On Hamilton decompositions of infinite circulant graphs

The natural infinite analogue of a (finite) Hamilton cycle is a two-way-infinite Hamilton path (connected spanning 2-valent subgraph). Although it is known that every connected 2k-valent infinite circulant graph has a two-way-infinite Hamilton path, there exist many such graphs that do not have a decomposition into k edge-disjoint two-way-infinite Hamilton paths. This contrasts with the finite case where it is conjectured that every 2k-valent connected circulant graph has a decomposition into k edge-disjoint Hamilton cycles. We settle the problem of decomposing 2k-valent infinite circulant graphs into k edge-disjoint two-way-infinite Hamilton paths for k=2, in many cases when k=3, and in many other cases including where the connection set is ±{1,2,...,k} or ±{1,2,...,k - 1, 1,2,...,k + 1}

Performance of Indian Indigo (Indigofera tinctoria L.) accessions as intercrop in coconut garden

Thirty accessions of Indian indigo (Indigofera tinctoria L.), collected from inside and outside Kerala, were grown in a coconut plantation so as to identify the superior accessions with respect to leaf yield and indigo dye content. Observations were taken at various growth stages namely pre-flowering (90 DAS), flowering (150 DAS) and seed maturation stages (240 DAS). The best ten accessions that recorded maximum leaf yield and glycoside content, obtained from phase I experiment were selected for the phase II experiment. Considerable variations were not noticed in plant height increment in different accessions during both the phases. The accessions differed significantly with respect to plant spread in both the phases. Among the accessions, those that revealed a trend to dominate in plant spread increment during both the phases were IT-105, IT-108 and IT-114. Accession IT-109 dominated in the increment of number of leaves during phase I experiment. Accessions IT-96, IT-99, IT-101, IT-106 and IT-108 were found superior with respect to shoot fresh weight and dry weight in both the phases of the experiment. IT-96, IT-99 and IT-101 were superior in terms of indigo dye content. The present study has revealed the genetic superiority of IT-96, IT-99 and IT-101 accessions in terms of leaf yield and indigo dye content, when grown as intercrop in coconut plantation

Evolutionary dynamics on strongly correlated fitness landscapes

We study the evolutionary dynamics of a maladapted population of self-replicating sequences on strongly correlated fitness landscapes. Each sequence is assumed to be composed of blocks of equal length and its fitness is given by a linear combination of four independent block fitnesses. A mutation affects the fitness contribution of a single block leaving the other blocks unchanged and hence inducing correlations between the parent and mutant fitness. On such strongly correlated fitness landscapes, we calculate the dynamical properties like the number of jumps in the most populated sequence and the temporal distribution of the last jump which is shown to exhibit a inverse square dependence as in evolution on uncorrelated fitness landscapes. We also obtain exact results for the distribution of records and extremes for correlated random variables

Screening of yard long bean (Vigna unguiculata subsp. sesquipedalis (L.) Verdcourt) genotypes for resistance to Colletotrichum gloeosporoides

Anthracnose is one of the most destructive fungal diseases caused by Colletotrichumgloeosporoides in yard long bean, leading to complete crop loss at all stages and its partslike hypocotyls, stem, peduncle, flowers, leaves and pods were seriously affected. Few bush type cowpea cultivars have been earlier identified as reliable sources of resistance while trailing types are susceptible, but high yielding. Breeding resistant varieties is suggested as the only practical strategy, especially under hot and humid condition. Fifty-yard-long bean genotypes belonging to bush, semi erect and pole types were screened against anthracnose disease through artificial inoculation under pot culture. The present study identified the resistant varieties of vegetable cowpea through artificial inoculation followed by detached leaf assay. Among the 50 varieties of yard long bean observed, Kanakamony, dual purpose yard long bean was found highly resistant with disease severity of 3.67% followed by Arimbra local

Performance of parthenocarpic and non-parthenocarpic grafts of cucumber

Effect of rootstock on yield and quality of cucumber scion was studied at Department of Vegetable Science, College of Agriculture, Vellayani, Thiruvananthapuram, Kerala during February-May, 2021. Parthenocarpic and non-parthenocarpic cucumber scions were grafted onto five different cultivated cucurbit species i.e. pumpkin, bottle gourd, oriental pickling melon, culinary melon and ash gourd. Significant variations were observed for all the traits under this study. The highest vine length (4.37 m) was observed in Heera scion grafted onto Lagenaria siceraria rootstock followed by Heera scion grafted onto Cucurbita moschata rootstock (4.13 m). The diameter of rootstock hypocotyl was higher in case of KPCH-1 grafted onto bottle gourd (1.48 mm) and Heera grafted onto bottle gourd (1.43 mm). KPCH-1 grafted on bottle gourd (29.33 days) and culinary melon (31 days) rootstocks showed early female flower initiation. The greater number of fruits was observed in graft combination of KPCH- 1 and bottle gourd (32) followed by parthenocarpic grafts with pumpkin (30.33) and ash gourd (30.33) rootstocks. A greater fruit weight was observed in graft combination of Heera and bottle gourd (7.51 kg) followed by Heera grafted onto pumpkin (7.38 kg). Results of this experiment suggest that these graft combinations can be employed in sustainable vegetable cultivation

Pod set and Pollen Viability Studies in Yard Long Bean (Vigna unguiculata sub sp. sesquipedalis)

A study was conducted in a yard long bean (Vigna unguiculata sup/ssp. sesquipedalis) hybrid VS 50 (Kakkamoola Local) x VS 26 (Vellayani Jyothika) to assess the percentage fruit set at two time intervals and to identify the best time interval for pollination in yard long bean hybrids. Hand pollination was done using VS 50 as female parent and VS 26 as male parent for seven consecutive days at two time intervals, 6.30 – 7.30 am and 7.30 – 8.30 am. Higher percentage of fruit set (36.8 %) was observed between 6:30 – 7:30 a.m. as compared to the time interval 7:30 – 8:30 am. (23.8%). Pollen viability was determined for the parents VS 50 (Kakkamoola Local) and VS 26 (Vellayani Jyothika) at 6.30, 7.30 and 8.30 am. Highest pollen viability for both the parents VS 50 and VS 26 was observed during 7.30 am. The present study shows that the best time interval for crossing in yard long bean is 6.30- 7.30 a.m

Battery Lifetime Extension Using Super capacitors in Small-Scale Wind-Energy System with fuzzy logic control

Because of the variable attributes of renewable era, batteries utilized as a part of renewable-force frameworks can experience numerous unpredictable, incomplete charge/release cycles. This study shows a technique for enhancing battery lifetime in a little scale remote-zone wind-power framework by the utilization of a battery/super capacitor half breed vitality stockpiling framework. An agent element model of the general framework, consolidating practical wind-speed and load power varieties has been produced