The fragmented Lok Sabha: a case for electoral engineering

Where there are numerous small political parties, as in India, the electoral system neither reflects the true views and opinions on important social and economic issues nor does it incorporate “social inclusiveness” . The fragmentation in our legislature can be corrected through appropriate electoral engineering. This study is an attempt to do so. It describes how the composition of the Lok Sabha has changed since 1967, paying particular attention to the trends in indices of fragmentation. It also discusses issues relating to the “ideal” composition of a legislature and of a government

An iterative procedure for general probability measures to obtain I-projections onto intersections of convex sets

The iterative proportional fitting procedure (IPFP) was introduced formally by Deming and Stephan in 1940. For bivariate densities, this procedure has been investigated by Kullback and R\"{u}schendorf. It is well known that the IPFP is a sequence of successive I-projections onto sets of probability measures with fixed marginals. However, when finding the I-projection onto the intersection of arbitrary closed, convex sets (e.g., marginal stochastic orders), a sequence of successive I-projections onto these sets may not lead to the actual solution. Addressing this situation, we present a new iterative I-projection algorithm. Under reasonable assumptions and using tools from Fenchel duality, convergence of this algorithm to the true solution is shown. The cases of infinite dimensional IPFP and marginal stochastic orders are worked out in this context.Comment: Published at http://dx.doi.org/10.1214/009053606000000056 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Non-extensive Statistics and Understanding Particle Production and Kinetic Freeze-out Process from pTp_T-spectra at 2.76 TeV

An approach, based on Tsallis non-extensive statistics, has been employed, here, to analyse, systematically, the $p_T$-spectra of various identified secondary hadrons like pions, kaons, protons and antiprotons, produced in different central $Pb+Pb$ interactions at LHC energy 2.76 TeV in terms of multiplicity and temperature fluctuations. The results, thus obtained, have been utilized to understand the various stages of different types of hadron production during evolution of the fireball produced in such collisions.Comment: 14 pages, 17 figures, 5 tables. arXiv admin note: substantial text overlap with arXiv:1408.581

Export promotion, exchange rates and commodity prices

The collapse of primary commodity prices in the 1980s has been prolonged and has severely affected many developing countries. While low commodity prices can be partly explained by sluggish demand due to slow growth in the industrialised countries, high interest rates and technological change, this does not seem a complete explanation. This paper examines the evidence in favour of the hypothesis that supply factors have partly been responsible. Many developing countries have faced severe balance of payments difficulties, in part due to the debt crisis, and have resorted to real exchange rate devaluations in order to boost export earnings. Such devaluations may have boosted export supplies, or prevented downward adjustments in capacity, and therefore put pressure on commodity prices. It also considers the policy implications of this externality, whereby attempts to boost export earnings in one primary producing country adversely affect the prices received by others

Primordial Gas Collapse in The Presence of Radiation: Direct Collapse Black Hole or Population III star?

The first billion years in the evolution of the Universe mark the formation of the first stars, black holes and galaxies. The radiation from the first galaxies plays an important role in determining the final state of primordial gas collapsing in a neighboring halo. This is due to the fact that the primary coolant for primordial gas is molecular hydrogen, which can be dissociated into atomic hydrogen by Lyman-Werner photons in the energy range $11.2 - 13.6$~eV. While cooling by molecular hydrogen leads to Pop. III star formation, cooling by atomic hydrogen can lead to the formation of a supermassive star (or quasi-star) which results in the formation of a massive $10^{4-5} M_\odot$ black hole, or a direct collapse black hole. The spectrum of this radiation field is critical in order to determine whether a primordial gas cloud forms a Pop. III star or a very massive black hole. We will in the following explore this scenario and discuss how the radiation spectrum influences the outcome of the collapse.Comment: Preprint~of~a~review volume chapter to be published in Latif, M., \& Schleicher, D.R.G., "Primordial Gas Collapse in The Presence of Radiation: Direct Collapse Black Hole or Population III star?", Formation of the First Black Holes, 2018 \textcopyright Copyright World Scientific Publishing Company, https://www.worldscientific.com/worldscibooks/10.1142/1065

On Nyman, Beurling and Baez-Duarte's Hilbert space reformulation of the Riemann hypothesis

There has been a surge of interest of late in an old result of Nyman and Beurling giving a Hilbert space formulation of the Riemann hypothesis. Many authors have contributed to this circle of ideas, culminating in a beautiful refinement due to Baez-Duarte. The purpose of this little survey is to dis-entangle the resulting web of complications, and reveal the essential simplicity of the main results.Comment: 10 page