Exponentially Localized Solutions of Mel'nikov Equation

The Mel'nikov equation is a (2+1) dimensional nonlinear evolution equation admitting boomeron type solutions. In this paper, after showing that it satisfies the Painlev\'{e} property, we obtain exponentially localized dromion type solutions from the bilinearized version which have not been reported so far. We also obtain more general dromion type solutions with spatially varying amplitude as well as induced multi-dromion solutions.Comment: 12 pages, 2 figures, to appear in Chaos, Solitons and Fractal

A REVIEW: LOVASTATIN PRODUCTION AND APPLICATIONS

Cholesterol is an organic compound, which is produced in humans by a complex metabolism. It acts as a precursor for the synthesis of many steroids, vitamin D and also helps in membrane transport. Increase of cholesterol in humans, leads to Cardio Vascular Disorders and finally death. This can be reduced by inhibiting the HMG-CoA reductase, which is an important precursor in formation of mevolanate from Acetyl CoA. Inhibition is done by statin drug, which is produced by many fungi through polyketide pathway. Many fungus produce lovastatin, while other statins like rosuvastatin, simvastatin, pravastatin, fluvastatin are synthesized from lovastatin and mevastatin. Other than reduction of cholesterol, lovastatin is shown to provide various medicinal properties like anti-cancer, bone maturation, multiple sclerosis. In this review, a detailed note on various organisms employed for the production of lovastatin and different fermentation techniques for the same was studied. This review also helps in understating the inhibition of HMG-CoA reducatse and various medicinal properties of lovastatin. Keywords: Lovastatin, Fungus, Submerged fermentation, Solid state fermentation, HMG-CoA reducatse

Long term performance of certain ortets and hybrid clones of Hevea brasiliensis in a high altitude region in Kerala, India

Long term performance of four hybrid Hevea clones and ten ortet selections including nine from a high elevation site within the traditional rubber growing tract of Kerala was studied. Significant variability was observed among the hybrids and ortets for all major agronomic traits. Growth of rubber trees was invariably poor in the high altitude region and tappability by the tenth year of planting was less than 50 per cent. The hybrid clones RRII 203 and RRIC 100 showed highest growth vigour with 80 per cent tappability by the 13th year of planting. Among the ortets, P 270 and Iritty 1 recorded the highest tappability of 64 per cent. The ortet P 270 was the best performer with the highest girth at the opening (61 cm), girth increment during immaturity (5.5 cm) on tapping (3.4 cm) and bole volume (0.1 m3). RRII 203 was the highest yielding clone with 56 g tree-1 tap-1 over eight years of tapping. High annual yield (48 g tree-1 tap-1) and lean season yield of P 270 combined with high drc on par with the highest yielding clone RRII 203 indicated the specific adaptability of this ortet to high elevation areas. The ortets P 213 and Iritty 1 and hybrid clone RRIC 100 were the other promising clones exhibiting growth adaptation and high yield potential under high altitude conditions

A (2+1) dimensional integrable spin model: Geometrical and gauge equivalent counterpart, solitons and localized coherent structures

A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schr\"odinger equation introduced by Zakharov and studied recently by Strachan. Using a Hirota bilinearised form, line and curved soliton solutions are obtained. Using certain freedom (arbitrariness) in the solutions of the bilinearised equation, exponentially localized dromion-like solutions for the potential is found. Also, breaking soliton solutions (for the spin variables) of the shock wave type and algebraically localized nature are constructed.Comment: 14 pages, LaTex, no figures; email of first author: [email protected] and [email protected]

Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlev\'e property. We then solve the LSRI equation using Painlev\'e truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.Comment: 13 pages, 6 figure

Growth and yield performance of some exotic clones of Hevea brasiliensis in North Kerala region

