Rajesh,K Thumabakara; Thrivikraman,T(Department of Mathematics, March , 2006)
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Abstract:
The fuzzy set theory has a wider scope of applicability than classical set theory in solving various problems. Fuzzy set theory in the last three decades as a formal theory which got formalized by generalizing the original ideas and concepts in classical mathematical areas and as a very powerful modeling language, that can cope with a large fraction of uncertainties of real life situations. In Intuitionistic Fuzzy sets a new component degree of non membership in addition to the degree of membership in the case of fuzzy sets with the requirement that their sum be less than or equal to one. The main objective of this thesis is to study frames in Fuzzy and Intuitionistic Fuzzy contexts.
The thesis proved some results such as ifµ is a fuzzy subset of a frame F, then µ is a fuzzy frame of F iff each non-empty level subset µt of µ is a subframe of F, the category Fuzzfrm of fuzzy frames has products and the category Fuzzfrm of fuzzy frames is complete. It define a fuzzy-quotient frame of F to be a fuzzy partition of F, that is, a subset of IF and having a frame structure with respect to new operations and study the notion of intuitionistic fuzzy frames and obtain some results and introduce the concept of Intuitionistic fuzzy Quotient frames. Finally it establish the categorical link between frames and intuitionistic fuzzy topologies.
Joy, E C; Dr.Joy, George(Cochin University Of Science And Technology, March 27, 1980)
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Abstract:
This thesis consists of a study of the effect of electrode films and overlayer films on the electrical properties of certain metal films. The films have been prepared on glass substrates by thermal evapouration in a vaccum 10 terr. The properties of Al films on Ag, Al,Au and Cu films on In electrodes ,and Bi/Ag bilayer films have been studied. The influence of annealing electrodes at higher temperature on the electrical properties of metal films has also been investigated. Further the effect of varying layer thickness in the bilayer films ,both annealed at higher temperature and annealed at room temperature have been examined.
Description:
Department Of Physics,Cochin University Of Science And Technology
Pradeep,B; Dr.Joy, George(Cochin University of Science And Technology, November , 1986)
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Abstract:
This thesis deals with the preparation and properties of two compounds of V-II family, viz.
bismuth telluride and bismuth oxide, in thin filmform. In the first chapter is given the resume of
basic solid state physics relevant to the work reported here. In the second chapter the different
methods of thin film preparationtia described. Third chapter deals with the experimental techniques used for preparation and characterization of the films. Fourth chapter deals with the preparation and propertiesof bismuth telluride films. In next four chapters, the preparation and properties of bismuth oxide films are discussed in detail. In the last chapter the use of Bi205 films in the fabrication of Heat mirrors is examined and discussed.
Description:
Department of physics, Cochin University of Science And Technology
Marina, Aloysius; Dr. Parameswaran, K(Space Physics Laboratory, Vikram Sarabhai Space Centre, January , 2010)
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Abstract:
The present study brings out the influence of transport dynamics on the
aerosol distribution over the Indian region at a few selected geographically distinct
locations. Over the Bay of Bengal the dominant pathway of aerosol transport during the
pre-monsoon period is through higher altitudes (~ 3 km); directed from the Indian main
land. In contrast, the aerosol pathways over the Arabian Sea during the same period are
quite complex. They are directed from geographically different environments around the
ocean through different altitudes. However in general, the day-to-day variability of AOD at
both these regions is significantly influenced by the features of atmospheric circulation
especially, the wind convergence at higher altitudes (around 3 km). Over the Ganga Basin
during the winter period, the wind convergence at lower altitudes (< I km) govems the
shon term variations in AOD, while the mean AOD distribution at this location is mainly
governed by the local anthropogenic sources.
