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81 
New analytical stellar models in general relativity.Thirukkanesh, Suntharalingam. January 2009 (has links)
We present new exact solutions to the Einstein and EinsteinMaxwell field equations that model the interior of neutral, charged and radiating stars. Several new classes of solutions in static spherically symmetric interior spacetimes are found in the presence of charge. These correspond to isotropic matter with a specified electric field intensity. Our solutions are found by choosing different rational forms for one of the gravitational potentials and a particular form for the electric field. The models generated contain results found previously including Finch and Skea (1989) neutron stars, Durgapal and Bannerji (1983) dense stars, Tikekar (1990) superdense stars in the limit of vanishing charge. Then we study the general situation of a compact relativistic object with anisotropic pressures in the presence of the electromagnetic field. We assume the equation of state is linear so that the model may be applied to strange stars with quark matter and dark energy stars. Several new classes of exact solutions are found, and we show that the densities and masses are consistent with real stars. We regain as special cases the Lobo (2006) dark energy stars, the Sharma and Maharaj (2007) strange stars and the realistic isothermal universes of Saslaw et al (1996). In addition, we consider relativistic radiating stars undergoing gravitational collapse when the fluid particles are in geodesic motion. We transform the governing equation into Bernoulli, Riccati and confluent hypergeometric equations. These admit an infinite family of solutions in terms of simple elementary functions and special functions. Particular models contain the Minkowski spacetime and the Friedmann dust spacetime as limiting cases. Finally, we model the radiating star with shear, acceleration and expansion in the presence of anisotropic pressures. We obtain several classes of new solutions in terms of arbitrary functions in temporal and radial coordinates by rewriting the junction condition in the form of a Riccati equation. A brief physical analysis indicates that these models are physically reasonable. / Thesis (Ph.D.)University of KwaZuluNatal, Westville, 2009.

82 
Embedding theorems and finiteness properties for residuated structures and substructural logicsHsieh, AiNi. January 2008 (has links)
Paper 1. This paper establishes several algebraic embedding theorems, each of which asserts that a certain kind of residuated structure can be embedded into a richer one. In almost all cases, the original structure has a compatible involution, which must be preserved by the embedding. The results, in conjunction with previous findings, yield separative axiomatizations of the deducibility relations of various substructural formal systems having double negation and contraposition axioms. The separation theorems go somewhat further than earlier ones in the literature, which either treated fewer subsignatures or focussed on the conservation of theorems only. Paper 2. It is proved that the variety of relevant disjunction lattices has the finite embeddability property (FEP). It follows that Avron’s relevance logic RMImin has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron’s result that RMImin is decidable. Paper 3. An idempotent residuated pomonoid is semiconic if it is a subdirect product of algebras in which the monoid identity t is comparable with all other elements. It is proved that the quasivariety SCIP of all semiconic idempotent commutative residuated pomonoids is locally finite. The latticeordered members of this class form a variety SCIL, which is not locally finite, but it is proved that SCIL has the FEP. More generally, for every relative subvariety K of SCIP, the latticeordered members of K have the FEP. This gives a unified explanation of the strong finite model property for a range of logical systems. It is also proved that SCIL has continuously many semisimple subvarieties, and that the involutive algebras in SCIL are subdirect products of chains. Paper 4. Anderson and Belnap’s implicational system RMO can be extended conservatively by the usual axioms for fusion and for the Ackermann truth constant t. The resulting system RMO is algebraized by the quasivariety IP of all idempotent commutative residuated pomonoids. Thus, the axiomatic extensions of RMO are in onetoone correspondence with the relative subvarieties of IP. It is proved here that a relative subvariety of IP consists of semiconic algebras if and only if it satisfies x (x t) x. Since the semiconic algebras in IP are locally finite, it follows that when an axiomatic extension of RMO has ((p t) p) p among its theorems, then it is locally tabular. In particular, such an extension is strongly decidable, provided that it is finitely axiomatized. / Thesis (Ph.D.)University of KwaZuluNatal, Westville, 2008.

