Discussion on Scalar Potential in Toroidal and Quasi-Toroidal Co-ordinate

Quasi - toroidal oscillations 1199 ?

Quasi-toroidal oscillations in slowly rotating stars are examined in the framework of general relativity. The oscillation frequency to rst order of the rotation rate is not a single value even for uniform rotation unlike the Newtonian case. All the oscillation frequencies of the r-modes are purely neutral and form a continuous spectrum limited to a certain range. The allowed frequencies are det...

Quasi-toroidal oscillations in rotating relativistic stars

Quasi-toroidal oscillations in slowly rotating stars are examined in the framework of general relativity. The oscillation frequency to first order of the rotation rate is not a single value even for uniform rotation unlike the Newtonian case. All the oscillation frequencies of the r-modes are purely neutral and form a continuous spectrum limited to a certain range. The allowed frequencies are d...

On Toroidal Rotating Drops

Functionals on Toroidal Surfaces

We show that the torus in R is a critical point of a sequence of functionalsFn (n = 1, 2, 3, . . .) defined over compact surfaces (closed membranes) in R. When the Lagrange function E is a polynomial of degree n of the mean curvatureH of the torus, the radii (a, r) of the torus are constrained to satisfy a 2 r2 = n−n n2−n−1 , n ≥ 2. A simple generalization of torus in R 3 is a tube of radius r ...

Minimum Tenacity of Toroidal graphs

The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...