The growth and yield performance of a set of exotic clones from Malaysia and Ivory Coast was evaluated in comparison with RRII 105, a popular high yielding indigenous clone, for their adaptability in the northern tract of Kerala. The region is characterised by absence of sufficient summer showers and relatively long dry spells. Analysis of growth up to 16 years after planting revealed significant clonal differences in growth pattern, only from the 10th year of planting. Girth and girth increment was the highest in IRCA 130, followed by PB 330. The lowest girth was observed in RRIM 703. The clone IRCA 130 also exhibited significantly high annual and summer yield followed by PB 255. Peak rubber yield was recorded in the month of September irrespective of clones. IRCA 130 showed significantly superior branching height and bole volume followed by PB 255. Incidence of tapping panel dryness (TPD) and pink disease in IRCA 130 was comparable to clone RRII 105. The suitability of the newly introduced clones for the region is discussed

Localized coherent structures of (2+1) dimensional generalizations of soliton systems

We briefly review the recent progress in obtaining (2+1) dimensional integrable generalizations of soliton equations in (1+1) dimensions. Then, we develop an algorithmic procedure to obtain interesting classes of solutions to these systems. In particular using a Painleve singularity structure analysis approach, we investigate their integrability properties and obtain their appropriate Hirota bilinearized forms. We identify line solitons and from which we introduce the concept of ghost solitons, which are patently boundary effects characteristic of these (2+1) dimensional integrable systems. Generalizing these solutions, we obtain exponentially localized solutions, namely the dromions which are driven by the boundaries. We also point out the interesting possibility that while the physical field itself may not be localized, either the potential or composite fields may get localized. Finally, the possibility of generating an even wider class of localized solutions is hinted by using curved solitons

High density planting in rubber plantations: Effect on growth and yield

Planting density is an important parameter influencing the growth and yield of trees. A field study was conducted at Central Experiment Station of Rubber Research Institute of India, Chethackal, Kerala with clone RRII 105 in split plot design with five densities as main plot treatments and two fertilizer quantities as sub plot treatment replicated four times to study the effect of density of planting on growth and yield of rubber. The five densities tested are 420 trees ha-1 (4.9 m x 4.9 m), 479 trees ha-1 (4.6 m x 4.6 m), 549 trees ha-1 (4.3 m x4.3 m), 638 trees ha-1 (4 m x 4 m) and 749 trees ha-1 (3.7 m x 3.7 m) and the two subplot treatments are recommended dose of fertilizer (RDF) on unit area basis and RDF on per plant basis. Growth of the plants was not significantly influenced by the different planting densities up to eighth year after planting, but in the later years increased planting density decreased the girth and trees in the lowest density of 420 trees ha-1 recorded significantly higher girth. The lowest density also recorded significantly higher per tree yield. However, the annual yield per hectare was the highest (2553 kg) in the highest density of 749 trees ha-1 which was comparable (2457 kg) with that of the density of 549 trees ha-1. Bole height increased with planting density. But the bole volume, 18 years after planting was not significantly influenced by the planting density. Bark thickness was the highest (9.76 mm) in the lowest density and it was comparable (9.40) with that of the density 549 trees ha-1. Effect of fertilizer application on per plant basis and area basis was not significant throughout the study period. Based on 7 years yield data highest BCR of 3.16 and IRR of 29.11 per cent were obtained for the density of 549 trees ha-1

Collision of Multimode Dromions and a Firewall in the Two Component Long Wave Short Wave Resonance Interaction Equation

In this paper, we investigate the two component long wave short wave resonance interaction (2CLSRI) equation and show that it admits the Painleve property. We then suitably exploit the recently developed truncated Painleve approach to generate exponentially localized solutions for the short wave components $S^{(1)}$ and $S^{(2)}$ while the long wave L admits line soliton only. The exponentially localized solutions driving the short waves $S^{(1)}$ and $S^{(2)}$ in the y direction are endowed with different energies (intensities) and are called "multimode dromions". We also observe that the multimode dromions suffer intramodal inelastic collision while the existence of a firewall across the modes prevents the switching of energy between the modes.Comment: published in J. Phys. A: Math. Theor. 42, 10200