As Time Goes by ???: Revisiting Fundamentals

published or submitted for publicatio

Rademacher-Carlitz Polynomials

We introduce and study the \emph{Rademacher-Carlitz polynomial} \RC(u, v, s, t, a, b) := \sum_{k = \lceil s \rceil}^{\lceil s \rceil + b - 1} u^{\fl{\frac{ka + t}{b}}} v^k where $a, b \in \Z_{>0}$, $s, t \in \R$, and $u$ and $v$ are variables. These polynomials generalize and unify various Dedekind-like sums and polynomials; most naturally, one may view \RC(u, v, s, t, a, b) as a polynomial analogue (in the sense of Carlitz) of the \emph{Dedekind-Rademacher sum} \r_t(a,b) := \sum_{k=0}^{b-1}\left(\left(\frac{ka+t}{b} \right)\right) \left(\left(\frac{k}{b} \right)\right), which appears in various number-theoretic, combinatorial, geometric, and computational contexts. Our results come in three flavors: we prove a reciprocity theorem for Rademacher-Carlitz polynomials, we show how they are the only nontrivial ingredients of integer-point transforms $$\sigma(x,y):=\sum_{(j,k) \in \mathcal{P}\cap \Z^2} x^j y^k$$ of any rational polyhedron $\mathcal{P}$, and we derive a novel reciprocity theorem for Dedekind-Rademacher sums, which follows naturally from our setup

Sodium sulfate: Vaporization thermodynamics and role in corrosive flames

Gaseous species over liquid Na2SO4 were identified by the technique of molecular beam mass spectrometry. The heat and entropy of vaporization of the Na2SO4 molecule were measured directly. Comparisons of the experimental entropy with values calculated using various molecular parameters were used to estimate the molecular structure and vibrational frequencies. The thermodynamic properties of gaseous and condensed phase Na2SO4, along with additional pertinent species, were used in a computer program to calculate equilibrium flame compositions and temperatures for representative turbine engine and burner rig flames. Compositions were calculated at various fuel-to-oxidant ratios with additions of sulfur to the fuel and the components of sea salt to the intake air. Temperatures for condensation of Na2SO4 were obtained as a function of sulfur and sea salt concentrations

DISCUSSION: THE SOUTHERN AGRICULTURAL ECONOMICS ASSOCIATION AND RESIDENT INSTRUCTION

Teaching/Communication/Extension/Profession,

Concept study of a UV coronagraph spectrometer for the pinhole-occulter facility

The results of a very short study to define an Ultraviolet Coronagraph-Spectrometer (UVCS) for the Pinhole/Occulter Facility (P/OF) are summarized. The P/OF instrument was based on docummentation from the Definition Phase of the Spacelab Coronographs Program which was effectively completed in August 1980. The primary differences between the P/OF instrument and the Spacelab experiment are the remote occulter mask, the telescope size , and the deployable structure to accommodate P/OF's length restrictions. Requirement for P/OF that are associated with these features are briefly considered, but further study is need to more fully consider the unusual implications, particularly in the interplay between the instrument pointing and the P/OF boom control