83 
The thermal SunyaevZel'dovich effect as a probe of cluster physics and cosmology.Warne, Ryan Russell. January 2010 (has links)
The universe is a complex environment playing host to a plethora of macroscopic and microscopic
processes. Understanding the interplay and evolution of such processes will help to
shed light on the properties and evolution of the universe. The juxtaposition is that in order to
study small scale effects one needs to observe large scale structure as the latter objects trace the
history of our universe. Galaxy groups and clusters are the largest known objects in the universe
and thus provide a means to probe the evolution of structure formation in the universe as
well as the underlying cosmology. In this thesis we investigate how clusters observed through
the SunyaevZel’dovich (SZ) effect can be used to constrain cosmological models. In addition,
we present the first results of the Atacama Cosmology Telescope (ACT), a mmwave telescope
measuring the smallscale microwave background anisotropy, and conclude with preliminary SZ
cluster detection performed on the latest ACT sky maps.
In the first part of this thesis we investigate the ability of high resolution cosmic microwave
background (CMB) experiments to detect hot gas in the outer regions of nearby group halos. We
construct two hot gas models for the halos; a simpler adiabatic formalism with the gas described
by a polytropic equation of state, and a more general gas description which incorporates feedback
effects in line with constraints from Xray observations. We calculate the thermal Sunyaev
Zel’dovich (tSZ) signal in these halos and compare it to the sensitivities of upcoming and current
tSZ survey experiments such as ACT, PLANCK and the South Pole Telescope (SPT). Through
the application of a multifrequency Wiener filter, we derive mass and redshift based tSZ detectability
limits for the various experiments, incorporating effects of galactic and extragalactic
foregrounds as well as the CMB. In this study we find that galaxy group halos with virial masses
below 1014M. can be detected at z ~< 0.05 with the mass limit dropping to 3 − 4 × 1013M. at
z ~< 0.01. Probing such halos with the tSZ effect allows one to map the hot gas in the outer regions,
providing a means to constrain gas processes, such as feedback, as well as the distribution
of baryons in the local universe.
In the fourth chapter, we extend this analysis and determine the ability of ACT to constrain
galactic feedback and star formation in clusters and groups using the tSZ effect. We present a
new microwave deblender, which provides a means of extracting accurate halo fluxes and radial
profiles from maps of the tSZ effect. Considering various surveys that could be performed by
ACT, we use multifrequency filtering on simulated sky maps to predict how well such surveys
will constrain gas properties using a Fisher matrix analysis. We find that the current ACT survey
will be unable to constrain any gas parameters. However, if ACT were to survey a smaller area
then we will be able to constrain feedback. Furthermore, with greater sensitivity, we will be able
to place interesting constraints on the gas feedback, and baryon and stellar fractions.
The fifth chapter in this thesis concerns itself with the first results of the Atacama Cosmology
Telescope Project. In this section we discuss the mapmaking method as well as telescope beam
characterisation, an understanding of which is important in any subsequent map analyses. In
addition, we present maps of eight clusters observed at 148 GHz via the SZ effect, and provide
flux and signal to noise estimates of the clusters.
In the final chapter we present a preliminary analysis of the latest 148 GHz ACT maps from
the 2008 observing season. We study the sky maps using single frequency wiener filtering,
allowing for CMB, dust and correlated noise contamination. To substantiate our results, we
compare the number counts, recovered fluxes and sample purity from simulated sky maps. The
compounding effects of CMB and correlated noise result in high contamination levels below a
signal to noise ratio of 6, however our investigation shows that above 8¾ our cluster sample is
¼ 80% pure. A cluster list containing 44 detections, of which 8 are previously known, is also
presented, along with a Table listing the candidate cluster positions and fluxes. The candidate
cluster catalogue will be used for followup studies using optical and Xray observations. / Thesis (Ph.D.)University of KwaZuluNatal, Westville, 2010.

