Dr. Blum's main thesis in this small volume is that from the origin of life, evolution has proceeded necessarily along certain channels, predetermined from without by the physical nature of the inorganic earth and by thermodynamic considerations from within. His interpretation of the free energy changes in biochemical reactions is particularly lucid. The exposition draws freely from the discipl...

Determining if two knots are not equivalent in an e cient manner is important in the study of knots. The arrow polynomial, which is calculated from a virtual knot diagram and is invariant under the Reidemeister moves, can be used to determine if two knots are not equivalent and determine a lower bound on the virtual crossing number. In this paper, we present the necessary data structures and al...

We consider permutations of {1, 2, . . . , n} in which each integer is given a direction; such permutations are called directed permutations. An integer k in a directed permutation is called mobile of its arrow points to a smaller integer adjacent to it. For example, for → 3 → 2 ← 5 → 4 → 6 → 1 , the integers 3, 5, and 6 are mobile. It follows that 1 can never be mobile since there is no intege...

We prove the existence of general equilibrium for continuous-time overlappinggenerations models. Previous theorems exclude all non-linear C.E.S. and von Neumann Morgenstern preferences and exclude production. Our primitive assumptions are satisfied by such preferences and by all Markovian production technologies satisfying Bewley's assumptions for Arrow Debreu models provided that storage is po...