• Title/Summary/Keyword: growth order

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GROWTH OF SOLUTIONS TO LINEAR DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS OF [p, q]-ORDER IN THE COMPLEX PLANE

  • Biswas, Nityagopal;Tamang, Samten
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1217-1227
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    • 2018
  • In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of [p, q]-order in the complex plane. We improve and extend some results due to T. B. Cao, J. F. Xu, Z. X. Chen, and J. Liu, J. Tu, L. Z. Shi.

ON GROWTH PROPERTIES OF TRANSCENDENTAL MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS OF HIGHER ORDER

  • Biswas, Nityagopal;Datta, Sanjib Kumar;Tamang, Samten
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1245-1259
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    • 2019
  • In the paper, we study the growth properties of meromorphic solutions of higher order linear differential equations with entire coefficients of [p, q] - ${\varphi}$ order, ${\varphi}$ being a non-decreasing unbounded function and establish some new results which are improvement and extension of some previous results due to Hamani-Belaidi, He-Zheng-Hu and others.

On the growth of Pinus Thunbergii (곰솔 성장(成長)에 대(對)하여)

  • Kim, Kap Duk
    • Journal of Korean Society of Forest Science
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    • v.8 no.1
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    • pp.17-20
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    • 1968
  • The growth of Pinus Thunbergii in the four areas was compared with each other, and the results obtained are as follows ; 1. The diameter growth in HAP-CHUN area was found the best, and that of WOOI-SAN, CHE-JU, and SUWON areas was followed in order. 2. The height growth was found the best in WOOI-SAN area, and followed SUWON, HAP-CHUN, and CHE-JU areas in order. 3. The volume growth was found the best in HAP-CHUN area, followed next in order were : WOOL-SAN CHE-JU, and SUWON. 4. Based on the above-mentioned results, it was concluded that the growth of Pinus Thunbergii in inland areas was better than that in islands or coastal areas. This is against the common understanding that Pinus Thunbergii species grow better in coastal areas.

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Effects of Ginseng on the Physical Growth of Children (인삼박(人蔘粕)의 이용(利用)에 관한 연구(硏究) -인삼박(人蔘粕)의 당화(糖化)엑기스가 소아(小兒)의 성장(成長)에 미치는 영향-)

  • Ju, Kyu-Hyun
    • Korean Journal of Pharmacognosy
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    • v.6 no.4
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    • pp.205-209
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    • 1975
  • Ginseng, Vitamin, and both were given to six-year-old children for three months to know effects of the drugs on the physical growth of the children. 1. Frequency of children's sickness was in order of vitamin plus ginseng, ginseng, vitamin alone and control groups. 2. Height, circumference of chest and weight of children were increased in order of vitamin plus ginseng, ginseng, vitamin, and control groups. 3. Ginseng, as compared with vitamin increased the children's growth, especially their weight and the circumference of chest.

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RELATIVE ORDER AND RELATIVE TYPE BASED GROWTH PROPERTIES OF ITERATED P ADIC ENTIRE FUNCTIONS

  • Biswas, Tanmay
    • Korean Journal of Mathematics
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    • v.26 no.4
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    • pp.629-663
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    • 2018
  • Let us suppose that ${\mathbb{K}}$ be a complete ultrametric algebraically closed field and $\mathcal{A}$ (${\mathbb{K}}$) be the ${\mathbb{K}}$-algebra of entire functions on K. The main aim of this paper is to study some newly developed results related to the growth rates of iterated p-adic entire functions on the basis of their relative orders, relative type and relative weak type.

RELATIVE (p, q)-𝜑 ORDER AND RELATIVE (p, q)-𝜑 TYPE ORIENTED GROWTH ANALYSIS OF COMPOSITE ENTIRE FUNCTIONS

  • Biswas, Tanmay
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.243-268
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    • 2019
  • The main aim of this paper is to study some growth properties of composite entire functions on the basis of relative $(p,q)-{\varphi}$ type and relative $(p,q)-{\varphi}$ weak type where p and q are any two positive integers and ${\varphi}(r):[0,+{\infty}){\rightarrow}(0,+{\infty})$ be a non-decreasing unbounded function.

RELATIVE (p, q, t)L-TH TYPE AND RELATIVE (p, q, t)L-TH WEAK TYPE ORIENTED GROWTH PROPERTIES OF WRONSKIAN

  • Biswas, Tanmay;Biswas, Chinmay
    • The Pure and Applied Mathematics
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    • v.29 no.1
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    • pp.69-91
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    • 2022
  • In the paper we establish some new results depending on the comparative growth properties of composite transcendental entire and meromorphic functions using relative (p, q, t)L-th order, relative (p, q, t)L-th type and relative (p, q, t)L-th weak type and that of Wronskian generated by one of the factors.

RELATIVE (p, q) - 𝜑 ORDER BASED SOME GROWTH ANALYSIS OF COMPOSITE p-ADIC ENTIRE FUNCTIONS

  • Biswas, Tanmay;Biswas, Chinmay
    • Korean Journal of Mathematics
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    • v.29 no.2
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    • pp.361-370
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    • 2021
  • Let 𝕂 be a complete ultrametric algebraically closed field and 𝓐 (𝕂) be the 𝕂-algebra of entire function on 𝕂. For any p-adic entire functions f ∈ 𝓐 (𝕂) and r > 0, we denote by |f|(r) the number sup {|f (x)| : |x| = r} where |·|(r) is a multiplicative norm on 𝓐 (𝕂). In this paper we study some growth properties of composite p-adic entire functions on the basis of their relative (p, q)-𝜑 order where p, q are any two positive integers and 𝜑 (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.

A Study on the Analysis Procedures of Nonlinear Growth Curve Models (비선형 성장곡선 모형의 분석 절차에 대한 연구)

  • 황정연
    • Journal of Korean Society for Quality Management
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    • v.25 no.1
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    • pp.44-55
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    • 1997
  • In order to determine procedures for a, pp.opriate model selection of technological growth curves, numerous time series that were representative of growth behavior were collected according to data characteristics. Three different growth curve models were fitted onto data sets in an attempt to determine which growth curve models achieved the best forecasts for types of growth data. The analysis of the results gives rise to an a, pp.oach for selecting a, pp.opriate growth curve models for a given set of data, prior to fitting the models, based on the characteristics of the goodness of fit test.

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