Vinod Kumar,P B; Thrivikraman,T(Department of Mathematics, September , 2001)
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Abstract:
The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.
Ancykutty, Joseph; Dr.Krishnamoorthy,A; Dr.Thrivikraman, T(Cochin University of Science and Technology, 2000)
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This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix
Description:
Department of mathematics, Cochin University of Science and Technology
Resmi, T; Dr. Lakshmi, B(Cochin University of Science and Technology, August 21, 2015)
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Abstract:
Queueing Theory is the mathematical study of queues or waiting lines.
Queues abound in every day life - in computer networks, in tra c islands,
in communication of electro-magnetic signals, in telephone exchange, in
bank counters, in super market checkouts, in doctor's clinics, in petrol
pumps, in o ces where paper works to be processed and many other
places.
Originated with the published work of A. K. Erlang in 1909 [16] on
congestion in telephone tra c, Queueing Theory has grown tremendously
in a century. Its wide range applications includes Operations Research,
Computer Science, Telecommunications, Tra c Engineering, Reliability
Theory, etc.
Dhanya, Shajin; Dr. B. Lakshmy(Cochin University of Science and Technology, November 12, 2015)
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Abstract:
Queueing theory is the mathematical study of ‘queue’ or ‘waiting lines’
where an item from inventory is provided to the customer on completion of
service. A typical queueing system consists of a queue and a server. Customers
arrive in the system from outside and join the queue in a certain way.
The server picks up customers and serves them according to certain service
discipline. Customers leave the system immediately after their service is completed.
For queueing systems, queue length, waiting time and busy period are of
primary interest to applications. The theory permits the derivation and calculation
of several performance measures including the average waiting time
in the queue or the system, mean queue length, traffic intensity, the expected
number waiting or receiving service, mean busy period, distribution of queue
length, and the probability of encountering the system in certain states, such
as empty, full, having an available server or having to wait a certain time to
be served.
Pramod,P K; Dr.Krishnamoorthy,A(Cochin University of Science & Technology, January , 2010)
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Abstract:
This thesis entitled' On
Queues with Interruptions and Repeat or Resumption of Service' introduces several
new concepts into queues with service interruption. It is divided into Seven chapters
including an introductory chapter. The following are keywords that we use
in this thesis: Phase type (PH) distribution, Markovian Arrival Process (MAP),
Geometric Distribution, Service Interruption, First in First out (FIFO), threshold
random variable and Super threshold random variable. In the second chapter we
introduce a new concept called the 'threshold random variable' which competes
with interruption time to decide whether to repeat or resume the interrupted service
after removal of interruptions. This notion generalizes the work reported so far
in queues with service interruptions. In chapter 3 we introduce the concept of what
is called 'Super threshold clock' (a random variable) which keeps track of the total
interruption time of a customer during his service except when it is realized before
completion of interruption in some cases to be discussed in this thesis and in other
cases it exactly measures the duration of all interruptions put together. The Super
threshold clock is OIl whenever the service is interrupted and is deactivated when service is rendered. Throughout this thesis the first in first out service discipline is
followed except for priority queues.
Description:
Department of Mathematics,
Cochin University of Science and Technology
Harikrishnan, K P; Dr.Nandakumaran,V M(Cochin University Of Science And Technology, November 3, 1989)
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Nature is full of phenomena which we call
"chaotic", the weather being a prime example.
What we mean by this is that we cannot predict it
to any significant accuracy, either because the
system is inherently complex, or because some of
the governing factors are not deterministic. However,
during recent years it has become clear that
random behaviour can occur even in very simple
systems with very few number of degrees of freedom,
without any need for complexity or indeterminacy.
The discovery that chaos can be generated even with
the help of systems having completely deterministic
rules - often models of natural phenomena - has
stimulated a lo; of research interest recently. Not
that this chaos has no underlying order, but it is
of a subtle kind, that has taken a great deal of
ingenuity to unravel. In the present thesis, the author
introduce a new nonlinear model, a ‘modulated’
logistic map, and analyse it from the view point of
‘deterministic chaos‘.
