• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.175-190
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• 2007

By employing the Riccati transformation technique some new oscillation criteria for the second-order neutral delay dynamic equation $$(y(t)+r(t)y({\tau}(t)))^{{\Delta}{\Delta}}+p(t)y(\delta(t))=0$$, on a time scale $\mathbb{T}$ are established. Our results as a special case when $\mathbb{T}=\mathbb{R}$ and $\mathbb{T}=\mathbb{N}$ improve some well known oscillation criteria for second order neutral delay differential and difference equations, and when $\mathbb{T}=q^{\mathbb{N}}$, i.e., for second-order $q$-neutral difference equations our results are essentially new and can be applied on different types of time scales. Some examples are considered to illustrate the main results.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.219-234
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• 2012

By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criterion for the second-order nonlinear delay dynamic equations $$(a(t)(x^{\Delta}(t))^{\gamma})^{\Delta}+q(t)f(x({\tau}(t)))=0$$ on a time scale $\mathbb{T}$, here ${\gamma}{\geq}1$ is the ratio of two positive odd integers with $a$ and $q$ real-valued positive right-dense continuous functions defined on $\mathbb{T}$. Our results not only extend and improve some known results, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.

• Korean Journal of Optics and Photonics
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• v.16 no.3
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• pp.287-294
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• 2005

In this paper, an optical true time-delay (TTD) for two-dimensional (2-D) phased array antennas (PAAs), composed of a multi-wavelength optical source and a fiber optic delay line matrix consisting of $2\times2$ optical switches with optical fiber connected between cross ports, has been proposed. A 2-bit $\times4-bit$ optical TTD for 10-GHz 2-D PAAs has been implemented by cascading a wavelength dependent TTD (WD-TTD) and a wavelength independent TTD (WI-TTD). The unit time delay for WD-TTD and WI-TTD have been chosen as ${\Delta}T=12ps$ and $\Delta\tau=6ps$, respectively. Time delay have been measured at all radiation angles. The maximum delay error for WD-TTD was measured to be 3 ps due to jitter incurred from gain switching. For the case of WI-TTD, error was within ${\pm}\;1\;ps$. The proposed optical TTD for a 2-D PAA has the following advantages: 1) higher gain compared to one-dimensional linear PAAs, 2) stabilization of optical power and wavelength by using a multi-wavelength optical source, and 3) fast beam scan and simple operation due to electronic control of the $2\times2$ optical switches matrix on a column-by-column basis.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.499-513
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• 2011

By using the Riccati transformation technique, we study the oscillation and asymptotic behavior for the third-order nonlinear delay dynamic equations $(c(t)(p(t)x^{\Delta}(t))^{\Delta})^{\Delta}+q(t)f(x({\tau}(t)))=0$ on a time scale T, where c(t), p(t) and q(t) are real-valued positive rd-continuous functions defined on $\mathbb{T}$. We establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Our oscillation results are essentially new. Some examples are considered to illustrate the main results.

• 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 Society of Propulsion Engineers
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• v.20 no.3
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• pp.78-86
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• 2016

In this paper we propose a new frame transfer function model describing the variations of a heat release rate in response to an external flow oscillation in gas turbine systems. A critical difference of our model compared to the so-called $n-{\tau}$ model which has been widely used for a prediction of combustion instability (CI), is that our model is able to describe a nonlinear relation between phase and frequency. In contrast, the phase part of the $n-{\tau}$ model is a pure time delay and thus the phase should be a linear function of frequency, which is inconsistent with many experimental results of real combustion systems. For an illustration, our new model is applied to experimental data and the effect of phase nonlinearity is investigated in the context of combustion instability.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.213-229
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• 2018

In this work, we establish oscillation of the second order sublinear neutral delay dynamic equations of the form:$$(r(t)((x(t)+p(t)x({\tau}(t)))^{\Delta})^{\gamma})^{\Delta}+q(t)x^{\gamma}({\alpha}(t))+v(t)x^{\gamma}({\eta}(t))=0$$ on a time scale T by means of Riccati transformation technique, under the assumptions $${\displaystyle\smashmargin{2}{\int\nolimits^{\infty}}_{t_0}}\({\frac{1}{r(t)}}\)^{\frac{1}{\gamma}}{\Delta}t={\infty}$$, and ${\displaystyle\smashmargin{2}{\int\nolimits^{\infty}}_{t_0}}\({\frac{1}{r(t)}}\)^{\frac{1}{\gamma}}{\Delta}t$ < ${\infty}$, for various ranges of p(t), where 0 < ${\gamma}{\leq}1$ is a quotient of odd positive integers.

• Korean Journal of Optics and Photonics
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• v.15 no.5
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• pp.399-404
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• 2004

We present a quantum interference experiment with frequency-entangled pairs of photons with wavelength of 640 nm and 660 nm produced in the process of parametric down-conversion. When photon pairs in different angular frequencies $\omega$$_1$and $\omega$$_2$are registered by two detectors the coincidence counts exhibits a two-photon fringe as a function of relative time delay $\delta$$\tau$ of two photons within the coherence time depending on the arrangement of the detector pairs.

• Journal of the Korean Society of Propulsion Engineers
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• v.22 no.3
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• pp.46-52
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• 2018

A simple Crocco's $n-{\tau}$ time delay model and linear analysis of fluid flow coupled with acoustics are combined to investigate the high frequency combustion instability in the combustion chamber of LOX/hydrocarbon engines. The partial differential equation of the velocity potential is separated into ordinary differential equations, and eigenvalues that correspond to tangential resonance modes in the cylindrical chamber are determined. A general solution is obtained by solving the differential equation in the axial direction, and boundary conditions at the injector face and nozzle entrance are applied in order to calculate the chamber admittance. Frequency analysis of the transfer function is used to evaluate the stability of system. Stability margin is determined from the system gain and phase angle for the desired frequency range of 1T mode. The chamber model with variable baffle length and configurations are also considered in order to enhance the 1T mode stability of the combustion chamber.

• 전기의세계
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• v.18 no.1
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• pp.15-23
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• 1969

A lot of recent researches have shown that a Pseudo Random Binary Signal is a quite effective test signal to measure the impulse response of a plant. Generally speaking, however, such a response itself is not satisfactory to determine the appropriate control parameters or control inputs. Here, the author intends to estimate the unknown parameters of the First Order Plant with Dead Time by means of correlation method using M-sequence signal. The time constant T and the dead time L of the plant are eatimated with one tracking loop by automatically adjusting delay time .tau. of M-sequence signal according to variations of T and L. In this paper, a three level M-sequence signal is used as a test signal in order to avoid troublesome operations to calculate partial derivatives of a given performance index with respect to the parameters which are usually required in the Model Method. Several experiments with analogue computer using low pass filters as averaging circuits showed good results as expected.