• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.45-51
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• 2000

We will investigate some properties of integro-delay-differential equations, $$x^{\prime}(t)=A(t)x(t-g_1(t,x_t))+{\int}_{t_0}^{t}B(t,s)x(s-g_2(s,x_s))ds,\;t_0{\geq}0,\\x(t_0)={\phi}$$,

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.101-113
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• 2000

In this paper, we study controllability of nonlinear delay parabolic equa-tions with nonlocal initial condition under boundary input.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.273-283
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• 2000

In this paper we consider two delay equations with in-finite delay. We will give two sufficient conditions for the positive and zero equilibriums of these equations to be a global attractor respectively.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.39-47
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• 2003

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7］are generalized and improved.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.273-284
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• 2006

In this paper, we study nonoscillatory solutions of a class of second order nonlinear neutral delay differential equations with positive and negative coefficients. Some sufficient conditions for existence of nonoscillatory solutions are obtained.

• 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.

• ETRI Journal
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• v.28 no.2
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• pp.231-234
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• 2006

The cancellation performance of a linearization loop is limited by the degree of an amplitude imbalance and a phase imbalance. A delay mismatch causes a phase variation as a function of frequency. Therefore, the cancellation performance and linearization bandwidth are limited by a delay mismatch. The expression for the effects of an amplitude imbalance, a phase imbalance, and a delay mismatch on the characteristics of a linearization loop is derived and analyzed. The simulation results are compared with the results obtained by means of using a commercial simulation tool and the exact agreement is reported. The derived equation could be used in designing a linearization loop and predicting the cancellation performance of the linearization loop usefully. Some useful characteristics, known from the simulation results obtained by using the derived equation, of a linearization loop for designing and implementing feedforward amplifiers are described in detail.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.2
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• pp.374-379
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• 2010

In this paper, we have mathematically analyzed lumped element type negative group delay circuit (NGDC) and derived general design equation. The applicability of the proposed design equation is validated with mathematical and circuit simulation as well as with experimental results for intentional mobile telecommunication 2000 (IMT-2000) downlink band. As a design example, single branch NGDC with -0.8ns of group delay (GD) for narrow bandwidth of the specific frequency is simulated and fabricated. Finally, $\pi$-network NGDC is proposed and validated to obtain wideband GD response of $-1.7{\pm}0.06$ nsec for 60 MHz.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.669-688
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• 2021

The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$\{{\frac{du}{dt}}+Au=F(t,\;u_t),\;t{\geq}s,\\\;u_s({\theta})={\phi}({\theta}),\;{\forall}{\theta}{\in}(-{{\infty}},\;0],\;s{\in}{\mathbb{R}},$$ where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.