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3: Paper Source PDF document

Paper's Title:

Some Inequalities Concerning Derivative and Maximum Modulus of Polynomials

Author(s):

N. K. Govil, A. Liman and W. M. Shah

Department of Mathematics & Statistics, 
Auburn University, Auburn,
Alabama 36849-5310,
U.S.A

Department of Mathematics,
National Institute of Technology,
Srinagar, Kashmir,
India - 190006

Department of Mathematics,
Kashmir University,
Srinagar, Kashmir,
India - 190006

govilnk@auburn.edu
abliman22@yahoo.com
wmshah@rediffmail.com

 
 

Abstract:

In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the inequalities obtained are sharp.



3: Paper Source PDF document

Paper's Title:

The Effect of Harvesting Activities on Prey-Predator Fishery Model with Holling type II in Toxicant Aquatic Ecosystem

Author(s):

Moh Nurul Huda, Fidia Deny Tisna Amijaya, Ika Purnamasari

Department of Mathematics, Faculty of Mathematics and Natural Science,
Mulawarman University,
Samarinda, East Kalimantan,75123
Indonesia.
E-mail: muh.nurulhuda@fmipa.unmul.ac.id
 fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id

Abstract:

This paper discussed prey-predator fishery models, in particular by analysing the effects of toxic substances on aquatic ecosystems. It is assumed in this model, that the prey population is plankton and the predator population is fish.\ Interaction between the two populations uses the Holling type II function. The existence of local and global critical points of the system are shown and their stability properties are analysed. Furthermore, Bionomic equilibrium and optimal control of harvesting are discussed. Finally, numerical simulations have been carried out to show in the interpretation of results.


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