• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.839-850
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• 2021

In this paper, we investigate the uniqueness problems of certain types of difference-differential polynomials of entire functions sharing a small function. The results of the paper improve and generalize the recent results due to Biswajit Saha [18].

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.597-607
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• 2019

In this article, we consider properties of transcendental meromorphic solutions of the complex differential-difference equation $$P_n(z)f^{(n)}(2+{\eta}_n)+{\cdots}+P_1(z)f^{\prime}(z+{\eta}_1)+P_0(z)f(z+{\eta}_0)=0$$, and its non-homogeneous equation. Our results extend earlier results by Liu et al. [9].

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.549-565
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• 2024

In this paper, we investigate the uniqueness of linear difference differential polynomials sharing a small function. By using the concepts of weakly weighted and relaxed weighted sharing of transcendental entire functions with finite order, we obtained the corresponding results, which improve and extend some results of Chao Meng [14].

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.983-1002
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• 2021

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.465-483
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• 2021

Let 𝓗(𝔻) be the space of analytic functions on the unit disc 𝔻. Let 𝜓 = (𝜓_j)ⁿ_j=0 and 𝚽 = (𝚽_j)ⁿ_j=0 be such that 𝜓_j, 𝚽_j ∈ 𝓗(𝔻). The linear differential operator is defined by T_𝜓(f) = ∑ⁿ_j=0 𝜓_jf^(j), f ∈ 𝓗(𝔻). We characterize the boundedness and compactness of the difference operator (T_𝜓 - T_𝚽)(f) = ∑ⁿ_j=0 (𝜓_j - 𝚽_j) f^(j) between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Proceedings of the KIEE Conference
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• 2002.07a
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• pp.16-18
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• 2002

This paper proposes a difference-blocked current differential relaying algorithm for power transformers. The proposed algorithm observes that the shape of the differential current is changed using the difference. If the change is detected, output of current differential relay is blocked for a certain time. In this way, the algorithm distinguishes internal faults from magnetizing inrush. The proposed algorithm uses only currents and is unaffected by the remanent flux.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.833-846
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• 1999

In this paper, we will study the relationship between the controlling factor of the solution to a difference equation and the solution of the corresponding differential equation. Many times the controlling factors are the same. But even the controlling factor of the two solutions may be different, we will discover a way to compute, for first order non-linear equations, the controlling factor of the solution to the difference equation using the solution of the differential equation.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.297-305
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• 2020

We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.