• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.395-414
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• 2016

In this work, we study on subdivision schemes reproducing polynomials and build a symmetric subdivision scheme reproducing polynomials of a certain predetermined degree, which is a slight variant of the family of Deslauries-Dubic interpolatory ones. Related to polynomial reproduction, a necessary and sufficient condition for a subdivision scheme to reproduce polynomials of degree L was recently established under the assumption of non-singularity of subdivision schemes. In case of stepwise polynomial reproduction, we give a characterization for a subdivision scheme to reproduce stepwise all polynomials of degree ${\leq}L$ without the assumption of non-singularity. This characterization shows that we can investigate the polynomial reproduction property only by checking the odd and even masks of the subdivision scheme. The minimal-support condition being relaxed, we present explicitly a general formula for the mask of (2n + 4)-point symmetric subdivision scheme with two parameters that reproduces all polynomials of degree ${\leq}2n+1$. The uniqueness of such a symmetric subdivision scheme is proved, provided the two parameters are given arbitrarily. By varying the values of the parameters, this scheme is shown to become various other well known subdivision schemes, ranging from interpolatory to approximating.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.499-512
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• 2011

The purpose of this paper is twofold. The first is to establish a uniqueness theorem for entire function sharing two polynomials with its ${\kappa}$-th derivative, by using the theory of normal families. Meanwhile, the theorem generalizes some related results of Rubel and Yang and of Li and Yi. Several examples are provided to show the conditions are necessary. The second is to generalize the Br$\"{u}$-ck conjecture with the idea of sharing polynomial.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.827-841
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• 2022

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions f(z) and g(z) of the following complex difference equation A₁(z)f(z + 1) + A₀(z)f(z) = F(z)e^𝛼(z) when they share 0, ∞ CM, where A₁(z), A₀(z), F(z) are non-zero polynomials, 𝛼(z) is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1365-1388
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• 2019

In this paper we consider a class of nonlinear nonlocal parabolic equations involving p-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.227-253
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• 2024

This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space BCL_-∞(H). We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.579-600
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• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.717-725
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• 2009

We show that to every real polynomial of degree n, there corresponds a certain basis for the space of polynomials of degree less than or equal to (n-1). As an application, we give a new proof for the existence and uniqueness of the partial fraction decomposition of a rational function.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.447-454
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• 2010

In this paper, we investigate the uniqueness problems of meromorphic functions that share a small function with its differential polynomials, and give a result which is related to a conjecture of R. Br$\"{u}$ck and improve the results of I. Lahiri and Q. C. Zhang.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.451-464
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• 2016

In this paper, we investigate the uniqueness problem of a meromorphic function sharing one small function with its differential polynomial, and give a result which is related to a conjecture of R. $Br{\ddot{u}}ck$.

• Journal of Information Technology Application
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• v.3 no.3
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• pp.71-90
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• 2001

Research on innovation has a long tradition from various disciplines. MIS research has also been interested in the innovation adoption because IS development and implementation can be regarded as an innovation process. To deal with IT innovations, MIS research adopted existing innovation(diffusion) theories which have been developed on general innovation phenomena. However, the MIS innovation research revealed that there exist some limitations in applying the innovation theories to IT innovations and proposed that research on IT innovations should reflect the unique characteristics of IT. The purpose of this study is twofold; first, to synthesize the past research and propose the uniqueness of IT innovations and second, to survey the Perceptions of managers on If innovations. Three unique characteristics of IT innovations are derived from the past research which are (1) knowledge barriers, (2) increasing returns, (3) organizational decision. Data collected from 68 Korean managers showed that the perceptions of managers support the uniqueness of IT innovations. Some recommendations to facilitate IT innovations are discussed and further research directions are suggested.