Let $$M^n=[0,R]\times \mathbb {S}^{n-1}$$ be an n-dimensional ( $$n\ge 2$$ ) smooth Riemannian manifold equipped with the warped product metric $$g=dr^2+h^2(r)g_{\mathbb {S}^{n-1}}$$ and diffeomorphic to a Euclidean ball. Assume that M has strictly convex boundary. First, for classical Steklov eigenvalue problem, we obtain optimal lower (upper, respectively) bound its spectrum in terms of $$h'(...

Copper (II) phthalocyanine and 2,9,16,23 tetrakis nitro copper (II) phthalocyaninehas been synthesized respectively from phthalonitrile and 4-nitro phthalonitrile under solvent-free condition using two different catalystsovernanodimensionalzeolites. 4-Nitro phthalonitrile synthesized from phthalimide in three steps. The newly prepared compounds have been characterized by IR, UV-Vis, 1</sup...