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

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

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.

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

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

Effect of Raoiella Indica Hirst (Acari: Tenuipalpidae) Infestation on Chlorophyll and Photosynthetic Efficiency of Areca Catechue

Areca catechu L. is one of the most important plantation crop cultivated in Kerala. Recent reports indicate that phytophagous mites could infest the foliage and nuts of areca palm and induce substantial damage, leading to various levels of economic loss. Among the mites, Raoiella indica Hirst, popularly called Red Palm Mite (RPM) has been recognized as a serious pest of areca palm in various localities of India. Various life stages of this mite were found colonizing and feeding on the lower surface of palm leaves, by de-sapping and which in turn would lead to the formation of yellowish speckles and bronzing in later stages and the ultimate drying up of the leaves. Photosynthesis, being a vital process determining the plant vigour and productivity should be addressed with great concern. In the present study, attention has been focused to analyse the feeding impact of the red palm mite, on the photosynthetic machinery of areca palms through the quantitative estimation of chlorophyll ‘a\u27, ‘b\u27, ‘total chlorophyll\u27 pigments and also ‘photosynthetic efficiency\u27 of mite infested and uninfested leaves. Results of the study revealed that the feeding activity of the mite on the leaves of A.catechu induced drastic reduction in the levels of chlorophyll ‘a\u27, ‘b\u27, ‘total chlorophyll\u27 and ‘photosynthetic efficiency\u27. The percentage loss in chl ‘a\u27, chl ‘b\u27 and ‘total chlorophyll\u27 were 62.21±0.63, 57.67±0.73 and 59.884±0.375 respectively in RPM infested Areca leaves. RPM infestation varied significantly in photosynthetic parameters such as minimum fluorescence (F0), maximum fluorescence ( Fm), variable fluorescence (Fv), quantum yield of photosynthesis (Fv/Fm), performance index (PI) and the Area which has a negatively impact on photosynthetic efficiency of areca palms. These data obtained from chlorophyll analysis and photosynthetic efficiency were found significant at 0.05level, up on statistical analysis using t-test, thereby establishing the pest status of RPM on A. catcheu

Recent exploitation trend of oil sardine along Tamil nadu - Pondicherry coast

The Indian oil sardine SardineUa lorgiceps.though a non-conventional resource of the east coast, supports now a regular fishery of high magnitude especially along Andhra Pradesh and TanJl Nadu - Pondicheny coasts. The estimated annual average landing from east coast during the period 1993-97 was 60.638 tonnes against 46.000 t obtained along west coast thereby showing the potential of this new resource, especially along the southern maritime states of the east coast. It has been observed that the oil sardine catch during 1993-97 increased to more than three fold in Andhra Pradesh from that of the previous five year period 1988-92 while along Tamil Nadu - Pondicheny coast the catch almost doubled and recorded 80% of the total oil sardine production of east coast

Bilinear Discrete Painleve-II and its Particular Solutions

By analogy to the continuous Painlev\'e II equation, we present particular solutions of the discrete Painlev\'e II (d-P$\rm_{II}$) equation. These solutions are of rational and special function (Airy) type. Our analysis is based on the bilinear formalism that allows us to obtain the $\tau$ function for d-P$\rm_{II}$. Two different forms of bilinear d-P$\rm_{II}$ are obtained and we show that they can be related by a simple gauge transformation.Comment: 9 pages in plain Te

Riemann zeros, prime numbers and fractal potentials

Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one-dimension. We also investigate the fractal properties of the reconstructed potentials and estimate the fractal dimensions to be $D=1.5$ for the Riemann zeros and $D = 1.8$ for the prime numbers. This result is somewhat surprising since the nearest-neighbour spacings of the Riemann zeros are known to be chaotically distributed whereas the primes obey almost poisson-like statistics. Our findings show that the fractal dimension is dependent on both the level-statistics and spectral rigidity, $\Delta_3$, of the energy levels.Comment: Five postscript figures included in the text. To appear in Phys. Rev.