Explicit Galois representations of automorphisms on holomorphic differentials in characteristic pp

We determine the representation of the group of automorphisms for cyclotomic function fields in characteristic $p > 0$ induced by the natural action on the space of holomorphic differentials via construction of an explicit basis of differentials. This includes those cases which present wild ramification and automorphism groups with non-cyclic $p$-part, which have remained elusive. We also obtain information on the gap sequences of ramified primes. Finally, we extend these results to rank one Drinfel'd modules.Comment: 18 page

The Interference Effects on an Airfoil of a Flat Plate at Mid-span Position

This report gives the results of an investigation of the mutual interference of an airfoil and a flat plate inserted at mid-span position. The tests were conducted in the Variable-Density Wind Tunnel of the National Advisory Committee for Aeronautics at a high value of the Reynolds Number. The interference effects of this combination were found to be small. Supplementary tests indicated that the use of fillets decreases both the lift and drag slightly. A bibliography of publication dealing with interference between wings and bodies, and with the effects of cut-outs and fillets is included

Counting roots of truncated hypergeometric series over finite fields

We consider natural polynomial truncations of hypergeometric power series defined over finite fields. For these truncations, we establish asymptotic upper bounds of order $O(p^{11/12})$ on the number of roots in the prime field $\mathbb{F}_p$. We discuss the correspondence to families of elliptic curves and K3 surfaces of certain such hypergeometric polynomials, for which sharp bounds are obtained in some cases. We include some computations to illustrate and supplement our results.Comment: Errors in paper uncorrected. Kenneth Ward passed away June 201

Values of twisted Artin LL-functions

This note gives a simple proof that certain values of Artin's $L$-function, for a representation $\rho$ with character $\chi_\rho$, are stable under twisting by an even Dirichlet character $\chi$, up to an element generated over $\mathbb Q$ by the values of $\chi$ and $\chi_\rho$, and a product with a power of the Gauss sum $\tau(\chi)$ equal to the dimension of $\rho$. This extends a result due to J. Coates and S. Lichtenbaum.Comment: 6 page

Macrofossil extinction patterns at Bay of Biscay Cretaceous-Tertiary boundary sections

Researchers examined several K-T boundary cores at Deep Sea Drilling Project (DSDP) core repositories to document biostratigraphic ranges of inoceramid shell fragments and prisms. As in land-based sections, prisms in the deep sea cores disappear well before the K-T boundary. Ammonites show a very different extinction pattern than do the inoceramids. A minimum of seven ammonite species have been collected from the last meter of Cretaceous strata in the Bay of Biscay basin. In three of the sections there is no marked drop in either species numbers or abundance prior to the K-T boundary Cretaceous strata; at the Zumaya section, however, both species richness and abundance drop in the last 20 m of the Cretaceous, with only a single ammonite specimen recovered to date from the uppermost 12 m of Cretaceous strata in this section. Researchers conclude that inoceramid bivalves and ammonites showed two different times and patterns of extinction, at least in the Bay of Biscay region. The inoceramids disappeared gradually during the Early Maestrichtian, and survived only into the earliest Late Maestrichtian. Ammonites, on the other hand, maintained relatively high species richness throughout the Maestrichtian, and then disappeared suddenly, either coincident with, or immediately before the microfossil extinction event marking the very end of the Cretaceous

Cubic Fields: A Primer

We classify all cubic extensions of any field of arbitrary characteristic, up to isomorphism, via an explicit construction involving three fundamental types of cubic forms. We deduce a classification of any Galois cubic extension of a field. The splitting and ramification of places in a separable cubic extension of any global function field are completely determined, and precise Riemann-Hurwitz formulae are given. In doing so, we determine the decomposition of any cubic polynomial over a finite field.Comment: 47 pages. Correction to Lemma 3.23.

The effect of small variations in profile of airfoils

This report deals with the effect of small variations in ordinates specified by different laboratories for the airfoil section. This study was made in connection with a more general investigation of the effect of small irregularities of the airfoil surface on the aerodynamic characteristics of an airfoil. These tests show that small changes in airfoil contours, resulting from variations in the specified ordinates, have a sufficiently large effect upon the airfoil characteristics to justify the taking of great care in the specification of ordinates for the construction of models

The number of roots of polynomials of large degree in a prime field

We establish asymptotic upper bounds on the number of zeros modulo $p$ of certain polynomials with integer coefficients, with $p$ prime numbers arbitrarily large. The polynomials we consider have degree of size $p$ and are obtained by truncating certain power series with rational coefficients that satisfy simple differential equations.Comment: 16 page

Interference Effects and Drag of Struts on a Monoplane Wing

Tests were conducted in the Variable Density Wind Tunnel of the NACA to determine the importance of the interference effects and drag of struts on a monoplane. Inclined struts were placed upon a Gottingen 387 airfoil in the lower surface positions and in two upper surface positions. Tests were made at values of Reynolds Number comparable with those obtained in flight. It was found that the interference drag of struts may be as great as the drag of the struts alone

An explicit triangular integral basis for any separable cubic extension of a function field

We determine an explicit triangular integral basis for any separable cubic extension of a rational function field over a finite field in any characteristic. We obtain a formula for the discriminant of every such extension in terms of a standard form in a tower for the Galois closure.Comment: 14 pages. Correction to Lemma 1.1(b