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.

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

Department of Mathematics, Cochin University of Science and Technology

Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.

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.

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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