What Do We Really Know About Cosmic Acceleration?

Essentially all of our knowledge of the acceleration history of the Universe - including the acceleration itself - is predicated upon the validity of general relativity. Without recourse to this assumption, we use SNeIa to analyze the expansion history and find (i) very strong (5 sigma) evidence for a period of acceleration, (ii) strong evidence that the acceleration has not been constant, (iii) evidence for an earlier period of deceleration and (iv) only weak evidence that the Universe has not been decelerating since z~0.3.Comment: 9 pages, 8 figure

Drag Coefficients of Varying Dimple Patterns

There are many golf balls on the market today with varying dimple sizes, shapes, and distribution. These proprietary differences are all designed to reduce drag on the balls during flight. There are limited published studies comparing how varying the dimples affects the reduction of drag. An experiment was developed in which golf balls were pulled through a water tank to measure the drag force acting on each ball. The water was chosen to allow for testing at slower velocities. A range of dimple patterns were tested and compared to determine which pattern has the lowest associated drag coefficient

Orthogonality preserving property for pairs of operators on Hilbert C∗C^*-modules

We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner product structure of a Hilbert $C^*$-module is determined essentially by the module structure and by the orthogonality structure, pairs of linear and local orthogonality-preserving mappings are investigated, not a priori bounded. The intuition is that most often $C^*$-linearity and boundedness can be derived from the settings under consideration. In particular, we obtain that if $\mathscr{A}$ is a $C^{*}$-algebra and $T, S:\mathscr{E}\longrightarrow \mathscr{F}$ are two bounded ${\mathscr A}$-linear mappings between full Hilbert $\mathscr{A}$-modules, then $\langle x, y\rangle = 0$ implies $\langle T(x), S(y)\rangle = 0$ for all $x, y\in \mathscr{E}$ if and only if there exists an element $\gamma$ of the center $Z(M({\mathscr A}))$ of the multiplier algebra $M({\mathscr A})$ of ${\mathscr A}$ such that $\langle T(x), S(y)\rangle = \gamma \langle x, y\rangle$ for all $x, y\in \mathscr{E}$. In particular, for adjointable operators $S$ we have $T=(S^*)^{-1}$, and any bounded invertible module operator $T$ may appear. Varying the conditions on the mappings $T$ and $S$ we obtain further affirmative results for local operators and for pairs of a bounded and of an unbounded module operator with bounded inverse, among others. Also, unbounded operators with disjoint ranges are considered. The proving techniques give new insights.Comment: 23 pages, In this last revision several new examples are added and some minor changes appeared in the text. To appear in Aequat. Mat

Positivity and topology in lattice gauge theory

The admissibility condition usually used to define the topological charge in lattice gauge theory is incompatible with a positive transfer matrix.Comment: 6 pages, revtex; revision has some clarifications and additional references, representing the final version to appear in Physical Revie