• Honam Mathematical Journal
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• v.37 no.3
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• pp.339-352
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• 2015

We aim at giving explicit expressions of $${\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}$$, where i = 0, ${\pm}1$, ${\ldots}$, ${\pm}9$ and $\{{\Delta}_n\}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.

• The KIPS Transactions:PartD
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• v.9D no.1
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• pp.21-30
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• 2002

The active database system introduces the active rules detecting specified state. As the condition evaluation of the active rules is performed every time an event occurs, the performance of the system has a great influence, depending on the conditions processing method. In this paper, we propose the conditions processing system with the preprocessor which determines the delta tree structure, constructs the classification tree, and generates the aggregate function table. Due to the characteristics of the active database through which the active rules can be comprehended beforehand, the preprocessor can be introduced. In this paper, the delta tree which can effectively process the join, selection operations, and the aggregate function is suggested, and it can enhance the condition evaluation performance. And we propose the classification tree which effectively processes the join operation and the aggregate function table processing the aggregate function which demands high cost. In this paper, the conditions processing system can be expected to enhance the performance of conditions processing in the active rules as the number of conditions comparison decreases because of the structure which is made in the preprocessor.

• Journal of Korean Society of Steel Construction
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• v.11 no.4 s.41
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• pp.417-424
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• 1999

In this paper a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity includes gradual yielding associated with flexural behaviors. The geometric nonlinearity includes the second-order effects associated with $P-{\delta}\;and\;P-{\Delta}$ effects. The material nonlinearity at the node is considered using the concept of P-M hinge consisting of many fibers. The geometric nonlinearity is considered by the use of stability function. The nonlinearity caused by shear and torsional interaction effects is neglected. The modified incremental displacement method is used as the solution technique. The load-displacements predicted by the proposed analysis compare well with those given by other approaches.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.3
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• pp.31-35
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• 2009

In this paper, tunable 4th order SC(switched capacitor) bandpass ${\sigma}-{\Delta}$(Sigma-Delta) modulator with advanced architecture that can adjust the IF by two coefficient values is proposed for data conversion in the wireless communication. Its architecture can optionally adjust all the 4th order noise transfer function in comparison with the conventional architecture. In order to adjust the IF, the conventional architecture needs the four variable coefficients values, basic clocks and eight clocks. On the other hand, the proposed architecture can adjust the IF by two variable coefficient values and basic clocks only.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.2
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• pp.135-139
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• 2008

In this paper, tunable SC(switched capacitor) 2nd order bandpass $\Sigma-\Delta$(Sigma-Delta) modulator with novel architecture that can adjust the IF band center frequency by one coefficient value is proposed for data conversion in the IF(Intermediate Frequency) band. Its architecture can optionally adjust all the 2nd order noise transfer function in comparison with the conventional architecture. In order to adjust the center frequency, the conventional architecture needs the two variable coefficient values, basic clock and eight clocks. On the other hand, the proposed architecture can adjust the center frequency by one variable coefficient value and basic clock only.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.777-789
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• 2016

In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term $$(r(t)x^{\Delta}(t))^{\Delta}+q({\sigma}(t))x^{\Delta}(t)+p(t)f(x({\tau}(t)))=e(t)$$, and $$(r(t)x^{\Delta}(t))^{\Delta}+q(t)x^{\Delta}(t)+p(t)f(x({\sigma}(t)))=e(t)$$, on a time scale ${\mathbb{T}}$, where r(t), p(t) and q(t) are real-valued right-dense continuous (rd-continuous) functions [1] defined on ${\mathbb{T}}$ with p(t) < 0 and ${\tau}:{\mathbb{T}}{\rightarrow}{\mathbb{T}}$ is a strictly increasing differentiable function and ${\lim}_{t{\rightarrow}{\infty}}{\tau}(t)={\infty}$. No restriction is imposed on the forcing term e(t) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.299-309
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• 2003

Let ${\pi}_1,...,{\pi}_{k}$k($\geq$2) independent logistic populations such that the cumulative distribution function (cdf) of an observation from the population ${\pi}_{i}$ is $$F_{i}\;=\; {\frac{1}{1+exp{-\pi(x-{\mu}_{i})/(\sigma\sqrt{3})}}},\;$\mid$x$\mid$<\;{\infty}$$ where ${\mu}_{i}(-{\infty}\; < \; {\mu}_{i}\; <\; {\infty}$ is unknown location mean and ${\delta}^2$ is known variance, i ＝ 1,..., $textsc{k}$. Let ${\mu}_{[k]}$ be the largest of all ${\mu}$'s and the population ${\pi}_{i}$ is defined to be 'good' if ${\mu}_{i}\;{\geq}\;{\mu}_{[k]}\;-\;{\delta}_1$, where ${\delta}_1\;>\;0$, i = 1,...,$textsc{k}$. A selection procedure based on sample median is proposed to select a subset of $textsc{k}$ logistic populations which includes all the good populations with probability at least $P^{*}$(a preassigned value). Simultaneous confidence intervals for the differences of location parameters, which can be derived with the help of proposed procedures, are discussed. If a population with location parameter ${\mu}_{i}\;<\;{\mu}_{[k]}\;-\;{\delta}_2({\delta}_2\;>{\delta}_1)$, i ＝ 1,...,$textsc{k}$ is considered 'bad', a selection procedure is proposed so that the probability of either selecting a bad population or omitting a good population is at most 1­ $P^{*}$.

• Bulletin of the Korean Chemical Society
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• v.14 no.4
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• pp.515-519
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• 1993

The retention behavior of proteins was investigated by using hydrophobic interaction chromatography (HIC), comparing to the results obtained in reversed-phase chromatography (RPC) described in the previous paper. A SynChropak propyl column was employed with 0.05 M phosphate buffer (pH 7.0) containing sodium sulfate. Conformational changes were recognized by examining Z values as a function of sodium sulfate concentration over a range of temperature between 5 and 65$^{\circ}C$. Z values did not change significantly at the range of the temperature showing the consistent ${\Delta}H^{\circ}$ and ${\Delta}S^{\circ}$ values. The sign and the magnitude of ${\Delta}H^{\circ}$ and ${\Delta}S^{\circ}$ of proteins in HIC were compared with those obtained in RPC. The signs of ${\Delta}H^{\circ}$ and ${\Delta}S^{\circ}$ of proteins in HIC were all positive, while those of proteins in RPC were all negative. These results suggested that the retention of proteins in HIC and in RPC were entropy-driven and enthalpy-driven process, respectively. From the two different investigations, it was concluded that the retention mechanism of RPC and HIC was based on the same fundamental principle in which separation is dependent on hydrophobicity, but the retention behavior of the proteins in HIC is clearly different from that observed in RPC.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.327-333
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• 2014

In this paper, we define the extension $f^*:[a,b]{\rightarrow}\mathbb{R}$ of a function $f:[a,b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale $\mathbb{T}$ and show that f is Riemann delta integrable on $[a,b]_{\mathbb{T}}$ if and only if $f^*$ is Riemann integrable on [a,b].