Some results on sum and product of relative growth factors of composite entire functions

On Different Relative Growth Factors of Entire Functions

Journal of the Indian Mathematical Society ◽

10.18311/jims/2020/24428 ◽

2020 ◽

Vol 87 (1-2) ◽

pp. 37

Author(s):

Sanjib Kumar Datta ◽

Banani Dutta ◽

Nityagopal Biswas

Keyword(s):

Growth Factors ◽

Entire Function ◽

Entire Functions ◽

Unbounded Function ◽

Relative Growth

In this paper we investigate some properties related to sum and product of different relative growth factors of an entire function with respect to another entire function in connection with a special type of non-decreasing, unbounded function ψ.

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RELATIVE GROWTH OF ENTIRE DIRICHLET SERIES WITH DIFFERENT GENERALIZED ORDERS

Bukovinian Mathematical Journal ◽

10.31861/bmj2021.02.02 ◽

2021 ◽

Vol 9 (2) ◽

pp. 22-34

Author(s):

M. Sheremeta ◽

O. Mulyava

Keyword(s):

Dirichlet Series ◽

Lower Order ◽

Entire Functions ◽

Entire Dirichlet Series ◽

Relative Growth ◽

Alpha Beta ◽

Generalized Order

For entire functions $F$ and $G$ defined by Dirichlet series with exponents increasing to $+\infty$ formulas are found for the finding the generalized order $\displaystyle \varrho_{\alpha,\beta}[F]_G = \varlimsup\limits_{\sigma\to=\infty} \frac{\alpha(M^{-1}_G(M_F(\sigma)))}{\beta(\sigma)}$ and the generalized lower order $\displaystyle \lambda_{\alpha,\beta}[F]_G=\varliminf\limits_{\sigma\to+\infty} \frac{\alpha(M^{-1}_G(M_F(\sigma)))}{\beta(\sigma)}$ of $F$ with respect to $G$, where $M_F(\sigma)=\sup\{|F(\sigma+it)|:\,t\in{\Bbb R}\}$ and $\alpha$ and $\beta$ are positive increasing to $+\infty$ functions.

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ON THE MEASUREMENT OF GROWTH PROPERTIES OF ENTIRE AND MEROMORPHIC FUNCTIONS FOCUSING THEIR RELATIVE TYPE AND RELATIVE WEAK TYPE

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi1605011d ◽

2017 ◽

pp. 1011

Author(s):

Sanjib Kumar Datta ◽

Tanmay Biswas

Keyword(s):

Meromorphic Functions ◽

Weak Type ◽

Entire Functions ◽

Order Type ◽

Relative Order ◽

Relative Growth ◽

Growth Properties ◽

Relative Type ◽

Growth Indicators

The concepts of relative growth indicators such as relative order, relative type, relative weak type, etc. have widely been used to avoid comparing growths of entire and meromorphic functions just with exp functions. Using the notions of several relative growth indicators as mentioned earlier, in this paper we would like to find out the limits in terms of classical growth indicators (i.e. order, type, weak type etc.) in which the relative type, relative weak type, etc. of meromorphic functions with respect to entire functions should lie.

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Generalized Relative Type and Generalized Weak Type of Entire Functions

Journal of Complex Analysis ◽

10.1155/2016/3468354 ◽

2016 ◽

Vol 2016 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Sanjib Kumar Datta ◽

Tanmay Biswas ◽

Debasmita Dutta

Keyword(s):

Entire Function ◽

Weak Type ◽

Entire Functions ◽

Relative Growth ◽

Growth Properties ◽

Relative Type

We study some relative growth properties of entire functions with respect to another entire function on the basis of generalized relative type and generalized relative weak type.

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Growth factors and the primary cilium in BALB/c 3T3 cells

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100128432 ◽

1987 ◽

Vol 45 ◽

pp. 830-831

Author(s):

R. W. Tucker ◽

N. S. More ◽

S. Jayaraman

Keyword(s):

Growth Factors ◽

Primary Cilium ◽

Cultured Cells ◽

Morphological Changes ◽

Calcium Ionophore ◽

Growth Stimulation ◽

Calcium Ionophore A23187 ◽

Ionophore A23187 ◽

3T3 Cells ◽

Microtubule Depolymerization

The mechanisms by which polypeptide growth factors Induce DNA synthesis in cultured cells is not understood, but morphological changes Induced by growth factors have been used as clues to Intracellular messengers responsible for growth stimulation. One such morphological change has been the transient disappearance of the primary cilium, a “9 + 0” cilium formed by the perinuclear centriole in interphase cells. Since calcium ionophore A23187 also produced both mitogenesis and ciliary changes, microtubule depolymerization might explain ciliary disappearance monitored by indirect immunofluorescence with anti-tubulin antibody. However, complete resorption and subsequent reformation of the primary cilium occurs at mitosis, and might also account for ciliary disappearance induced by growth factors. To settle this issue, we investigated the ultrastructure of the primary cilium using serial thin-section electron microscopy of quiescent BALB/c 3T3 cells before and after stimulation with serum.

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New insights into heparan sulphate biosynthesis from the study of mutant mice

Biochemical Society Symposium ◽

10.1042/bss0690047 ◽

2002 ◽

Vol 69 ◽

pp. 47-57 ◽

Cited By ~ 8

Author(s):

Catherine L. R. Merry ◽

John T. Gallagher

Keyword(s):

Growth Factors ◽

Biosynthetic Pathway ◽

Heparan Sulphate ◽

Mutant Mice ◽

Gene Products ◽

Multiple Gene ◽

Adhesion Proteins ◽

Ligand Interactions

Heparan sulphate (HS) is an essential co-receptor for a number of growth factors, morphogens and adhesion proteins. The biosynthetic modifications involved in the generation of a mature HS chain may determine the strength and outcome of HS–ligand interactions. These modifications are catalysed by a complex family of enzymes, some of which occur as multiple gene products. Various mutant mice have now been generated, which lack the function of isolated components of the HS biosynthetic pathway. In this discussion, we outline the key findings of these studies, and use them to put into context our own work concerning the structure of the HS generated by the Hs2st-/- mice.

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