Primordial nucleosynthesis in higher dimensional cosmology

We investigate nucleosynthesis and element formation in the early universe in the framework of higher dimensional cosmology. For this purpose we utilize a previous solution of the present author, which may be termed as the generalized Friedmann-Robertson-Walker model. We find that temperature decays less rapidly in higher dimensional cosmology, which we believe may have nontrivial consequences \emph{vis-a-vis} primordial physics

Utility and productivity enhancing public capital in a growing economy

We examine the impact of fiscal policy on macroeconomic performance and welfare when public capital provides both productive and utility services to the private sector. When these services are subject to congestion, a consumption tax is distortionary, generating a dynamic adjustment that contrasts with that of an income tax. In correcting for congestion, an income tax-consumption sub-sidy combination is the preferred policy when factor-substitutability in production is limited. On the other hand, an increase in the elasticity of substitution in production raises the e¢ cacy of a consumption tax as an alternative to the income tax. Not recognizing the relative importance of public capital in utility services might lead the fiscal authority to incorrectly estimate the impact of public policies on welfare. The design of optimal scal policy demonstrates the possibilities for using both income and consumption-based fiscal instruments as opposed to relying on only the income tax rate

Nature of the glassy magnetic state in Cu2.84_{2.84}Mn0.44_{0.44}Al0.72_{0.72} shape memory alloy

The magnetic ground state of the ferromagnetic shape memory alloy of nominal composition Cu$_{2.84}$Mn$_{0.44}$Al$_{0.72}$ was investigated. The sample shows reentry of a glassy magnetic phase below the martensitic transition temperature, which is found to have complex character with two distinct anomalies in the temperature dependent ac susceptibility data. The sample retains its glassy phase even below the second transition as evident from the magnetic memory measurements in different protocols. Existence of two transitions along with their observed nature suggest that the system can be described by the mean field Heisenberg model of reentrant spin glass as proposed by Gabay and Toulous. \cite{rsg-GT1} The sample provides a fascinating example where a Gabay-Toulous type spin glass state is triggered by a first order magneto-structural transition

The large deviation principle for the Erd\H{o}s-R\'enyi random graph

What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and proof of the main result uses the recent development of the theory of graph limits by Lovasz and coauthors and Szemeredi's regularity lemma from graph theory. As a basic application of the general principle, we work out large deviations for the number of triangles in G(n,p). Surprisingly, even this simple example yields an interesting double phase transition.Comment: 24 pages. To appear in European J. Comb. (special issue on graph limits

Spherical collapse of a heat conducting fluid in higher dimensions without horizon

We consider a scenario where the interior spacetime,described by a heat conducting fluid sphere is matched to a Vaidya metric in higher dimensions.Interestingly we get a class of solutions, where following heat radiation the boundary surface collapses without the appearance of an event horizon at any stage and this happens with reasonable properties of matter field.The non-occurrence of a horizon is due to the fact that the rate of mass loss exactly counterbalanced by the fall of boundary radius.Evidently this poses a counter example to the so-called cosmic censorship hypothesis.Two explicit examples of this class of solutions are also given and it is observed that the rate of collapse is delayed with the introduction of extra dimensions.The work extends to higher dimensions our previous investigation in 4D.Comment: 6 page