In this appealing and well-written text, Richard BronsonВ starts with the concrete and computatio... more In this appealing and well-written text, Richard BronsonВ starts with the concrete and computational, and leads the reader to a choice of major applications. The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced andВ key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. Prerequisite: One year of calculus is recommended. Introduces deductive reasoning and helps the reader develop a facility with mathematical proofsProvides a balanced approach to computation and theory by offering com...
This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I sp... more This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I space–time with a variable gravitational constant G and cosmological constant Λ. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. We find a variety of solutions in which the cosmological parameter varies inversely with time t. We also discuss in detail the behavior of associated fluid parameters and kinematical parameters. This paper pictures cosmic history when the radiation and matter content of the universe are in an interactive phase. Here, Ω is closing to 1 throughout the cosmic evolution.
In this paper we present a class of solutions of Einstein's field equations describing two-fluid ... more In this paper we present a class of solutions of Einstein's field equations describing two-fluid models of the universe in a locally rotationally symmetric Bianchi type II space-time. In these models one fluid is the radiation distribution which represents the cosmic microwave background and the other fluid is the perfect fluid representing the matter content of the universe. It is found that both the fluids are comoving in the locally rotationally symmetric Bianchi type II space-time. The behaviour of the radiation density, matter density, the ratio of the matter density to the radiation density and the pressure has been discussed. A subclass of solutions is found to describe models of a spatially homogeneous and partially isotropic universe evolving from a radiation dominated era to a pressure free matter dominated era.
By making use of Letelier’s form of energy—momentum tensor for a cloud of stringdust we present s... more By making use of Letelier’s form of energy—momentum tensor for a cloud of stringdust we present some classes of solutions of general relativistic field equations which describe cosmological string-dust models in Bianchi type I space-time. Some of the classes of models obey Takabayashi’s equation of state whereas a class of models exhibits inflation in the initial stage. Two of the classes presented here have Kasner’s space-time as past asymptote
In this paper we present anisotropic, homogeneous two-fluid cosmological models in a Bianchi I sp... more In this paper we present anisotropic, homogeneous two-fluid cosmological models in a Bianchi I space-time. These classes of cosmological models picture two different scenarios of cosmic history; viz., when the radiation and matter content of the universe are in interactive phase and another when the two are non-interacting. The universe is highly anisotropic in the initial stages, however, anisotropy tapers out to insignificance in due course of cosmic evolution. In every model the anisotropy of the space-time is determined by the density parameter Ω0 at the present epoch. For Ω0=1, the anisotropy is washed out before long. An interesting class of models, having an inflationary epoch in finite future, is discovered.
In this appealing and well-written text, Richard BronsonВ starts with the concrete and computatio... more In this appealing and well-written text, Richard BronsonВ starts with the concrete and computational, and leads the reader to a choice of major applications. The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced andВ key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. Prerequisite: One year of calculus is recommended. Introduces deductive reasoning and helps the reader develop a facility with mathematical proofsProvides a balanced approach to computation and theory by offering com...
This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I sp... more This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I space–time with a variable gravitational constant G and cosmological constant Λ. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. We find a variety of solutions in which the cosmological parameter varies inversely with time t. We also discuss in detail the behavior of associated fluid parameters and kinematical parameters. This paper pictures cosmic history when the radiation and matter content of the universe are in an interactive phase. Here, Ω is closing to 1 throughout the cosmic evolution.
In this paper we present a class of solutions of Einstein's field equations describing two-fluid ... more In this paper we present a class of solutions of Einstein's field equations describing two-fluid models of the universe in a locally rotationally symmetric Bianchi type II space-time. In these models one fluid is the radiation distribution which represents the cosmic microwave background and the other fluid is the perfect fluid representing the matter content of the universe. It is found that both the fluids are comoving in the locally rotationally symmetric Bianchi type II space-time. The behaviour of the radiation density, matter density, the ratio of the matter density to the radiation density and the pressure has been discussed. A subclass of solutions is found to describe models of a spatially homogeneous and partially isotropic universe evolving from a radiation dominated era to a pressure free matter dominated era.
By making use of Letelier’s form of energy—momentum tensor for a cloud of stringdust we present s... more By making use of Letelier’s form of energy—momentum tensor for a cloud of stringdust we present some classes of solutions of general relativistic field equations which describe cosmological string-dust models in Bianchi type I space-time. Some of the classes of models obey Takabayashi’s equation of state whereas a class of models exhibits inflation in the initial stage. Two of the classes presented here have Kasner’s space-time as past asymptote
In this paper we present anisotropic, homogeneous two-fluid cosmological models in a Bianchi I sp... more In this paper we present anisotropic, homogeneous two-fluid cosmological models in a Bianchi I space-time. These classes of cosmological models picture two different scenarios of cosmic history; viz., when the radiation and matter content of the universe are in interactive phase and another when the two are non-interacting. The universe is highly anisotropic in the initial stages, however, anisotropy tapers out to insignificance in due course of cosmic evolution. In every model the anisotropy of the space-time is determined by the density parameter Ω0 at the present epoch. For Ω0=1, the anisotropy is washed out before long. An interesting class of models, having an inflationary epoch in finite future, is discovered.
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