Probing a Four Flavour vis-a-vis Three Flavour Neutrino Mixing for UHE Neutrino Signals at a 1 Km2{\rm Km}^2 Detector

We consider a four flavour scenario for the neutrinos where an extra sterile neutrino is introduced with the three families of active neutrinos and study the deviation from three flavour scenario in the ultra high energy (UHE) regime. We calculate the possible muon and shower yields at a 1 Km$^2$ detector such as ICECUBE for these neutrinos from distant UHE sources namely Gamma Ray Bursts (GRBs) etc. Similar estimations for muon and shower yields are also obtained for three flavour case. Comparing the two results we find considerable differences of the yields for these two cases. This can be useful for probing the existence of a fourth sterile component using UHE neutrino flux.Comment: 23 pages LaTeX, 5 eps figures, minor changes and corrected typo

Two component WIMP-FImP dark matter model with singlet fermion, scalar and pseudo scalar

We explore a two component dark matter model with a fermion and a scalar. In this scenario the Standard Model (SM) is extended by a fermion, a scalar and an additional pseudo scalar. The fermionic component is assumed to have a global ${\rm U(1)}_{\rm DM}$ and interacts with the pseudo scalar via Yukawa interaction while a $\mathbb{Z}_2$ symmetry is imposed on the other component -- the scalar. These ensure the stability of both the dark matter components. Although the Lagrangian of the present model is CP conserving, however the CP symmetry breaks spontaneously when the pseudo scalar acquires a vacuum expectation value (VEV). The scalar component of the dark matter in the present model also develops a VEV on spontaneous breaking of the $\mathbb{Z}_2$ symmetry. Thus the various interactions of the dark sector and the SM sector are progressed through the mixing of the SM like Higgs boson, the pseudo scalar Higgs like boson and the singlet scalar boson. We show that the observed gamma ray excess from the Galactic Centre, self-interaction of dark matter from colliding clusters as well as the 3.55 keV X-ray line from Perseus, Andromeda etc. can be simultaneously explained in the present two component dark matter model.Comment: 35 pages, 5 figure

Algebraic Independence over Positive Characteristic: New Criterion and Applications to Locally Low Algebraic Rank Circuits

The motivation for this work comes from two problems--test algebraic independence of arithmetic circuits over a field of small characteristic, and generalize the structural property of algebraic dependence used by (Kumar, Saraf CCC\u2716) to arbitrary fields. It is known that in the case of zero, or large characteristic, using a classical criterion based on the Jacobian, we get a randomized poly-time algorithm to test algebraic independence. Over small characteristic, the Jacobian criterion fails and there is no subexponential time algorithm known. This problem could well be conjectured to be in RP, but the current best algorithm puts it in NP^#P (Mittmann, Saxena, Scheiblechner Trans.AMS\u2714). Currently, even the case of two bivariate circuits over F_2 is open. We come up with a natural generalization of Jacobian criterion, that works over all characteristic. The new criterion is efficient if the underlying inseparable degree is promised to be a constant. This is a modest step towards the open question of fast independence testing, over finite fields, posed in (Dvir, Gabizon, Wigderson FOCS\u2707). In a set of linearly dependent polynomials, any polynomial can be written as a linear combination of the polynomials forming a basis. The analogous property for algebraic dependence is false, but a property approximately in that spirit is named as ``functional dependence\u27\u27 in (Kumar, Saraf CCC\u2716) and proved for zero or large characteristic. We show that functional dependence holds for arbitrary fields, thereby answering the open questions in (Kumar, Saraf CCC\u2716). Following them we use the functional dependence lemma to prove the first exponential lower bound for locally low algebraic rank circuits for arbitrary fields (a model that strongly generalizes homogeneous depth-4 circuits). We also recover their quasipoly-time hitting-set for such models, for fields of characteristic smaller than the ones known before. Our results show that approximate functional dependence is indeed a more fundamental concept than the Jacobian as it is field independent. We achieve the former by first picking a ``good\u27\u27 transcendence basis, then translating the circuits by new variables, and finally approximating them by truncating higher degree monomials. We give a tight analysis of the ``degree\u27\u27 of approximation needed in the criterion. To get the locally low algebraic rank circuit applications we follow the known shifted partial derivative based methods

Genetic variability studies for yield and its contributing traits in okra [Abelmoschus esculentus (L.) Moench]

The experiment comprising 30 okra (Abelmoschus esculentus) genotypes were grown and analysed for yield and its attributing traits at the Department of Vegetable science, Kumarganj, Faizabad during Zaid (2011) period. All the characters studied showed a wide range of variation. The variability for yield among the accessionsevaluated was also remarkable. The magnitude phenotypic coefficient of variation was higher than genotypic coefficient of variation for all traits. Both phenotypic coefficient of variation (PCV) and genotypic coefficient of variation (GCV) were high for plant height (11.10 and 10.60, respectively). Fruit weight exhibited low value of GCV (2.31) and PCV (4.74) and likely to show less response under selection. High heritability (91.3) with high genetic advance (26.74) was recorded for plant height, whereas, ridges per fruit had high heritability (97.0) with moderate genetic advance (18.45). This study aimed to evaluate okra genotypes for variability with a view to providing information on the development of high yielding genotypes to meet the growing food demand of the populace

Seasonal incidence of pod fly (Melanogromyza Obtusa Malloch) and pod bug (Clavigralla Gibbosa Spinola) in short duration pigeon pea

The present study was aimed at observing the incidence pattern of pod fly and pod bug in pigeonpea ecosystem. The experiment was conducted at Agricultural Research Farm, Banaras Hindu University, Varanasi during the kharif season of the year 2010-11.The short duration pigeon pea was infested with the number of insect pests at various stages of crop growth. Out of which the incidence pattern of pod fly M. obtusa and pod bug C. gibbosa was studied. The first appearance of pod fly M. obtusa was noticed in the 42 standard week with a mean population of 0.10 maggot/Plant whose maggot population peaked in 45 standard weeks with a mean population of 0.30 maggot/Plant during year 2010-11. Similarly the first occurrence of pod bug C. gibbosa was recorded in 40 standard weeks with a mean population of 0.03 larvae/Plant which attained the peak during 44 and 45 standard weeks, in both the week themean population was 0.40 larvae/Plant. The incidence of all the insect pests although declined after attainment of their respective peak, but pod bug were noticed in the field till the harvest of the crop. To undertake an effective IPM strategy in pigeonpea crop, location specific information on occurrence and seasonal dynamics of insect pests is indispensible