The isometry degree of a computable copy of ℓp\ell^p

When $p$ is a computable real so that $p \geq 1$, the isometry degree of a computable copy $\mathcal{B}$ of $\ell^p$ is defined to be the least powerful Turing degree that computes a linear isometry of $\ell^p$ onto $\mathcal{B}$. We show that this degree always exists and that when $p \neq 2$ these degrees are precisely the c.e. degrees

Review of "Teaching Innovations in Economics: Strategies and Innovations for Interactive Instruction" (Edited by Michael K. Salemi and William B. Walstad)

Teaching Innovations in Economics is one result of a series of workshops, online training, and support for scholarly work organised by two economists prominent in the field of economic education, Michael Salemi and William Walstad. The 30 contributors to this volume were active in a National Science Foundation funded Teaching Innovations Program, either as workshop organisers or participants. The workshop programme was intended to encourage economists to investigate, adopt and disseminate new teaching techniques. The book continues this mission.

On the Bragg, Leibfried, and Modified Leibfried Numbers

The Bragg, Leibfried, and modified Leibfried numbers are defined in the context of a theory of dislocation-mediated melting, and their values are determined from the properties of the dislocation ensemble at the melting temperature. The approximate numerical coincidence of the Bragg and modified Leibfried numbers is explained. The parameter K in the definition of the modified Leibfried number is shown to be the natural logarithm of the effective coordination number. Our analysis reveals that the Bragg number can be considered an elemental constant, in contrast to the Leibfried and modified Leibfried numbers.Comment: 5 pages, LaTe

Polynomial Space Randomness in Analysis

We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko\u27s framework for polynomial space computability in R^n to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem characterizes weakly pspace random points. That is, a point x is weakly pspace random if and only if the Lebesgue differentiation theorem holds for a point x for every pspace L_1-computable function

Caesar's Connection With the Conspiracies at Rome in 66-62 B. C.

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