CONGRUENCES MODULO 2 FOR CERTAIN PARTITION FUNCTIONS

DOI: 10.1017/S000497271500136

DESIGN &FABRICATION OF TILTING VEHICLE

This project report includes information regarding “TILTING MECHANISM” of a four wheel vehicle .The main objective of the project is to design and a fabricate a four wheel tilting vehicle. The vehicle consists of the independent suspension system. The design of the vehicle is to be obtained by setting up parameters such as track width, vehicle length and ride height. By discussing and calculating the basic dimensions of the vehicle the main frame was designed in Solid Works and the frame was analyzed using Solid Works-Simulation and after the design was finished according to several attempts. The manufacturing part is to be done in a workshop where all tools needed are available at exposal. The report also determines the suspension profile needed for the mechanism to avoid the load factors. It also contains the profile of wishbones used in the front suspension part of the types of joints used for the free movement of the wheels during bumps and uneven roads, upgrade in the design of knuckle hubs, tie rod linkages. The operation carried out in the process of fabricating the whole vehicle is included in the report

New modular relations for cubics class invariants

In this paper, we establish several new P–Q mixed modular equations involving theta–functions which are similar to those recorded by Ramanujan in his notebooks. As an application, we establish several new explicit evaluations of cubic class invariants and cubic singular moduli

Congruences modulo 22 for certain partition functions

DOI: 10.1017/S000497271500136

Influence of abiotic factors on population dynamics of leaf webber Diaphania pulverulentalis and its natural enemies in mulberry

ABSTRACT Mulberry the only host plant for rearing silkworms (Bombyx mori) is affected by tukra mealy bug Maconellicoccus hirsutus and leaf webber Diaphania pulverulentalis among many other pests. The incidence of tukra mealy bug M. hirsutus and leaf webber D. pulverulentalis and its natural enemies coccinellids and spiders (Nos./20 plants) were subjected to survery and surveillance for four years. The infestation of tukra mealy bug M. hirsutus and leaf webber D. pulverulentalis was observed through out the year and high (8.18% and 17.13%) in July and November respectively. The population of coccinellids and spiders was high (6.5 and 10.32/20 plants) during November. The infestation of leaf webber (above ETL of 10%) and population of its natural enemies on three varieties (local, MR2 and V1) were correlated with abiotic factors viz., temperature, relative humidity, rainfall and rainy days. Results indicated that the population of parasitoids had significant positive correlation with rainfall. The population of coccinellids, spiders and parasitoids had positive correlation with rainy days and leaf webber infestation. The natural enemies observed in the study were mostly the ladybird predators Chilomenus sexmaculatus and unidentified species of spiders and braconid parasitoids. The braconid parasitoid was marked only in the V1 variety, where leaf webber incidence was higher. Spiders and ladybird were common on both V1 and MR2 varieties during the peak incidence of both tukra mealy bug and leaf webber during October to December