We discuss a Brane World scenario where we live on a 3-brane with massive gravity in the infinite-volume bulk. The bulk graviton can be much heavier than the inverse Hubble size, as heavy as the bulk Planck scale, whose lower bound is roughly the inverse of 0.1 mm. The 4D Einstein-Hilbert term on the brane shields the brane matter from both strong bulk gravity and large bulk graviton mass. Gravity on the brane does not become higher-dimensional at large distances. Instead, at distance scales above the bulk Planck length, gravity on the brane behaves as 4D gravity with small graviton mass roughly of the order of or below the inverse Hubble size. Unlike the massless case, with massive gravity in the bulk one can have: (i) 4D tensor structure on a codimension-1 brane; and (ii) no infrared tachyon for smoothed-out higher codimension branes. The effects of the brane dynamics on the bulk are exponentially suppressed away from the brane. One consequence is that there are no "self-accelerated" solutions. In codimension-2 cases, there exist nonsingular solutions with a flat 3-brane † This address is used by the author for no purpose other than to indicate his professional affiliation as is customary in scientific publications. In particular, the contents of this paper are limited to theoretical physics, have no commercial or other such value, are not intended as an investment, legal, tax or any other such advice, and in no way represent views of Quantigic Solutions LLC, the website www.quantigic.com or any of their other affiliates.(1671) 1672 Z. Kakushadze for a continuous positive range of the brane tension. In higher codimension cases, as in the massless case, higher curvature terms are required to obtain such solutions.

Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrödinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.

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