Mathematics

The effect of pyrophosphate on the distribution and the rates of exchange of calcium and phosphate in hydroxyapatite crystals was studied. Analysis of disappearance of45Ca,32P [Pi] and32P [PPi] from the solution onto the crystals was performed using a compartmental model. The disappearance curves were described by the sum of 4 exponentials, which was interpreted as a four-compartment model in series.

ABSTRACT A large number of information and communication technology (ICT) initiatives have been taken up at the national as well as state level for dissemination of knowledge and information to the rural population. ITC Ltd. initiated e-choupal in June 2000 to cater to agriculture-related needs of the farmers. One major factor that directly affects adoption of any ICT initiative and success is the attitude of the audience towards it. Thus, an effort has been made to study the attitude of the user farmers and non-user farmers towards this programme. The study has been carried out in the Tarai region of Uttarakhand. Purposive sampling was done to select the Udham Singh Nagar district and simple random sampling was done to select the centres from two hubs - Kashipur and Kichcha. In all, 220 farmers (110 users and 110 non-users) were selected for the study. The findings indicate that e-choupal has considerably provided some insights into the attitude of farmers towards the programme. The attitude of the users was better than that of the non-users towards e-choupal and its components, as majority of the users had moderately favourable attitude towards the ITC Ltd. sanchalak as well as services provided at the e-choupal, whereas comparatively less number of non-users felt so.

For Gorenstein quotient spaces $C^d/G$, a direct generalization of the classical McKay correspondence in dimensions $d\geq 4$ would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstein abelian quotient singularities, which are embeddable as complete intersections of hypersurfaces in an affine space, have torus-equivariant projective crepant resolutions in all dimensions. We use techniques from toric and discrete geometry.

Experiments have been performed to study the effect of selection at the Odh locus in Drosophila melanogaster populations using different alcohol concentrations in the medium. The data can be best interpreted by assuming frequency-dependent selection. When genotype frequencies are considered as independent variables and values of Wrightian fitness as dependent variables, it turns out that different functions describe the selection of the coexisting genotypes. A linear equation is used for the SF genotype and a hyperbolic function for the FF genotype. No function of good fit could be found for the SS genotype. Simulation experiments using these functions fit our data well.

Modelling joint motion in three dimensions is often based on techniques taken from classical dynamics, each analysis resulting in a set of six parameters describing the relative motion between two body segments. The literature on joint kinematics has been difficult to compare due to use of different anatomical landmarks, axis nomenclature, and analytical methods. It is here shown that with care in sequence definition, the three alignment-based systems (Euler, Cardan, floating axis) give identical results for angular parameters. While the equivalent screw displacement axis system can be related simply to the other methods only if the functional axis of motion is aligned with a coordinate axis, the basic matrix for relating rigid body positions before and after a motion can always be reconstructed. Therefore the changes in alignment angles may be obtained from screw displacement parameters, permitting the results of different analyses to be compared. Translation parameters are most di...