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.
Description:
Department of Statistics, Cochin
University of Science and Technology
Thomas, Joseph; Dr.Jathavedan, M(Cochin University of Science and Technology, June , 1993)
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This thesis contains a study of conservation laws of
fluid mechanics. These conservation laws though classical, have
been put to extensive studies in t:he past many decades
Description:
Department of Mathematics And Statistics, Cochin University of Science And Technology
Sojan Lal,P; Unnikrishnan, A; Poulose Jacob,K(Cochin University of Science and Technology, 2000)
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The thesis introduced the octree and addressed the complete nature of problems encountered, while building and imaging system based on octrees. An efficient Bottom-up recursive algorithm and its iterative counterpart for the raster to octree conversion of CAT scan slices, to improve the speed of generating the octree from the slices, the possibility of utilizing the inherent parallesism in the conversion programme is explored in this thesis. The octree node, which stores the volume information in cube often stores the average density information could lead to “patchy”distribution of density during the image reconstruction. In an attempt to alleviate this problem and explored the possibility of using VQ to represent the imformation contained within a cube. Considering the ease of accommodating the process of compressing the information during the generation of octrees from CAT scan slices, proposed use of wavelet transforms to generate the compressed information in a cube. The modified algorithm for generating octrees from the slices is shown to accommodate the eavelet compression easily. Rendering the stored information in the form of octree is a complex task, necessarily because of the requirement to display the volumetric information. The reys traced from each cube in the octree, sum up the density en-route, accounting for the opacities and transparencies produced due to variations in density.
Sreekumar, R; Thrivikraman,T; Chakravarti, R S(Department of Mathematics, Faculty of Science, 2002)
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The main purpose of the study is to extent concept of the class of spaces called ‘generalized metric spaces’ to fuzzy context and investigates its properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of ‘generalized metric spaces’. But the term is meant for classes, which are ‘close’ to metrizable spaces in some under certain kinds of mappings. The theory of generalized metric spaces is closely related to ‘metrization theory’. The class of spaces likes Morita’s M- spaces, Borges’s w-spaces, Arhangelskii’s p-spaces, Okuyama’s spaces have major roles in the theory of generalized metric spaces. The thesis introduces fuzzy metrizable spaces, fuzzy submetrizable spaces and proves some characterizations of fuzzy submetrizable spaces, and also the fuzzy generalized metric spaces like fuzzy w-spaces, fuzzy Moore spaces, fuzzy M-spaces, fuzzy k-spaces, fuzzy -spaces study of their properties, prove some equivalent conditions for fuzzy p-spaces. The concept of a network is one of the most useful tools in the theory of generalized metric spaces. The -spaces is a class of generalized metric spaces having a network.
Noble,A; Dr.Silas, E G(Cochin University of Science and Technology, February , 1986)
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Mackerel fishery at many places in the country including Cochin
as well as at all—India level, besides its seasonal changes to
have long-term flucations apparently evincing a ten-year cycle.
Published literature on the fishery and biology of mackerel at
many places are available. But attempts on population studies
and assessment of stock are scanty. The researchers attention
at this juncture turned to investigations on population dynamics
of the mackerel .On account of the long-term Fluctuations
in the fishery, it was felt desirable to have data For a
number of years together to facilitate adequate coverage of a
unit of time in the 10-year cycle. Investigations on length weight
relationships for 16 seasons were hence carried out.
This thesis is written eection'by section embodying‘ the
results and_findings of the work carried out under different
subject areas. It contains sections on identity of the species,
information on its spatial and temporal distribution along the
Indian coast, study on length-weight relationships, growth and
age determination, population studies and stock assessment, and
discussions.This dissertation is the outcome of the works of the
candidate on the Indian mackerel. The work, however is based
on exploited resource of the inshore waters. In the course
of this analysis, lacunae existing in the investigations on
the Indian mackerel are therefore identified and presented
For future work
Babu, Sundar S; Dr.Thrivikraman, T(Cochin University Of Science And Technology, March 21, 1989)
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It is believed that every fuzzy generalization should be
formulated in such a way that it contain the ordinary set
theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9]
with an arbitrary complete and distributive lattice as the
membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy
topologies on a set. It is proved that in general, the
lattice of fuzzy topologies is not complemented. Complements
of some fuzzy topologies are found out. It is observed that
(L,X) is not uniquely complemented. However, a complete
analysis of the problem of complementation in the lattice
of fuzzy topologies is yet to be found out
Description:
Depantment of Mathematics and Statistics
Cochin University of Scince
and Technology
Baby,B V; Dr.Babu, Joseph K(Cochin University of Science and Technology, April 3, 1985)
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Abstract:
An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes
one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear
operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.
Description:
Department of Physics, Cochin University of Science and Technology
Saji, Susan Mathew; Dr. Chennubhotla, V S K(Cochin University of Science and Technology, January , 1991)
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In the present thesis , observations on the ecology of seaweed flora of Kerala, their distribution and zonation pattern, monthly/seasonal density of seaweeds at each station, frequency of occurrence, standing crop, monthly/seasonal/place-wise data on physico—chemical characters of ambient waters at the stations and their influence on seaweed density have been made. This data will help us in the farming of economically important seaweeds, by providing information on the ideal conditions of seaweed biomass production. Biochemical observations on protein, carbohydrate and lipid contents of different species of nutritive value. Seaweeds with high content of proteins, carbohydrates and lipids can be recommended for food and feed formulations after subjecting them to toxicological studies. The study on monthly/seasonal/placewise variation in biochemical composition of seaweeds will provide necessary information on the appropriate time and place of harvesting the algal species for exploiting its constituents .
Rosa, M V; Dr.Thrivikraman, T(Cochin University Of Science And Technology, May 6, 1994)
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Abstract:
This thesis is a study of abstract fuzzy convexity
spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop
a fuzzy convexity theoryin abstract situations. The
purpose of this thesis is to introduce fuzzy convexity
theory in abstract situations
Description:
Department
of Mathematics and Statistics, Cochin University of
Science and Technology
Ramachandran,P T; Dr.Thrivikraman, T(Cochin University of Science and Technology, 1985)
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In this thesis we investigate some problems in set theoretical topology related to the concepts of
the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms.
This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention
Description:
Department of Mathematics and Statistics, Cochin University of Science and Technology
Velukutty, K K; Dr.Wazir, Hasan Abdi(Cochin University of Science and Technology, February 15, 1982)
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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.
Description:
Department of Mathematics and Statistics, Cochin University of Science & Technology