Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

Evidence for the existence of Sarkovskii ordering in a two-dimensional map

We analyse numerically the bifurcation structure of a two-dimensional noninvertible map and show that different periodic cycles are arranged in it exactly in the same order as in the case of the logistic map. We also show that this map satisfies the general criteria for the existence of Sarkovskii ordering, which supports our numerical result. Incidently, this is the first report of the existence of Sarkovskii ordering in a two-dimensional map.

Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Child labour in India

This thesis entitled “Child labour in india”Children are "supremely important assets" of the nation, India proudly asserts in the National Policy for Children (1974) gracefully acknowledging that they are future citizens on whose shoulders the destiny of our nation rests.Childhood is a time of discovery as the world and all it contains are new to children. It is a time of excitement and anticipation. lt is a time of dreams and fantasies. And it is a time of receiving love and appreciation. Paradoxically, a picture of contrast is a common experience in India as a vast majority of children who are starved of basic needs of nutrition, health and education are made to work at an early age in exploitative conditions. The specter of child labour is a glaring anomaly in a country graciously adorning human right. In an exposition of the problem involving human rights abuse, Chapters from Two to Five of this study have shot into focus the human rights jurisprudence with special reference to the rights of children. Children have a particular identity as children and they also have a universal identity as human beings.The concern for mankind expressed unequivocally and transcending the globe will be real and moving and not mere rhetoric and ritual if and only when it begins with children, as, to quote the words of Nehru, the human being counts much more as a child than as a grown up.The first three of these rights namely right to health, right to nutritive food and right to education are dealt with in Chapter Four. Finally, the positive effects of education have been sketched in that chapter to impress upon its significance in the development of human capitals.legitimization. The theme of legitimacy was rationalised on the ground of poverty as a strategy for achieving eradication of child labour ultimately by enforcing minimum wages, shorter working hours, leave compensation, non-formal education etc., as the employer would soon discover that child labour is not cheap and would be obliged to substitute adult labour. However, humanising the work life is only a promise to the detriment of children as the Act of 1986 enacted as a part of the new strategy is nearingcompletion of a decade of existence but nowhere near the fulfilment of the mission.As similar urge is more necessary and overdue, it has been suggested that a special body be established with all powers for cognisance of human rights abuse of children.It is proposed to conclude this study with a brief summary of the inferences drawn from the foregoing chapters along with a few suggestions emerging out of those inferences

The Fishing Industry in Kerala - Problem and Potentials

importance of fishing and other allied industries in the economy was realised only very recently. Consequently only very few studies are available on the subject. Here an attempt is made to survey the available literature on the subject.

On the generalized obnoxious center problem: antimedian subsets

The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered.

Evidence for the existence of multiple equilibrium states in cobalt phthalocyanine tetramer: a study by dielectric spectroscopy

In any investigation, information about the molecules under consideration is very essential for tailoring their properties. Evaluation of dispersion parameters, namely optical dielectric constant, static dielectric constant, relaxation time and spreading factor, assumes significance in this context. Dielectric spectroscopy is a useful tool for estimating these parameters. Not only does it reveal details about these constants but it also gives insight into the mechanism of conduction. In this paper the evaluation of dispersion parameters of cobalt phthalocyanine tetramer in the temperature range 300–393K is attempted using Cole–Cole plots. The temperature variation of the spreading factor indicates the existence of multiple equilibrium positions in the case of cobalt phthalocyanine tetramer. To the best of our knowledge, the evaluation of dispersion parameters for cobalt phthalocyanine tetramer is reported for the first time

Reinforcement Learning approaches to Economic Dispatch problem

This paper presents Reinforcement Learning (RL) approaches to Economic Dispatch problem. In this paper, formulation of Economic Dispatch as a multi stage decision making problem is carried out, then two variants of RL algorithms are presented. A third algorithm which takes into consideration the transmission losses is also explained. Efficiency and flexibility of the proposed algorithms are demonstrated through different representative systems: a three generator system with given generation cost table, IEEE 30 bus system with quadratic cost functions, 10 generator system having piecewise quadratic cost functions and a 20 generator system considering transmission losses. A comparison of the computation times of different algorithms is also carried out.

Reinforcement Learning Solution for Unit Commitment Problem Considering Minimum Start Up and Shut Down Times

Unit Commitment Problem (UCP) in power system refers to the problem of determining the on/ off status of generating units that minimize the operating cost during a given time horizon. Since various system and generation constraints are to be satisfied while finding the optimum schedule, UCP turns to be a constrained optimization problem in power system scheduling. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision making task and an efficient Reinforcement Learning solution is formulated considering minimum up time /down time constraints. The correctness and efficiency of the developed solutions are verified for standard test systems

Reinforcement Learning solution for Unit Commitment Problem through pursuit method

Unit commitment is an optimization task in electric power generation control sector. It involves scheduling the ON/OFF status of the generating units to meet the load demand with minimum generation cost satisfying the different constraints existing in the system. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision task and Reinforcement Learning solution is formulated through one efficient exploration strategy: Pursuit method. The correctness and efficiency of the developed solutions are verified for standard test systems

Testing Isotropy and a related Random Walk problem

One comes across directions as the observations in a number of situations. The first inferential question that one should answer when dealing with such data is, “Are they isotropic or uniformly distributed?” The answer to this question goes back in history which we shall retrace a bit and provide an exact and approximate solution to this so-called “Pearson’s Random Walk” problem.

Employment Realm in Technical Education in Kerala-A Study on the Problem of Unemployment among Engineers

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