We consider families of embedded, screw motion invariant minimal surfaces in R 3 which limit to parking garage structures. We derive balance equations for the nodal limit and regenerate to obtain surfaces corresponding to solutions. We thus prove the existence of many new examples with helicoidal or planar ends.

Let A denote an associative unital real algebra of finite dimension. We discuss the structure of of sequences and numerical series over A. We also study convergence of power series over A. The ratio, root and geometric series results are modified due to both the submultiplicativity of the norm and the calculational novelty of zero-divisors. The termby-term differentiation theorem for power series on A is established and we use power series to construct and analyze exponential, trigonometric and hyperbolic functions on arbitrary A.

No abstract

No abstract

No abstract