• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.119-130
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• 2024

In this paper we discuss on the growth properties of composite entire and meromorphic functions on the basis of generalized (α, β, γ) order and generalized (α, β, γ) type comparing to their corresponding left and right factors.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.355-376
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• 2021

In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.52-61
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• 2022

The main aim of this paper is to study some growth properties of p -adic entire functions on the basis of generalized relative order (𝛼, 𝛽) where 𝛼 and 𝛽 are continuous non-negative functions on (-∞, +∞).

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.125-139
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• 2022

In this paper we wish to establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized relative order (α, β) and generalized relative lower order (α, β) where α and β are continuous non-negative functions defined on (-∞, +∞).

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.155-185
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• 2021

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of generalized relative order (𝛼, 𝛽), generalized relative type (𝛼, 𝛽) and generalized relative weak type (𝛼, 𝛽) of entire functions with respect to another entire function where 𝛼, 𝛽 are continuous non-negative functions on (-∞, +∞).

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.201-212
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• 1998

In the present paper we define the codes which assign D-alphabet one-one codeword to each outcome of a random variable and the functions which represent possible transormations from one-one codes of size D to suitable codes. By using these functions we obtain lower bounds on the exponentiated mean codeword length for one-one codes in terms of the generalized entropy of order $\alpha$ and type $\beta$ and study the particular cases also.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.715-723
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• 2021

In this paper we wish to introduce the concept of generalized relative index-pair (𝛼, 𝛽) of a p-adic entire function with respect to another p-adic entire function and then prove some results relating to the growth rates of composition of two p-adic entire functions with their corresponding left and right factors.

• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.139-154
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• 2023

In this paper we wish to prove some results relating to the growth rates of composite entire and meromorphic functions with their corresponding left and right factors on the basis of their generalized relative order (α, β) and generalized relative lower order (α, β), where α and β are continuous non-negative functions defined on (-∞, +∞).

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.121-136
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• 2021

In this paper we wish to prove some results relating to the growth rates of composite entire and meromorphic functions with their corresponding left and right factors on the basis of their generalized order (��, ��) and generalized lower order (��, ��), where �� and �� are continuous non-negative functions defined on (-∞, +∞).

• Bulletin of the Korean Chemical Society
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• v.7 no.4
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• pp.257-262
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• 1986

Thixotropy is a time-dependent shear-thinning phenomenon. We derived a new thixotropic formula which is based on the generalized viscosity formula of Ree and Eyring, $f={\Sigma}\frac{X_i}{{\alpha}_i}sinh^{-1}$ () (Refer to the text concerning the notation.) The following is postulated: (1) thixotropy occurs when small flow units attached to a large flow unit separate from the latter under stress (2) elastic energy(${\omega}$) is stored on the large flow unit during the flow process, and (3) the stored energy contributes to decrease the activation energy for flow. A new thixotropic formula was derived by using these postulations, $f={\frac}{X_0{\beta}_0}{\alpha_0}{\dot{s}}+{\frac}{X_1{\beta}_1}{{\alpha}_1}{\dot{s}}+{\frac}{X_2}{{\alpha_x}}sinh^{-1}$[$({\beta}_0)_2$ exp $(-C_2{\dot{s}}^2/RT){\cdot}{\dot{s}}$] f is the shear stress, and s is the rate of shear. In case of concentrated solutions where the Newtonian flow units have little contribution to the viscosity of the system, the above equation becomes, $f=\frac{X_2}{\alpha_2}sinh^{-1}$[$({\beta}_0)_2$ exp $(-C_2{\dot{s}}^2/RT){\cdot}{\dot{s}}$]. In order to confirm these formulas, we applied to TiO2(anatase and rutile)-water, printing ink and mayonnaise systems. Good agreements between the experiment and theory were observed.