ન્યાયમજરીમાં રજૂ થયેલ પ્રત્યક્ષ પ્રમાણનું તુલનાત્મક અને સમીક્ષાત્મક અધ્યયન

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Zariski Closures and Subgroup Separability

The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a free or surface group.Comment: Final version. To appear in Selecta Mat

Effect of growth regulators and stages of spray on seed yield and seed quality parameters of ridge gourd [Luffa acutangula (Roxb) L.]

The experiment was undertaken to study the influence of different growth regulators on seed yield and seed quality parameters in ridge gourd [Luffa acutangula (Roxb) L.]. There were 30 treatment combinations comprising of two factors; plant growth stage as main plot treatment, and plant growth regulators as sub plot treatment embedded in a split plot design. The results indicated that significantly the highest average fruit weight (32.76 g), matured fruit yield per plant (65.84 g), 100 seed weight (13.41 g) and seed yield per plant (12.79 g) was recorded with spraying of 500 ppm ethereal, whereas significantly the maximum fruit length (20.89 cm) and fruit diameter (5.15 cm) with 25 ppm GA3. Significantly the highest seed germination (69.22 %) was recorded with spraying of 250 ppm ethereal, while application of NAA at 50 ppm recorded significantly the highest vigour index I (2737.85) and vigour index II (5029.33). Spraying of PGR at two to four leaf stage recorded the higher fruit length (20.19 cm), fruit yield per plant (47.49 g), 100 seed weight (13.18 g) and seed yield per plant (11.98 g) as well as highest germination (60.90%), vigour index I (2460.80) and vigour index II (4377.66). It is concluded that spraying of 500 ppm etherel at two to four leaf stage increased the higher fruit length, fruit yield per plant, 100 seed weight and seed yield per plant as well as highest germination, vigour index I and vigour index II

Charged analogue of Finch-Skea stars

We present solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes with a specified form of the electric field intensity. The condition of pressure isotropy yields three category of solutions. The first category is expressible in terms of elementary functions and does not have an uncharged limit. The second category is given in terms of Bessel functions of half-integer order. These charged solutions satisfy a barotropic equation of state and contain Finch-Skea uncharged stars. The third category is obtained in terms of modified Bessel functions of half-integer order and does not have an uncharged limit. The physical features of the charged analogue of the Finch-Skea stars are studied in detail. In particular the condition of causality is satisfied and the speed of sound does not exceed the speed of light. The physical analysis indicates that this analogue is a realistic model for static charged relativistic perfect fluid spheres.Comment: 17 pages, To appear in Int. J. Mod. Phys.

Medical negligence and res ipsa loquitur in South Africa

The inter-relationship between Medicine and Law is most commonly brought to the fore by cases involving medical negligence. This relationship needs to protect all parties concerned based on the probability of reasonableness in terms of who performs the act as well as the patient affected by the act in question. The res ipsa loquitur (the case speaks for itself) doctrine is currently not being used in the South African courts. This paper discusses what is considered medical negligence and the use of the res ipsa loquitur doctrine. A short overview of the international perspective is given, followed by a discussion on how negligence matters are dealt with by the South African courts. South African Journal of Bioethics & Law Vol. 1 (2) 2008: pp. 57-6