Sunny, Kuriakose A; Dr.Thrivikraman, T(Department of Mathematics and Statistics, August , 1993)
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Abstract:
In this study we combine the notions of fuzzy order
and fuzzy topology of Chang and define fuzzy ordered
fuzzy topological space. Its various properties are
analysed. Product, quotient, union and intersection
of fuzzy orders are introduced. Besides, fuzzy order
preserving maps and various fuzzy completeness are
investigated. Finally an attempt is made to study the
notion of generalized fuzzy ordered fuzzy topological
space by considering fuzzy order defined on a fuzzy subset.
Ramakrishnan, T V; Dr.Thrivikraman, T(Cochin University of Science And Technology, November , 1995)
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Abstract:
Mathematical models are often used to describe
physical realities. However, the physical realities are
imprecise while the mathematical concepts are required to be
precise and perfect. Even mathematicians like H. Poincare
worried about this. He observed that mathematical models
are over idealizations, for instance, he said that only in
Mathematics, equality is a transitive relation. A first
attempt to save this situation was perhaps given by K.
Menger in 1951 by introducing the concept of statistical
metric space in which the distance between points is a
probability distribution on the set of nonnegative real
numbers rather than a mere nonnegative real number. Other
attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A.
Sklar and others. An aspect in common to all these
approaches is that they model impreciseness in a
probabilistic manner. They are not able to deal with
situations in which impreciseness is not apparently of a
probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.
Description:
Department of mathematics, Cochin University of Science And Technology
Ramakrishnan, T V; Dr.Thrivikraman, T(Cochin University of Science and Technology, November , 1995)
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Abstract:
Mathematical models are often used to describe
physical realities. However, the physical realities are
imprecise while the mathematical concepts are required to be
precise and perfect. The 1st chapter give a brief summary of the
arithmetic of fuzzy real numbers and the fuzzy normed
algebra M(I). Also we explain a few preliminary definitions
and results required in the later chapters. Fuzzy real
numbers are introduced by Hutton,B [HU] and Rodabaugh,
S.E[ROD]. Our definition slightly differs from this with an
additional minor restriction. The definition of Clementina
Felbin [CL1] is entirely different. The notations of
[HU]and [M;Y] are retained inspite of the slight difference
in the concept.the 3rd chapter In this chapter using the completion M'(I) of M(I)
we give a fuzzy extension of real Hahn-Banch theorem. Some
consequences of this extension are obtained. The idea of
real fuzzy linear functional on fuzzy normed linear space is
introduced. Some of its properties are studied. In the
complex case we get only a slightly weaker analogue for the
Hahn-Banch theorem, than the one [B;N] in the crisp case
Description:
School of Mathematical Sciences , Cochin University of Science
and Technology
Shaju, K Y; Ramesh Babu, T(Cochin University of Science And Technology, November , 2013)
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Abstract:
Study on variable stars is an important topic of modern astrophysics. After
the invention of powerful telescopes and high resolving powered CCD’s, the
variable star data is accumulating in the order of peta-bytes. The huge amount
of data need lot of automated methods as well as human experts. This thesis
is devoted to the data analysis on variable star’s astronomical time series data
and hence belong to the inter-disciplinary topic, Astrostatistics.
For an observer on earth, stars that have a change in apparent brightness
over time are called variable stars. The variation in brightness may be regular
(periodic), quasi periodic (semi-periodic) or irregular manner (aperiodic) and
are caused by various reasons. In some cases, the variation is due to some
internal thermo-nuclear processes, which are generally known as intrinsic vari-
ables and in some other cases, it is due to some external processes, like eclipse
or rotation, which are known as extrinsic variables. Intrinsic variables can
be further grouped into pulsating variables, eruptive variables and flare stars.
Extrinsic variables are grouped into eclipsing binary stars and chromospheri-
cal stars. Pulsating variables can again classified into Cepheid, RR Lyrae, RV
Tauri, Delta Scuti, Mira etc. The eruptive or cataclysmic variables are novae,
supernovae, etc., which rarely occurs and are not periodic phenomena. Most
of the other variations are periodic in nature.
