Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

Fish habitats and species assemblage in the selected rivers of Kerala and investigation on life history traits of Puntius carnaticus(Jerdon,1849)

This thesis entitled Fish habitats and species assemblage in the selected rivers of kerala and investigation on life history traits of puntius carnaticus (JERDON,1849). Ecology is a new and exceedingly complex field of study, even though its concept was recognized by the Apostles in their use of the phrase ‘all flesh is grass.central role to play both in order to understand better the biodiversity phenomenon and to be able to draw up clear guidelines for careful resource management. In a review by WWF, IUCN and UNEP on the ways of conserving genetic diversity of freshwater fish it was recommended that the best way to conserve species diversity is to conserve habitat.The habitat studies in freshwater ecosystems are very essential for the proper understanding and management of human impact on fish diversity, to study the relationship between habitat variables and fish species assemblage structure, quantification of ecosystem degradation, habitat quality and biotic integrity of the ecosystems, development of habitat suitability index (I-ISI) models and classification of river reaches based on their physico-chemical properties. Therefore in the present study an attempt was made to assess the biodiversity potential and the relationship between habitat variables and fish species assemblage structure in six major river systems of Kerala which would be very useful in impressing upon the seriousness of habitat degradIn the present study, in Kabbini river system 15 locations encompassing between 721 946m above MSL were surveyed.ation and biotic devastation undergone in the major river systems of Kerala.During the present study the Habitat Quality Score (HQ) developed by the Ohio EPA was applied for the first time in India.The result of the present study revealed that, among various variables analysed, altitude has a very significant influence in deciding the fish diversity in six major river systems of Kerala. The fish diversity studied on the basis of Shanon-Weiner and Simpson diversity indices revealed that even though some minor variations occur with the suitability and complexity of habitats, the altitude showed inverse relationship with fish diversity.The present study revealed that the National Policy on the interlinking of rivers would permanently alter the HSI indices of the above mentioned fish species, which are now solely protected by the individuality of the rivers where their limited occurrence was notice.

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Systematics, Life history traits, abundance andstock assessment of cobia, Rachycentron canadum ( Linnaeus, 1766) occurring in Indian waters with special reference to the north west coast in India

This thesis entitled Systematics,life history traits ,abundance and stock assessment of cobia rachycentron canadum (linnaeus ,1766) occurring in indian waters with special reference to the northwest coast of india.Cobia, Rachycentron canadum is a fast growing pelagic fish belonging to the monotypic family Rachycentridae. They show worldwide distribution in tropical and sub tropical waters. Cobia is exploited commercially in various countries like Taiwan, Pakistan, India, United State of America, Australia, Gulf of Mexico and the Caribbean. Recreational fishery of Cobia exists in different parts of the world. In India Cobia is caught as bycatch of trawlers, gillnet and hook and line fishery.This study also focuses on to bring out the distribution pattern and also to assess the biomass and estimate sustainable yield of Cobia inhabiting in Indian EEZ. In addition to above, present study standardised live collection methods and also reviewed culture prospects.Results of osteological study and morphological studies indicate its close resemblance to Remora and support the view that Cobia was evolved from Dolphin fishes and remoras followed it. Study also confirmed that Cobia does not have any relative or similar species and is a monotypic species belonging to the family Rachycentridae. Re description of the species was done based on the characters identified. In this study, feeding intensity was also assessed following methods like Gastrosomatic index, Mean index of feeding intensity and Index of fullness. Sex wise, month wise and length group wise fluctuations in the feeding intensity also were studied. Cobia actively fed during post monsoon period. In general, adult fed actively than the juveniles. Trophic level value estimated (4.36) indicates that Cobia occupy top level position in the food chain.

Discrete Time Inventory Models with/without Positive Service Time

In everyday life different flows of customers to avail some service facility or other at some service station are experienced. In some of these situations, congestion of items arriving for service, because an item cannot be serviced Immediately on arrival, is unavoidable. A queuing system can be described as customers arriving for service, waiting for service if it is not immediate, and if having waited for service, leaving the system after being served. Examples Include shoppers waiting in front of checkout stands in a supermarket, Programs waiting to be processed by a digital computer, ships in the harbor Waiting to be unloaded, persons waiting at railway booking office etc. A queuing system is specified completely by the following characteristics: input or arrival pattern, service pattern, number of service channels, System capacity, queue discipline and number of service stages. The ultimate objective of solving queuing models is to determine the characteristics that measure the performance of the system

Discrete commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Some problems of discrete function theory

An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.

Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis

Analysis discrete function theory

There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H.

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.