84 
Aspects of functional variations of domination in graphs.Harris, Laura Marie. January 2003 (has links)
Let G = (V, E) be a graph. For any real valued function f : V >R and SCV, let f (s) = z ues f(u). The weight of f is defined as f(V). A signed ksubdominating function (signed kSF) of G is defined as a function f : V > {I, I} such that f(N[v]) > 1 for at least k vertices of G, where N[v] denotes the closed neighborhood of v. The signed ksubdomination number of a graph G, denoted by yks11(G), is equal to min{f(V) I f is a signed kSF of G}. If instead of the range {I, I}, we require the range {I, 0, I}, then we obtain the concept of a minus ksubdominating function. Its associated parameter, called the minus ksubdomination number of G, is denoted by ytks101(G). In chapter 2 we survey recent results on signed and minus ksubdomination in graphs. In Chapter 3, we compute the signed and minus ksubdomination numbers for certain complete multipartite graphs and their complements, generalizing results due to Holm [30]. In Chapter 4, we give a lower bound on the total signed ksubdomination number in terms of the minimum degree, maximum degree and the order of the graph. A lower bound in terms of the degree sequence is also given. We then compute the total signed ksubdomination number of a cycle, and present a characterization of graphs G with equal total signed ksubdomination and total signed lsubdomination numbers. Finally, we establish a sharp upper bound on the total signed ksubdomination number of a tree in terms of its order n and k where 1 < k < n, and characterize trees attaining these bounds for certain values of k. For this purpose, we first establish the total signed ksubdomination number of simple structures, including paths and spiders. In Chapter 5, we show that the decision problem corresponding to the computation of the total minus domination number of a graph is NPcomplete, even when restricted to bipartite graphs or chordal graphs. For a fixed k, we show that the decision problem corresponding to determining whether a graph has a total minus domination function of weight at most k may be NPcomplete, even when restricted to bipartite or chordal graphs. Also in Chapter 5, linear time algorithms for computing Ytns11(T) and Ytns101(T) for an arbitrary tree T are presented, where n = n(T). In Chapter 6, we present cubic time algorithms to compute Ytks11(T) and Ytks101l(T) for a tree T. We show that the decision problem corresponding to the computation of Ytks11(G) is NPcomplete, and that the decision problem corresponding to the computation of Ytks101 (T) is NPcomplete, even for bipartite graphs. In addition, we present cubic time algorithms to computeYks11(T) and Yks101(T) for a tree T, solving problems appearing in [25]. / Thesis (Ph.D.)University of Natal, Pietermaritzburg, 2003.

85 
Bounds on distance parameters of graphs.Van den Berg, Paul. January 2007 (has links)
No abstract available. / Thesis (Ph.D.)University of KwaZuluNatal, Westville, 2007.

