Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde

Enhancement of magnetoresistance in manganite multilayers

Magnanite multilayers have been fabricated using La0.67Ca0.33MnO3 as the ferromagnetic layer and Pr0.7Ca0.3MnO3 and Nd0.5Ca0.5MnO3 as the spacer layers. All the multilayers were grown on LaAlO3 (100) by pulse laser deposition. An enhanced magnetoresistnace (defined (RH- R0)/R0) of more than 98% is observed in these multilayers. Also a low field magnetoresistance of 41% at 5000 Oe is observed in these multilayer films. The enhanced MR is attributed to the induced double exchange in the spacer layer, which is giving rise to more number of conducting carriers. This is compared by replacing the spacer layer with LaMnO3 where Mn exists only in 3+ state and no enhancement is observed in the La0.67Ca0.33MnO3 / LaMnO3 multilayers as double exchange mechanism can not be induced by external magnetic fields.Comment: 13 pages, 5 Figure

Chemical Oscillations in Mn2+-catalysed Belousov-Zhabotinskii Reaction in Orthophosphoric Acid Medium

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The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field

Let k be a global field and let k_v be the completion of k with respect to v, a non-archimedean place of k. Let \mathbf{G} be a connected, simply-connected algebraic group over k, which is absolutely almost simple of k_v-rank 1. Let G=\mathbf{G}(k_v). Let \Gamma be an arithmetic lattice in G and let C=C(\Gamma) be its congruence kernel. Lubotzky has shown that C is infinite, confirming an earlier conjecture of Serre. Here we provide complete solution of the congruence subgroup problem for \Gamm$ by determining the structure of C. It is shown that C is a free profinite product, one of whose factors is \hat{F}_{\omega}, the free profinite group on countably many generators. The most surprising conclusion from our results is that the structure of C depends only on the characteristic of k. The structure of C is already known for a number of special cases. Perhaps the most important of these is the (non-uniform) example \Gamma=SL_2(\mathcal{O}(S)), where \mathcal{O}(S) is the ring of S-integers in k, with S=\{v\}, which plays a central role in the theory of Drinfeld modules. The proof makes use of a decomposition theorem of Lubotzky, arising from the action of \Gamma on the Bruhat-Tits tree associated with G.Comment: 27 pages, 5 figures, to appear in J. Reine Angew. Mat

Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold

We investigate an operator ordering problem in two-dimensional N=1 supersymmetric model which consists of n real superfields. There arises an operator ordering problem when the target space is curved. We have to fix the ordering in quantum operator properly to obtain the correct supersymmetry algebra. We demonstrate that the super-Poincar\'{e} algebra fixes the correct operator ordering. We obtain a supercurrent with correct operator ordering and a central extension of supersymmetry algebra.Comment: 7 page

Behaviour of Magnetic Tubes in Neutron Star's Interior

It is found from Maxwell's equations that the magnetic field lines are good analogues of relativistic strings. It is shown that the super-conducting current in the neutron star's interior causes local rotation of magnetic flux tubes carrying quantized flux.Comment: 6 pages, no figure

Preparation of transversely isotropic test specimen of natural FRP composite - an innovative approach-II

Fiber Reinforced Plastic (FRP) composites can be broadly classified as synthetic and natural, based on the type of fibers incorporated. Abundantly available natural fibers like toddy palm, sisal, jute and banana are attracting the attention of researchers due to ever increasing demand for lighter, stronger and eco-friendly materials from the industry. However, natural fibers are limited in length, not so uniform in size and behave differently in different atmospheric conditions. Added to this, the inherent tendency of natural fibers to twist and curl in dry conditions poses many problems to researchers while preparing test specimens. Researchers in general and academicians in particular are handicapped by non-availability of relevant literature on fabrication techniques to prepare natural FRP composite test specimens close to their analytical models. Present paper addresses typical problems faced by researchers during preparation of unidirectional continuous fiber reinforced composite test specimen ensuring transversely isotropic nature. Using simple hand tools coupled with a few precautions taken as described herein, prospective researchers can condition natural fibers and prepare composite specimen to suit their requirements.&nbsp