Discrete systems related to some equations of the Painlev\'e-Gambier classification

We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six transcendental Painlev\'e equations were obtained. In the case of the Gambier equation we give the contiguity relations for both the continuous and the discrete system.Comment: 10 page

Natural Suppression of the Aquatic Weed Salvinia molesta D.S. Mitchell, by Two Previously Unreported Fungal Pathogens

Salvinia molesta D. S. Mitchell (Salviniaceae), variously called giant salvinia, water fern or African payal, is a vegetatively reproducing, perennial, free-floating, aquatic weed, native to southeastern Brazil (Waterhouse and Norris 1987). It (hereafter called salvinia) is a very serious weed in most regions outside its native range (Harley and Mitchell 1981) including India. The purpose of this paper is to report on two fungal pathogens that were found to be the cause of a sudden decline in salvinia in Bangalore.(PDF has 4 pages.

Notched and Unnotched Fatigue Behavior of Angle-Ply Graphite/Epoxy Composites

The axial fatigue behavior of both notched and unnotched graphite/epoxy composites was studied. In unnotched studies, conducted on a 0/+ or - 30 3S AS/3501 laminate, S-N curves were determined for various stress ratios R using simply supported test specimens. Apparent fatigue limits in tension-tension (T-T) and compression-compression (C-C) cycling occurred at about 60% of the respective static strengths. The overall results were expressed in the form of a constant life diagram showing the relationship between mean stress and stress amplitude. The diagram illustrates a skew-symmetry in fatigue life caused by the relatively low compressive strength of the unrestrained test specimens used. In effect, a maximum in fatigue properties occurs at a positive value of mean stress. Results are of significance in situations where structural members are buckling or crippling critical in design

Comparative Analysis of Performance Efficiency of Fertilizer Industry in India

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Integrable systems without the Painlev\'e property

We examine whether the Painlev\'e property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlev\'e continuous linearisable systems. We find that while these discrete systems are themselves linearisable, they possess nonconfined singularities

Constructing Integrable Third Order Systems:The Gambier Approach

We present a systematic construction of integrable third order systems based on the coupling of an integrable second order equation and a Riccati equation. This approach is the extension of the Gambier method that led to the equation that bears his name. Our study is carried through for both continuous and discrete systems. In both cases the investigation is based on the study of the singularities of the system (the Painlev\'e method for ODE's and the singularity confinement method for mappings).Comment: 14 pages, TEX FIL

Singularity confinement and algebraic integrability

Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with the local analysis of singularities. In this paper, the relationship between these two notions is explored for birational autonomous mappings. Two types of results are obtained: first, algebraically integrable mappings are shown to have the singularity confinement property. Second, a proof of the non-existence of algebraic conserved quantities of discrete systems based on the lack of confinement property is given.Comment: 18 pages, no figur

Effect of ethanolic extract of Centella asiatica on maximal electroshock seizure in albino mice

Background: Animal models had always served as integral part in introducing newer drugs for epilepsy. India has long tradition of using herbal medicines. Centella asiatica is an ingredient of various ayurvedic preparations to treat brain related disorders like insanity, memory loss and epilepsy. This research is done to find out the usefulness of Centella asiatica in epilepsy.  Methods: Ethanolic extract of the plant is prepared using Soxhlet apparatus. Experimental seizure is induced in albino mice by maximal electroshock method. Resulting seizure goes through different phases. Duration of the phase of hind limb extension was the measured data. Clinically used anti epileptic drugs can abolish hind limb extension. Effect is compared to that of standard drug phenytoin. Four different doses of the plant extract; 100mg, 200mg, 500mg and 1000mg per kilogram bodyweight was given orally. Statistical analysis of data was done by one way ANOVA and Dunnett test.Results: Ethanolic extract of Centella asiatica exhibited statistically significant protection from maximal electroshock seizures. All given doses of the extract had p<0.05 when compared to control.Conclusions: Centella asiatica is potential source of anti-epileptic drug. Detailed phytochemical studies and animal experiments are recommended