In this thesis, we explore three alternatives to the current paradigm of the standard inflationary big bang scenario. The three alternative themes are spin torsion (or Einstein-Cartan-Kibble-Sciama) theories, extra dimensions (braneworld cosmology) and changing global symmetry. In the spin torsion theories, we found new cosmological solutions with a cosmological constant as alternative to the s...

Proof. One can relate the singular values of the Hadamard product Z 2 to those of the Kronecker product Z ⊗ Z. In particular, as Z Z can be obtain from Z ⊗ Z by deleting some rows and columns, Lemma A.1 tells us that σmin(Z Z) ≥ σmin(Z ⊗ Z) and σmax(Z Z) ≤ σmax(Z ⊗ Z). Then the lemma follows as the Kronecker product Z⊗Z is known to have the property that σmin(Z⊗ Z) = (σmin(Z)) 2 and σmax(Z ⊗ Z)...

Let A be a central simple algebra over a field F . Let k1, . . . , kr be cyclic extensions of F such that k1 ⊗F · · · ⊗F kr is a field. We investigate conditions under which A is a tensor product of symbol algebras where each ki is in a symbol F -algebra factor of the same degree as ki. As an application, we give an example of an indecomposable algebra of degree 8 and exponent 2 over a field of...

Recent advances in application fields such as blind deconvolution and independent component analysis have revived the interest in higher-order statistics (HOS), showing them to be an indispensable tool for providing piercing solutions to these problems. Multilinear algebra and in particular tensor analysis provide a natural mathematical framework for studying HOS in view of the inherent multiin...

Various analytic expressions have been proposed for the density profile of dark matter halos. We consider six of these expressions for which the density profile has a power-law fall-off ρ ∝ r−3 at large radii and a power-law cusp ρ ∝ r−γ (γ = 0, 1 2 , 1, 3 2) at small radii. The phase-space distribution function for these models is calculated assuming spherical symmetry and either an isotropic ...

We suggest a new dimensionless relativistic invariant variable R = ∆mX/ν which may be interpreted as the ratio of the excitation energy to the full transferred energy; therefore this variable measures a ”degree of inelasticity” of the scattering. Existing data on the tensor analysing power of the p(~ d, d ′)X and 12C(~ d, d ′)X inelastic scattering at momenta from 4.2 to 9 GeV/c are analysed in...

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

The power generation industry is facing challenges from ever-tightening environmental constraints, increased competition and deregulation of the markets. Modelling and simulation of novel power generation cycles is vital in proposing technically and economically feasible solutions which are environmentally friendly. The development of a Virtual Plant Demonstration Model (VPDM) in the UK is addr...

We study a class of generalized inflation models in which the inflaton is coupled to the Ricci scalar by a general f(φ,R) term. The scalar power spectrum, the spectral index, the running of the spectral index, the tensor mode spectrum and a new consistency relation of the model are calculated. We discuss in detail the issues of how to diagonize the coupled perturbation equations, how to deal wi...

Conventional non-negative tensor factorization (NTF) methods assume there is only one tensor that needs to be decomposed to low-rank factors. However, in practice data are usually generated from different time periods or by different class labels, which are represented by a sequence of multiple tensors associated with different labels. This raises the problem that when one needs to analyze and ...