• 대한수학회논문집
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• 제33권4호
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• pp.1181-1203
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• 2018

In this paper, we are mainly devoted to find out the general meromorphic solution of some specific type of differential equation. We have also answered an open question posed by Banerjee-Chakraborty [4] by extending their results in a large extent. We have provided an example showing that the conclusion of the results of Zhang-Yang [16] is not general true. Some examples have been exhibited to show that certain claims are true in our main result. Finally some questions have been posed for the future research in this direction.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.261-272
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• 2005

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $x'(t) = F(t, x(\cdot)), t > t^{\ast} {\Delta}x(t_{k})= I(t_{k}, x(t_{k}^{-})), k = 1,2,...$ By using Lyapunov functions and Razumikhin technique, some new Razumikhin-type theorems on boundedness are obtained.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.507-513
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• 2022

In this paper, we investigate some results on complex delay-differential equations of the classical Malmquist theorem. A classic illustrations of their results states us that if a complex delay equation w(t + 1) + w(t - 1) = R(t, w) with R(t, w) rational in both arguments admits (concede) a transcendental meromorphic solution of finite order, then deg_wR(t, w) ≤ 2. Development and upgrade of such results are presented in this paper. In addition, Borel exceptional zeros and poles seem to appear in special situations.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.197-208
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• 2024

In the present paper, we establish Ulam-Hyres and Ulam-Hyers-Rassias stabilities for nonlinear impulsive integro-differential equations with non-local condition in Banach space. The generalization of Grownwall type inequality is used to obtain our results.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.485-502
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• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• Korean Journal of Mathematics
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• 제8권2호
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• pp.163-172
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• 2000

Let $\mathcal{S}^{\prime}(\mathbb{R})$ be the dual of the Schwartz spaces $\mathcal{S}(\mathbb{R})$), A be a self-adjoint operator in $L^2(\mathbb{R})$ and ${\Gamma}(A)^*$ be the adjoint operator of ${\Gamma}(A)$ which is the second quantization operator of A. It is proven that under a suitable condition on A there exists a nuclear subspace $\mathcal{S}$ of a fundamental space $\mathcal{S}_A$ of Hida's type on $\mathcal{S}^{\prime}(\mathbb{R})$) such that ${\Gamma}(A)\mathcal{S}{\subset}\mathcal{S}$ and $e^{-t{\Gamma}(A)}\mathcal{S}{\subset}\mathcal{S}$, which enables us to show that a stochastic differential equation: $$dX(t)=dW(t)-{\Gamma}(A)^*X(t)dt$$, arising from the central limit theorem for spatially extended neurons has an unique solution on the dual space $\mathcal{S}^{\prime}$ of $\mathcal{S}$.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• 천문학논총
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• 제8권1호
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• pp.67-82
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• 1993

We developed a real-time CCD photometric program for IBM PC compatibles. This program can perform several functions necessary for CCD photometry such as telescope control. filter rotation, CCD camera control and data acquisition, two-dimensional image processing, simple aperture photometry and automatic differential photometry. The image processing of a spiral galaxy M51 observed with the SNU 61cm reflector shows a well developed spiral structure. Simple aperture photometric results of 14 stars in open cluster NGC 6871 almost accorded with those from IRAF/APPHOT. And we could confirm the light variation of eclipsing binary EM Cep by simultaneous automatic differential photometry of 7stars in NGC 7160. Due to the excellence in the precision and efficiency of automatic differential photometry using CCD. this program is very useful for the study of small amplitude ${\delta}$ Sct type variables and of the photometric stability of B ${\sim}$ F type stars.

• 전자공학회논문지A
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• 제31A권4호
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• pp.39-46
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• 1994

In this paper, the idea of using a multiple symbol obervation interval to improve error probability performance is applied to differential detection of MTCM(multiple trellis code modulation) with ${\Pi}$/4 shift QPSK, 8DPSK and 16DPSK. We propose two types of sliding multiple symbol differential detection algorithm, type 1 and type 2. The two types of sliding detection scheme are examined and compared with conventional(symbol-by-symbol) detection and bolck detection with these modulation formats in an additive white Gaussian noise(AWGN) using the Monte Carlo simulation. We show that the amount of improvement over conventional and block detection depends on the number of phases and the number of additional symbol intervals added to the observation. Computer simulagtion results are presented for 2,4,8 states in AWGN channel.

• Journal of Biosystems Engineering
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• 제22권4호
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• pp.497-502
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• 1997

Automation facilities of greenhouses have been continuously developed. However, the conventional two-stage worm gear reducer reveals some problems, including low transmission efficiency. The worm gear reducer also have some difficulties in manufacturing and short life. Therefore, this study was performed to develop a planetary gear reducer, having a high Sear reduction ratio and high torque transmission efficiency. The planetary gear system consisted of a fixed ring gear and a 2-teeth differential ring gear turning slow, as the planetary pinion orbits fast around the fixed ring gear. The developed gear system can achieve a high speed reduction rate at one stage. The reducing system was employed to the greenhouse ventilation system. The reducer has the transmission efficiency of 70.5%, 2∼3 times longer life time, and twofold roll-up torque at an affordable price, comparing with conventional reducers. This reducer can be also applied to many industrial equipments, such as industrial crane, hoist, elevator and gondola etc.