86 
FischerClifford theory and character tables of group extensions.Mpono, Zwelethemba Eugene. January 1998 (has links)
The smallest Fischer sporadic simple group Fi22 is generated by a conjugacy class D of 3510 involutions called 3transpositions such that the product of any noncommuting pair is an element of order 3. In Fi22 there are exactly three conjugacy classes of involutions denoted by D, T and N and represented in the ATLAS [26] by 2A, 2B and 2C, containing 3510, 1216215 and 36486450 elements with corresponding centralizers
2·U(6,2), (2 x 2~+8:U(4,2)):2 and 25+8:(83 X 32:4) respectively. In Fi22 , we have Npi22(26) = 26:8P(6,2), where 26 is a 2Bpure group, and thus the maximal subgroup 26:8P(6, 2) of Fi22 is a 2local subgroup. The full automorphism group of Fi22 is denoted by Fi22 . In Fi22 , there are three involutory outer automorphisms of Fi22 which are denoted bye, f and 0 and
represented in the ATLAS [26] by 2D, 2F and 2E respectively. We obtain that Fi22 = Fi22 :(e) and it can be easily shown that Fi22 = Fi22 :(e) = Fi22 :(f) = Fi22 :(0). As e, f and 0 act on Fi22 , then we obtain the subgroups CPi22 (e) rv 0+(8,2):83, CPi22 (f) rv 8P(6,2) x 2 and CPi22 (()) rv 26:0(6,2) of Fi22 which are generated by CD(e), Cn(f) and CD(0) respectively.
In this thesis we are concerned with the construction of the character tables of certain groups which are associated with Fi22 and its automorphism group Fi22 . We use the technique of the FischerClifford matrices to construct the character tables of these groups, which are split extensions. These groups are 26:8P(6, 2), 26:0(6,2) and 27:8P(6, 2). The study of the group 26:8P(6, 2) is essential, as the other groups studied in this thesis are related to it. The groups 8P(6,2) and 0 (6,2) of 6 x 6
matrices over GF(2), played crucial roles in our construction of the group 8P(6, 2) as a group of 7 x 7 matrices over GF(2) which would act on 27 . Also the character table of 25:86 , the affine subgroup of 8P(6, 2) fixing a nonzero vector in 26 , is constructed by using the technique of the FischerClifford matrices. This character table is used in the construction of the character table 26:SP(6, 2). The character tables computed in this thesis have been accepted for incorporation into GAP and will be available in the latest version of GAP. / Thesis (Ph.D.)  University of Natal, Pietermaritzburg, 1998.

87 
Some Mal'cev conditions for varieties of algebras.Moses, Mogambery. January 1991 (has links)
This dissertation deals with the classification of varieties according to
their Mal'cev properties. In general the so called Mal'cevtype theorems
illustrate an interplay between first order properties of a given class of
algebras and the lattice properties of the congruence lattices of algebras of
the considered class.
CHAPTER 1. A survey of some notational conventions, relevant definitions
and auxiliary results is presented. Several examples of less frequently
used algebras are given together with the important properties of some of
them. The term algebra T(X) and useful results concerning 'term' operations
are established. A Kreflection is defined and a connection between
a Kreflection of an algebra and whether a class K satisfies an identity of
the algebra is established.
CHAPTER 2. The Mal'cevtype theorems are presented in complete
detail for varieties which are congruence permutable, congruence distributive,
arithmetical, congruence modular and congruence regular. Several
examples of varieties which exhibit these properties are presented together
with the necessary verifications.
CHAPTER 3. A general scheme of algorithmic character for some
Mal'cev conditions is presented. R. Wille (1970) and A. F. Pixley (1972)
provided algorithms for the classification of varieties which exhibit strong
Mal'cev properties. This chapter is largely devoted to a modification of
the WillePixley schemes. It must be noted that this modification is quite
different from all such published schemes. The results are the same as in
Wille's scheme but slightly less general than in Pixley's. The text presented
here, however is much simpler. As an example, the scheme is used
to confirm Mal'cev's original theorem on congruence permutable varieties.
Finally, the socalled Chinese var£ety is defined and Mal'cev conditions are
established for such a variety of algebras .
CHAPTER 4. A comprehensive survey of literature concerning Mal'cev
conditions is given in this chapter. / Thesis (M.Sc.)University of Natal, Durban, 1991.

