Rank 2 local systems and abelian varieties II

LetX/Fq be a smooth, geometrically connected, quasi projective scheme. Let Ebe a semisimple over convergent F-isocrystal on X. Suppose that irreducible summands Ei of E have rank 2, determinant ̄Qp (−1), and infinite monodromy at∞. Suppose further that for each closed point x of X, the characteristic polynomial of E at x is in Q[t]⊂Qp[t]. Then there exists a non-trivial open set U⊂X such that E|U comes from a family of abelian varieties on U. As an application, let L1 be an irreducible lisse ̄Ql sheaf on X that has rank 2, determinant ̄Ql(−1), and infinite monodromy at∞. Then all crystalline companions to L1 exist (as predicted by Deligne’s crystalline companions conjecture) if and only if there exists a non-trivial open set U⊂X and an abelian scheme πU: AU→U such that L1|U is a summand of R1(πU)∗ ̄Ql

Variation in the Biomolecular Interactions of Nickel(Ii) Hydrazone Complexes Upon Tuning the Hydrazide Fragment

Three new bivalent nickel hydrazone complexes have been synthesised from the reactions of [NiCl2(PPh3)(2)] with H2L {L = dianion of the hydrazones derived from the condensation of o-hydroxynaphthaldehyde with furoic acid hydrazide (H2L1) (1)/thiophene-2-acid hydrazide (H2L2) (2)/isonicotinic acid hydrazide (H2L3) (3)} and formulated as [Ni(L-1)(PPh3)] (4), [Ni(L-2)(PPh3)] (5) and [Ni(L-3)(PPh3)] (6). Structural characterization of these compounds 4-6 were accomplished by using various physico-chemical techniques. Single crystal X-ray diffraction data of complexes 4 and 5 proved their distorted square planar geometry. In order to ascertain the potential of the above synthesised compounds towards biomolecular interactions, additional experiments involving interaction with calf thymus DNA (CT DNA) and bovine serum albumin (BSA) were carried out. All the ligands and corresponding nickel(II) chelates have been screened for their scavenging effect towards O-2(-), OH and NO radicals. The efficiency of complexes 4-6 to arrest the growth of HeLa, HepG-2 and A431 tumour cell lines has been studied along with the cell viability test against the non-cancerous NIH 3T3 cells under in vitro conditions.University Grants Commission, New Delhi under the UGC-SAP-DRSRobert A. Welch Foundation F-0003Chemistr

A collage of results on the divisibility and indivisibility of class numbers of quadratic fields

The investigation of the ideal class group $Cl_K$ of an algebraic number field $K$ is one of the key subjects of inquiry in algebraic number theory since it encodes a lot of arithmetic information about K. There is a considerable amount of research on many topics linked to quadratic field class groups notably intriguing aspect is the divisibility of the class numbers. This article discusses a few recent results on the divisibility of class numbers and the Izuka conjecture. We also discuss the quantitative aspect of the Izuka conjecture.Comment: Comments are welcome.11 page

Blood Donor Adverse Reactions.

Blood Donors are the backbone of a Blood Transfusion service. Ensuring the safety of Blood Donors is of utmost importance as is ensuring safe blood to the recipient. Since blood donors are altruistic volunteers, they should be protected as much as possible from adverse reactions. The reality that many first time donors do not return for donation can be explained by the occurrence of adverse reactions. Blood donor’s physical experience affects the blood donor return rate . Efforts should be taken to retain adequate number of repeat donors. If the donors are ensured of a pleasant experience they will be motivated to become regular repeat donors. This can be accomplished by way of preventing adverse reactions in the donor. Preventive strategies to avoid adverse reactions in blood donors should include: a) proper elicitation of donor history like time since last meal, nature of their occupation & whether they had a good sleep on the day prior to donation b) proper screening procedures like ensuring adequate hydration of donors c) reassuring first time donors d) providing a comfortable couch at camp sites & proper phlebotomy techniques by an experienced phlebotomist e) ensuring adequate ventilation and a comfortable environment (preferably 24*C ) f) observing the donor for atleast 10 min post donation while he still remains on the donor couch and then sending him for refreshments and g) giving post donation instructions and h)donors experiencing adverse reactions should be moved to a separate area so that other donors do not get demotivated. At no point of time should a Donor be left unattended