t$ relationship. It was found that for SE(B) specimens, the $J-{\delta}_t$ relationship can be applied to relate J to ${\delta}_t$ as follows $J=m_j{\times}{\sigma}_i{\times}{\delta}_t$ where $m_j=1.27773+0.8307({\alpha}/W)$, ${\sigma}_i:{\sigma}_U$, ${\sigma}_{U-F}={\frac{1}{2}} ({\sigma}_U+{\sigma}_F$), ${\sigma}_F$, ${\sigma}_F}$ $Y=({\sigma}_F+{\sigma}_Y)$, ${\sigma}_Y$

• The Korean Journal of Applied Statistics
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• v.4 no.1
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• pp.1-11
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• 1991

It is of great interest to consider the homogeniety of covariance matrices in MANOVA of discriminant analysis. If we lock at the problem of testing hypothesis, H : $\Sigma_1 = \Sigma_2$ from an invariance point of view where $\Sigma_i$ are the covariance matrix of two independent p-variate distribution, the testing problem is invariant under the group of nonsingular transformations and the hypothesis becomes H : $\delta_1 = \delta_2 = \cdots = \delta_p = 1$ where $\delta = (\delta_1, \delta_2, \cdots, \delta_p)$ is a vector of latent roots of $\Sigma$. Bias-corrected estimators of eigenvalues and sampling distribution of the test statistics proposed are obtained. Pooled-bootstrap method also considered for Bartlett's modified likelihood ratio statistics.

• Journal of the Korean Chemical Society
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• v.7 no.4
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• pp.238-244
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• 1963

Linear relationships between thermodynamic parameters, ,${\Delta}{\Delta}H^{\neq}=a{\sigma}+b{\Delta}{\Delta}S^{\neq}$, and $\Delta{\Delta}F^\neq=a\sigma+(b-T)\Delta{\Delta}S^\neq$, which were derived in the previous report have been tested with 57 reactions from literature. Linearities of plots $\Delta{\Delta}H^\neq-a\sigma$ vs. $\Delta{\Delta}S^\neq$ were generally good and the average correlation coefficient was 0.983 and the average of standard deviations from regression lines was 0.11. For 15 out of 57 reactions, Hammett plots were unsatisfactory and most of the reaction did not satisfy the Leffler equation. The general applicability of the new equations has been confirmed by the analysis of each reaction for which existing equations failed to correlate.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.29 no.6
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• pp.457-463
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• 2018

This paper compares the results of ${\Sigma}{\Delta}-STAP$ applied to actual radar test data and simulation data. The radar received a target signal from a virtual target generator and the clutter signal from a signal generator in an anechoic chamber. The simulation data were generated from ideal baseband radar signal modeling using the same parameter as that for the test radar. The ${\Sigma}{\Delta}-STAP$ results of the test and simulation data are similar in terms of the target signal shape and noise level. The SINR(Signal-to-Interfrence-plus-Noise Ratio) loss also had similar aspects, but the simulation result shows 1~2 dB higher SINR loss than the test result. This result verified that the simulation data can be a reasonable alternative test data when the ${\Sigma}{\Delta}-STAP$ is applied.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.28 no.4
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• pp.336-346
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• 2017

Applications of Sigma-Delta STAP, and a method of GMTI processing are presented for GMTI(Ground Moving Target Indication) mode of airborne radar with sigma, delta, and guard channels. We showed results of performance analyses of presented methods by clutter simulation with ICM(Internal Clutter Motion), signal processing simulation and MDV(Minimum Detectable Velocity). Presented methods for Sigma-Delta STAP and GMTI processing are easy to apply practically in GMTI mode of airborne radar without restriction by specific airborne radar system.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.19 no.9
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• pp.800-807
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• 2006

To enhance the conversion speed more fast, we separate the determination process of MSB and LSB with the two independent ADC circuits of the Incremental Sigma Delta ADC. After the 1st Incremental Sigma Delta ADC conversion finished, the 2nd Incremental Sigma Delta ADC conversion start while the 1st Incremental Sigma Delta ADC work on the next input. By determining the MSB and the LSB independently, the ADC conversion speed is improved by two times better than the conventional Extended Counting Incremental Sigma Delta ADC. In processing the 2nd Incremental Sigma Delta ADC, the inverting sample/hold circuit inverts the input the 2nd Incremental Sigma Delta ADC, which is the output of switched capacitor integrator within the 1st Incremental Sigma Delta ADC block. The increased active area is relatively small by the added analog circuit, because the digital circuit area is more large than analog. In this paper, a 14 bit Extended Counting Incremental Sigma-Delta ADC is implemented in $0.25{\mu}m$ CMOS process with a single 2.5 V supply voltage. The conversion speed is about 150 Ksamples/sec at a clock rate of 25 MHz. The 1 MSB is 0.02 V. The active area is $0.50\;x\;0.35mm^{2}$. The averaged power consumption is 1.7 mW.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.85-101
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• 2004

Let A be a Hopf algebra with a linear form ${\sigma}:k{\rightarrow}A{\otimes}A$, which is convolution invertible, such that ${\sigma}_{21}({\Delta}{\otimes}id){\tau}({\sigma}(1))={\sigma}_{32}(id{\otimes}{\Delta}){\tau}({\sigma}(1))$. We define Hopf algebras, ($A_{\sigma}$, m, u, ${\Delta}_{\sigma}$, ${\varepsilon}$, $S_{\sigma}$). If B and C are opposite skew copaired Hopf algebras and $A=B{\otimes}_kC$ then we find Hopf algebras, ($A_{[{\sigma}]}$, $m_B{\otimes}m_C$, $u_B{\otimes}u_C$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}B{\otimes}{\varepsilon}_C$, $S_{[{\sigma}]}$). Let H be a finite dimensional commutative Hopf algebra with dual basis $\{h_i\}$ and $\{h_i^*\}$, and let $A=H^{op}{\otimes}H^*$. We show that if we define ${\sigma}:k{\rightarrow}H^{op}{\otimes}H^*$ by ${\sigma}(1)={\sum}h_i{\otimes}h_i^*$ then ($A_{[{\sigma}]}$, $m_A$, $u_A$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}_A$, $S_{[{\sigma}]}$) is the dual space of Drinfeld double, $D(H)^*$, as Hopf algebra.