Primordial Non-Gaussianity in the Cosmic Microwave Background

In the last few decades, advances in observational cosmology have given us a standard model of cosmology. We know the content of the universe to within a few percent. With more ambitious experiments on the way, we hope to move beyond the knowledge of what the universe is made of, to why the universe is the way it is. In this review paper we focus on primordial non-Gaussianity as a probe of the physics of the dynamics of the universe at the very earliest moments. We discuss 1) theoretical predictions from inflationary models and their observational consequences in the cosmic microwave background (CMB) anisotropies; 2) CMB--based estimators for constraining primordial non-Gaussianity with an emphasis on bispectrum templates; 3) current constraints on non-Gaussianity and what we can hope to achieve in the near future; and 4) non-primordial sources of non-Gaussianities in the CMB such as bispectrum due to second order effects, three way cross-correlation between primary-lensing-secondary CMB, and possible instrumental effects.Comment: 27 pages, 8 figures; Invited Review for the Journal "Advances in Astronomy"; references adde

Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data

In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result

Orthogonal Ramanujan Sums, its properties and Applications in Multiresolution Analysis

Signal processing community has recently shown interest in Ramanujan sums which was defined by S.Ramanujan in 1918. In this paper we have proposed Orthog- onal Ramanujan Sums (ORS) based on Ramanujan sums. In this paper we present two novel application of ORS. Firstly a new representation of a finite length signal is given using ORS which is defined as Orthogonal Ramanujan Periodic Transform.Secondly ORS has been applied to multiresolution analysis and it is shown that Haar transform is a spe- cial case

Effect of pressure cycling on Iron: Signatures of an electronic instability and unconventional superconductivity

High pressure electrical resistivity and x-ray diffraction experiments have been performed on Fe single crystals. The crystallographic investigation provides direct evidence that in the martensitic $bcc \rightarrow hcp$ transition at 14 GPa the $\lbrace 110\rbrace_{bcc}$ become the $\lbrace 002\rbrace_{hcp}$ directions. During a pressure cycle, resistivity shows a broad hysteresis of 6.5 GPa, whereas superconductivity, observed between 13 and 31 GPa, remains unaffected. Upon increasing pressure an electronic instability, probably a quantum critical point, is observed at around 19 GPa and, close to this pressure, the superconducting $T_{c}$ and the isothermal resistivity ($0<T<300\,$K) attain maximum values. In the superconducting pressure domain, the exponent $n = 5/3$ of the temperature power law of resistivity and its prefactor, which mimics $T_{c}$, indicate that ferromagnetic fluctuations may provide the glue for the Cooper pairs, yielding unconventional superconductivity

CSPOB-Continuous Spectrophotometry of Black Holes

The goal of a small and dedicated satellite called the "Continuous Spectro-Photometry of Black Holes" or CSPOB is to provide the essential tool for the theoretical understanding of the hydrodynamic and magneto-hydrodynamic flows around black holes. In its life time of about three to four years, only a half a dozen black holes will be observed continuously with a pair of CSPOBs. Changes in the spectral and temporal variability properties of the high-energy emission would be caught as they happen. Several important questions are expected to be answered and many puzzles would be sorted out with this mission.Comment: 4 Pages, 3 Figures, Proceeding of the 2nd Kolkata Conference on "Observational Evidence for the Black Holes in the Universe", Published in AIP, 200

Triplication of Deciduous Teeth: A Rare Dental Anomaly

Fusion of teeth is the union of two or more tooth germs, which are usually separated. Depending upon the stage of odontogenesis, it can be complete or incomplete. The present case describes fusion between the maxillary  primary right central and lateral incisor with a supernumerary tooth. Clinical and radiographic examination revealed the presence of fused triple teeth. The fused teeth were extracted, sectioned and were visualized under  stereomicroscope at three levels and the diagnosis of fusion of three teeth was confirmed histologically.Keywords: Fusion, primary teeth, supernumerary tooth, triple teet