88 
A measuretheoretic approach to chaotic dynamical systems.Singh, Pranitha. January 2001 (has links)
The past few years have witnessed a growth in the study of the longtime behaviour of physical, biological and economic systems using measuretheoretic and probabilistic methods. In this dissertation we present a study of the evolution of dynamical systems that display various types of irregular behaviour for large times. Large systems, containing many elements, like e.g. bacteria populations or ensembles of gas particles, are very difficult to analyse and contain elements of uncertainty. Also, in general, it is not necessary to know the evolution of each bacteria or each gas particle. Therefore we replace the "pointwise" description of the evolution of the system with that of the evolution of suitable averages of the population like e.g. the gas or the bacteria spatial density. In particular cases, when the quantity in the evolution that we analyse has the probabilistic interpretation, say, the probability of finding the particle in certain state at certain time, we will be talking about the evolution of (probability) densities. We begin with the establishment of results for discrete time systems and this is later followed with analogous results for continuous time systems. We observe that in many cases the system has two important properties: at each step it is determined by a nonnegative function (for example the spatial density or the probability density) and the overall quantity of the elements remains preserved. Because of these properties the most suitable framework to investigate such systems is the theory of Markov operators. We shall discuss three levels of "chaotic" behaviour that are known as ergodicity, mixing and exactness. They can be described as follows: ergodicity means that the only invariant sets are trivial, mixing means that for any set A the sequence of sets Sn(A) becomes, asymptotically, independent of any other set B, and exactness implies that if we start with any set of positive measure, then, after a long time the points of this set will spread and completely fill the state space. In this dissertation we describe an application of two operators related to the generating Markov operator to study and characterize the abovementioned properties of the evolution system. However, a system may also display regular behaviour. We refer to this as the asymptotic stability of the Markov operator generating this system and we provide some criteria characterizing this property. Finally, we demonstrate the use of the above theory by applying it to a system that is modeled by the linear Boltzmann equation. / Thesis (M.Sc.)University of Natal, Durban, 2001.

89 
Computer analysis of equations using Mathematica.Jugoo, Vikash R. January 2001 (has links)
In this thesis we analyse particular differential equations that arise in physical situations.
This is achieved with the aid of the computer software package called
Mathematica. We first describe the basic features of Mathematica highlighting its
capabilities in performing calculations in mathematics. Then we consider a first order
Newtonian equation representing the trajectory of a particle around a spherical
object. Mathematica is used to solve the Newtonian equation both analytically and
numerically. Graphical plots of the trajectories of the planetary bodies Mercury,
Earth and Jupiter are presented. We attempt a similar analysis for the corresponding
relativistic equation governing the orbits of gravitational objects. Only numerical
results are possible in this case. We also perform a perturbative analysis of the relativistic
equation and determine the amount of perihelion shift. The second equation
considered is the EmdenFowler equation of order two which arises in many physical
problems, including certain inhomogeneous cosmological applications. The analytical
features of this equation are investigated using Mathematica and the Lie analysis
of differential equations. Different cases of the related autonomous form of the
EmdenFowler equation are investigated and graphically represented. Thereafter, we
generate a number of profiles of the energy density and the pressure for a particular
solution which demonstrates that a numerical approach for studying inhomogeneity,
in cosmological models in general relativity, is feasible. / Thesis (M.Sc.)University of Natal, Durban, 2001.

90 
Cosmological models and the deceleration parameter.Naidoo, Ramsamy. January 1992 (has links)
In this thesis we utilise a form for the Hubble constant first proposed by Berman
(1983) to study a variety of cosmological models. In particular we investigate the
RobertsonWalker spacetimes, the Bianchi I spacetime, and the scalartensor theory
of gravitation of Lau and Prokhovnik (1986). The Einstein field equations with variable
cosmological constant and gravitational constant are discussed and the Friedmann
models are reviewed. The relationship between observation and the Friedmann
models is reviewed. We present a number of new solutions to the Einstein
field equations with variable cosmological constant and gravitational constant in the
RobertsonWalker spacetimes for the assumed form of the Hubble parameter. We explicitly
find forms for the scale factor, cosmological constant, gravitational constant,
energy density and pressure in each case. Some of the models have an equation of
state for an ideal gas. The gravitational constant may be increasing in certain regions
of spacetime. The Bianchi I spacetime, which is homogeneous and anisotropic,
is shown to be consistent with the Berman (1983) law by defining a function which
reduces to the scale factor of RobertsonWalker. We illustrate that the scalartensor
theory of Lau and Prokhovnik (1986) also admits solutions consistent with the Hubble
variation proposed by Berman. This demonstrates that this approach is useful
in seeking solutions to the Einstein field equations in general relativity and alternate
theories of gravity. / Thesis (M.Sc.)University of Natal, 1992.

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