An infinite family of exactly-solvable and integrable potentials on a plane is introduced.It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular cases of this family. The underlying algebraic structure of the new potentials is revealed as well as its hidden algebra. We conjecture that all members of the family are also superintegrable and demonstrate this for the first few cases. A quasi-exactly-solvable and integrable generalization of the family is found.

We show that all bounded trajectories in the two dimensional classical system with the potential V (r, ϕ) = ω 2 r 2 + and does not depend on k. This agrees with our earlier conjecture suggesting that the quantum version of this system is superintegrable.

A complete classification is presented of quantum and classical superintegrable systems in E2 that allow the separation of variables in polar coordinates and admit an additional integral of motion of order three in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painlevé transcendent or in terms of the Weierstrass elliptic function.

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Low-field magnetoresistance measurements for compensated, n-type three-dimensional GaAs with net donor concentration just below the metal-insulator transition show a quadratic field dependence for values of 8 less than 750 G. Temperature-dependent measurements in zero 6eldshow that transport is by variable-range hopping, and are consistent with the presence of a Coulomb gap which narrows close to the transition. It is found that the temperature dependence of the eff'ective area in which the Aux is enclosed is not related to the temperature dependence of