We discuss a famous problem about right triangles with rational side lengths. This elementarysounding problem is still not completely solved; the last remaining step involves the Birch and Swinnerton-Dyer conjecture, which is one of the most important open problems in number theory (right up there with the Riemann hypothesis). 6.

We refine the techniques of our previous paper [KM1] to prove that the average order of vanishing of L-functions of primitive automorphic forms of weight 2 and prime level q satisfies ∑ f∈S2(q)∗ ords= 1 2 L(f, s) ≤ C|S2(q) ∗| with C = 6.5, for all q large enough. On the Birch and Swinnerton-Dyer conjecture, this implies rank J0(q) ≤ C dim J0(q) for q prime large enough.

"777 oil" is a code drug of the Siddha system of medicine used in the treatment of Psoriasis. The drug is derived from the leaves Wrightia tinctoria by insolation, with coconut oil as base. The present study is aimed at comparing the drug prepared by insolation with that prepared in darkness.Analytical studies carried out in both the drugs showed difference in acid number without exposing to su...

The causative agents of skin infection are bacteria, fungi and in specific dermatophytes. Many infectious diseases have been treated with plant extracts. The free and bound flavonoids fractions of Wrightia tinctoria (Roxb) R.Br. (Apocynaceae), leaves were tested against 10 bacterial, 3 fungal and 4 dermatophytic strains affecting the skin using disc diffusion and broth micro dilution method. Th...

Chronic myelagenous leukemia (CML) is a slowly progressive disease characterized by the overproduction of granulocytes (neutrophils, eosinophils and basophils). A blood smear shows moderate elevations in white blood cell counts that may persist for years and be benign. Platelets are increased in number although their function is impaired, resulting in symptoms of easy bleeding (purpura, swollen...