Supply Side Constrains in Production of Pulses in India: A Case Study of Lentil

In India, annual production of pulses ranges from 11 Mt to 15 Mt, with yield of about 600 kg/ha. Due to the wide gap between supply and demand, import of pulses has increased from 0.38 Mt in 1993 to 2.82 Mt in 2008. Lentil is an important rabi pulse crop with a production of 0.85-0.95 Mt in India, after gram. The study has used both secondary and primary data collected from on-farm demonstrations and farmers’ fields to examine the ways to enhance the domestic supply of lentil. The study has found that there is a scope of increasing area under lentil during the rabi season, as its cost per hectare is less with higher net returns than the competing crops like wheat, gram and mustard in water-deficit and resource-poor conditions. There are large returns for adoption of disease management (80 per cent increase in net return), and improved small-seeded varieties (about 40 per cent increase in net return) in lentil. The study has found that lentil-based cropping systems are profitable and also have high water productivity, hence are suitable for mostly un-exploited rice-fallows under water-deficit conditions. Even though marketed surplus ratios have increased in recent years, there is a post-harvest loss to the extent of 7 per cent of production which needs to be curtailed to increase overall supply for final consumption. There is a case for larger institutional and policy support for pulse crops, keeping visible effects of pulse crops in increasing yield of subsequent crops in crop rotations.Agricultural and Food Policy,

Non-singular circulant graphs and digraphs

We give necessary and sufficient conditions for a few classes of known circulant graphs and/or digraphs to be singular. The above graph classes are generalized to $(r,s,t)$-digraphs for non-negative integers $r,s$ and $t$, and the digraph $C_n^{i,j,k,l}$, with certain restrictions. We also obtain a necessary and sufficient condition for the digraphs $C_n^{i,j,k,l}$ to be singular. Some necessary conditions are given under which the $(r,s,t)$-digraphs are singular.Comment: 12 page

Radio and Far-Infrared Emission as Tracers of Star Formation and AGN in Nearby Cluster Galaxies

We have studied the radio and far-infrared (FIR) emission from 114 galaxies in the 7 nearest clusters (<100 Mpc) with prominent X-ray emission to investigate the impact of the cluster environment on the star formation and AGN activity in the member galaxies. The X-ray selection criterion is adopted to focus on the most massive and dynamically relaxed clusters. A large majority of cluster galaxies show an excess in radio emission over that predicted from the radio-FIR correlation, the fraction of sources with radio excess increases toward cluster cores, and the radial gradient in the FIR/radio flux ratio is a result of radio enhancement. Of the radio-excess sources, 70% are early-type galaxies and the same fraction host an AGN. The galaxy density drops by a factor of 10 from the composite cluster center out to 1.5 Mpc, yet galaxies show no change in FIR properties over this region, and show no indication of mass segregation. We have examined in detail the physical mechanisms that might impact the FIR and radio emission of cluster galaxies. While collisional heating of dust may be important for galaxies in cluster centers, it appears to have a negligible effect on the observed FIR emission for our sample galaxies. The correlations between radio and FIR luminosity and radius could be explained by magnetic compression from thermal ICM pressure. We also find that simple delayed harassment cannot fully account for the observed radio, FIR, and mid-IR properties of cluster galaxies.Comment: 21 pages, 15 figures, Accepted by Ap

Representation of Cyclotomic Fields and Their Subfields

Let \K be a finite extension of a characteristic zero field \F. We say that the pair of $n\times n$ matrices $(A,B)$ over \F represents \K if \K \cong \F[A]/ where \F[A] denotes the smallest subalgebra of M_n(\F) containing $A$ and $$ is an ideal in \F[A] generated by $B$. In particular, $A$ is said to represent the field \K if there exists an irreducible polynomial q(x)\in \F[x] which divides the minimal polynomial of $A$ and \K \cong \F[A]/. In this paper, we identify the smallest circulant-matrix representation for any subfield of a cyclotomic field. Furthermore, if $p$ is any prime and \K is a subfield of the $p$-th cyclotomic field, then we obtain a zero-one circulant matrix $A$ of size $p\times p$ such that (A,\J) represents \K, where \J is the matrix with all entries 1. In case, the integer $n$ has at most two distinct prime factors, we find the smallest 0-1 companion-matrix that represents the $n$-th cyclotomic field. We also find bounds on the size of such companion matrices when $n$ has more than two prime factors.Comment: 17 page