Variable stars can be observed through many ways such as photometry,
spectrophotometry and spectroscopy. The sequence of photometric observa-
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tions on variable stars produces time series data, which contains time, magni-
tude and error. The plot between variable star’s apparent magnitude and time
are known as light curve. If the time series data is folded on a period, the plot
between apparent magnitude and phase is known as phased light curve. The
unique shape of phased light curve is a characteristic of each type of variable
star. One way to identify the type of variable star and to classify them is by
visually looking at the phased light curve by an expert. For last several years,
automated algorithms are used to classify a group of variable stars, with the
help of computers.
Research on variable stars can be divided into different stages like observa-
tion, data reduction, data analysis, modeling and classification. The modeling
on variable stars helps to determine the short-term and long-term behaviour
and to construct theoretical models (for eg:- Wilson-Devinney model for eclips-
ing binaries) and to derive stellar properties like mass, radius, luminosity, tem-
perature, internal and external structure, chemical composition and evolution.
The classification requires the determination of the basic parameters like pe-
riod, amplitude and phase and also some other derived parameters. Out of
these, period is the most important parameter since the wrong periods can
lead to sparse light curves and misleading information.
Time series analysis is a method of applying mathematical and statistical
tests to data, to quantify the variation, understand the nature of time-varying
phenomena, to gain physical understanding of the system and to predict future
behavior of the system. Astronomical time series usually suffer from unevenly
spaced time instants, varying error conditions and possibility of big gaps. This
is due to daily varying daylight and the weather conditions for ground based
observations and observations from space may suffer from the impact of cosmic
ray particles.
Many large scale astronomical surveys such as MACHO, OGLE, EROS,
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ROTSE, PLANET, Hipparcos, MISAO, NSVS, ASAS, Pan-STARRS, Ke-
pler,ESA, Gaia, LSST, CRTS provide variable star’s time series data, even
though their primary intention is not variable star observation. Center for
Astrostatistics, Pennsylvania State University is established to help the astro-
nomical community with the aid of statistical tools for harvesting and analysing
archival data. Most of these surveys releases the data to the public for further
analysis.
There exist many period search algorithms through astronomical time se-
ries analysis, which can be classified into parametric (assume some underlying
distribution for data) and non-parametric (do not assume any statistical model
like Gaussian etc.,) methods. Many of the parametric methods are based on
variations of discrete Fourier transforms like Generalised Lomb-Scargle peri-
odogram (GLSP) by Zechmeister(2009), Significant Spectrum (SigSpec) by
Reegen(2007) etc. Non-parametric methods include Phase Dispersion Minimi-
sation (PDM) by Stellingwerf(1978) and Cubic spline method by Akerlof(1994)
etc.
Even though most of the methods can be brought under automation, any of
the method stated above could not fully recover the true periods. The wrong
detection of period can be due to several reasons such as power leakage to
other frequencies which is due to finite total interval, finite sampling interval
and finite amount of data. Another problem is aliasing, which is due to the
influence of regular sampling. Also spurious periods appear due to long gaps
and power flow to harmonic frequencies is an inherent problem of Fourier
methods. Hence obtaining the exact period of variable star from it’s time
series data is still a difficult problem, in case of huge databases, when subjected
to automation. As Matthew Templeton, AAVSO, states “Variable star data
analysis is not always straightforward; large-scale, automated analysis design
is non-trivial”. Derekas et al. 2007, Deb et.al. 2010 states “The processing of
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huge amount of data in these databases is quite challenging, even when looking
at seemingly small issues such as period determination and classification”.
It will be beneficial for the variable star astronomical community, if basic
parameters, such as period, amplitude and phase are obtained more accurately,
when huge time series databases are subjected to automation. In the present
thesis work, the theories of four popular period search methods are studied, the
strength and weakness of these methods are evaluated by applying it on two
survey databases and finally a modified form of cubic spline method is intro-
duced to confirm the exact period of variable star. For the classification of new
variable stars discovered and entering them in the “General Catalogue of Vari-
able Stars” or other databases like “Variable Star Index“, the characteristics
of the variability has to be quantified in term of variable star parameters.