• Korean Journal of Mathematics
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• v.27 no.1
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• pp.93-117
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• 2019

In this paper we wish to study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of (p, q)-th relative Ritt order, (p, q)-th relative Ritt type and (p, q)-th relative Ritt weak type where p and q are integers such that $p{\geq}0$ and $q{\geq}0$.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.889-896
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• 2021

Let 𝜙 be an entire self map on ℂ and let 𝜓 be an entire function on ℂ. A weighted composition operator induced by 𝜙 with weight 𝜓 is given by C_𝜓,𝜙. In this paper we investigate under what conditions the weighted composition operators C_𝜓,𝜙 on the Fock space over ℂ induced by 𝜙 with weight of the form $k_c({\zeta})=e^{{\langle}{\zeta},c{\rangle}-{\frac{{\mid}c{\mid}^2}{2}}}$ is normaloid and essentially normaloid.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.473-481
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• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• Journal of the Korea Safety Management & Science
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• v.16 no.1
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• pp.201-206
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• 2014

GCM(Green Chain Management) is being spread by that companies which apply with eco-friendly concept in entire SCM(Supply Chain Management) perspective is being increased for resolving some recent environmental problems. There are reasons that numerous companies focus on GCM. At first various governments began to directly manage components and material contents about various noxious substances. Second, environment problem management in the entire logistics process from procurement of product materials to distribution of product became to be important according to introduction of certification system that evaluate the environmental impact throughout life-cycle of products. Purposes of this paper are 1) to analyze the GCM process whose important is more increasing in the recent logistics environment change, 2) to comprehend places and sources that generate environmental elements like energy consumption and greenhouse gas emissions in elements of logistics function, and 3) to construct integrated GCM system for observing activity of logistics function throughout life-cycle of products.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.819-829
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• 2016

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation $$f^{(k)}+A_{k-1}e^{az}f^{(k-1)}+{\cdots}+A_1e^{az}f^{\prime}+A_0e^{az}f=F_1e^{az}+F_2e^{bz}$$, where $A_j(z)$ (${\not\equiv}0$) ($j=0,1,{\cdots},k-1$), $F_j(z)$ (${\not\equiv}0$) (j = 1, 2) are entire functions and a, b are complex numbers such that $ab(a-b){\neq}0$.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1371-1385
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• 2022

For setting a general weight function on n dimensional complex space ℂⁿ, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.943-957
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• 2001

In this paper, we propose an efficient encryption algorithm, without exchanging session keys of a symmetric cryptosystem. The proposed scheme, called as the FAKE(Fast Asymmetric Key Encryption), first scrambles an entire input message and then encrypts small parts of the scrambled message using an asymmetric key encryption scheme. We use the all-or-nothing transform based on the hash function as a scrambling function, which was proposed by Shin, et al. Furthermore, the proposed scheme can additionally provide a digital signature service with only small overhead.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.447-458
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• 2018

In this paper, we investigate the uniqueness problems of certain types of difference polynomials sharing a small function. The results of the paper improve and generalize the recent results due to H.P. Waghamore [Tbilisi Math. J. 11(2018), 1-13], P. Sahoo and B. Saha [App. Math. E-Notes. 16(2016), 33-44].

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.37-50
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• 2022

The purpose of the paper is to study the uniqueness problems of certain type of difference polynomials sharing a small function. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo and G. Biswas [Tamkang Journal of Mathematics, 49(2)(2018), 85-97].

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.489-507
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• 2020

In this paper we discussed some growth properties of entire functions of several complex variables on the basis of (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weal type where p, q are positive integers and 𝜑(R) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.