Description:
Department of Physics, Cochin University of
Science and Technology
Vijayakrishnan,S; Chakravarti,R S; Thrivikraman,T(Department of Mathematics,Faculty OF Science, 2002)
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The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the
classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions
Sajeev, S Nair; Dr.Krishnamoorthy,A(Cochin University of Science and Technology, September 2, 2011)
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In this thesis we have developed a few inventory models in which items are served to the customers after a processing time. This leads to a queue of demand even when items are available. In chapter two we have discussed a problem involving search of orbital customers for providing inventory. Retrial of orbital customers was also considered in that chapter; in chapter 5 also we discussed retrial inventory model which is sans orbital search of customers. In the remaining chapters (3, 4 and 6) we did not consider retrial of customers, rather we assumed the waiting room capacity of the system to be arbitrarily large. Though the models in chapters 3 and 4 differ only in that in the former we consider positive lead time for replenishment of inventory and in the latter the same is assumed to be negligible, we arrived at sharper results in chapter 4. In chapter 6 we considered a production inventory model with production time distribution for a single item and that of service time of a customer following
distinct Erlang distributions. We also introduced protection of production and service stages and investigated the optimal values of the number of stages to be protected.
Description:
Department of Mathematics,
Cochin University of Science And Technology.
Remadevi,S; Narayanan Namboodiri,M N(Department of Mathematics,Faculty of Science, 2003)
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This study is to look the effect of change in the ordering of the Fourier system on Szegö’s classical observations of asymptotic distribution of eigenvalues of finite Toeplitz forms.This is done by checking proofs and Szegö’s properties in the new set up.The Fourier system is unconditional [19], any arbitrary ordering of the Fourier system forms a basis for the Hilbert space L2 [-Π, Π].Here study about the classical Szegö’s theorem.Szegö’s type theorem for operators in L2(R+) and check its validity for certain multiplication operators.Since the trigonometric basis is not available in L2(R+) or in L2(R) .This study discussed about the classes of orderings of Haar System in L2 (R+) and in L2(R) in which Szegö’s Type TheoreT Am is valid for certain multiplication operators.It is divided into two sections. In the first section there is an ordering to Haar system in L2(R+) and prove that with respect to this ordering, Szegö’s Type theorem holds for general class of multiplication operators Tƒ with multiplier ƒ ε L2(R+), subject to some conditions on ƒ.Finally in second section more general classes of ordering of Haar system in L2(R+) and in L2(R) are identified in such a way that for certain classes of multiplication operators the asymptotic distribution of eigenvalues exists.
Veena Gopalan, E; Dr.Anantharaman, M R(Cochin University of Science & Technology, June , 2009)
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Abstract:
This thesis lays importance in the preparation and characterization of a
few selected representatives of the ferrite family in the nanoregime. The candidates being manganese zinc ferrite and cobalt ferrite prepared by coprecipitation
and sol-gel combustion techniques respectively. The thesis not only
stresses importance on the preparation techniques and optimization of the reaction
conditions, but emphasizes in investigating the various properties namely
structural, magnetic and electrical. Passivated nickel nanocomposites are
synthesized using polystyrene beads and adopting a novel route of ion exchange
reduction. The structural and magnetic properties of these magnetic
nanocomposites are correlated. The magnetocaloric effect (MCE) exhibited by
these materials are also investigated with a view to finding out the potential of
these materials as magnetic refrigerants. Calculations using numerical methods
are employed to evaluate the entropy change on selected samples.
Description:
Department of Physics,
Cochin University of Science & Technology
Hysen, Thomas; Anantharaman, M R(Cochin University of Science and Technology, June , 2013)
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Abstract:
The development of new materials has been the hall mark of human civilization. The quest for making new devices and new materials has prompted humanity to pursue new methods and techniques that eventually has given birth to modern science and technology. With the advent of nanoscience and nanotechnology, scientists are trying hard to tailor materials by varying their size and shape rather than playing with the composition of the material. This, along with the discovery of new and sophisticated imaging tools, has led to the discovery of several new classes of materials like (3D) Graphite, (2D) graphene, (1D) carbon nanotubes, (0D) fullerenes etc. Magnetic materials are in the forefront of applications and have beencontributing their share to remove obsolescence and bring in new devices based on magnetism and magnetic materials. They find applications in various devices such as electromagnets, read heads, sensors, antennas, lubricants etc. Ferromagnetic as well as ferrimagnetic materials have been in use in the form of various devices. Among the ferromagnetic materials iron, cobalt and nickel occupy an important position while various ferrites finds applications in devices ranging from magnetic cores to sensors.
Description:
Department of Physics, Cochin University of Science and Technology