• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.545-562
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• 2022

Using the conception of weakly weighted sharing we discussed the value distribution of the differential product functions constructed with a polynomial and difference operator of entire function. Here we established two uniqueness result on product of difference operators when two such functions share a small function.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.117-125
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• 2024

In this paper, our focus is on exploring value sharing problems related to a transcendental entire function f and its associated differential-difference polynomials. We aim to establish some results which are related to differential-difference counterpart of the Brück conjecture.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.465-472
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• 2010

In this paper, we investigate the extent of the set on which the modulus of a meromorphic function is lower bounded by a term related to some Nevanlinna Theory functionals. A. I. Shcherba estimate the size of the set on which the modulus of an entire function is lower bounded by 1. Our theorem in this paper shows that the same result holds in the case that the lower bound is replaced by$lT(r,f)$, $0{\leq}l$ < 1, which improves Shcherba's result. We also give a similar estimation for meromorphic functions.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.573-583
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• 2005

For a certain set G in the complex plane, we construct a transcendental entire function f whose translated family ${f(2^{n}z)}$ is normal only at z in G and establish the relation between the normal family and the Julia direction of f(z).

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.13-33
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• 2015

In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1209-1219
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• 2013

In the paper, we have two purposes. Firstly, we estimate the hyper-order of an entire function which shares two functions with it's first derivative, and two examples are given to show the conclusion is sharp. Secondly, we generalize the Br$\ddot{u}$ck conjecture with the idea of sharing functions.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1471-1479
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• 2013

In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form $$f^n+Q(z,f)=h$$, where $n{\geq}2$ is an integer, $Q(z,f)$ is a differential-difference polynomial in $f$ with polynomial coefficients, and $h$ is a meromorphic function of order ${\leq}1$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1992.04a
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• pp.133-142
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• 1992

A kineamatic nonlinear multivariable laundher is modeled of which the azimoth and elevation axes are drived simultaneously and SISO and MIMO LQG/LTR controllers are designed and evaluated for this system. Also, the suitable command input function is suggested for the desired command following performance and the LQG/LTR control system with disturbances and load variation is evaluated for the entire operating range by computer simulation. It is found that the linear SISO LQG/LTR controller can be used for the kinematic nonlinear multivariable launder in the entire operating range and is effective for disturbance rejection and load variation.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.75-82
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• 2017

In this paper, we investigate the proper shape and location of the maximum curve of transcendental entire functions $e^{az^2+bz+c}$. We show that the alpha curve of $e^{az^2+bz+c}$ is a subset of a rectangular hyperbola, and the maximum curve is the connected set originating from the origin as a subset of the alpha curve.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.131-143
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• 2004

Let Ε and F be locally convex spaces over C. We assume that Ε is a nuclear space and F is a Banach space. Let f be a holomorphic mapping from Ε into F. Then we show that f is of uniformly bounded type if and only if, for an arbitrary locally convex space G containing Ε as a closed subspace, f can be extended to a holomorphic mapping from G into F.