Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

Financial Analysis of Pruning Combined with Low Density Management of Southern Yellow Pine in East Texas: An Assessment

Time study was conducted on pruning of research plots in a IZyear-old loblolly pine (Pinus taeda) plantation thinned to 58 square feet basal area (190 trees) per acre. Pruning times with labor and equipment costs were used to determine per acre and per tree pruning costs. Pruning costs were used to find values necessary to break-even on a pruning investment. Soil expectation value (SEV) calculations were used to compare profitability of management utilizing heavy thinning with pruning to traditional management regimes. Calculations were performed using a current hourly wage of $8.00, stumpage price of$400.00, per thousand board feet (MBF) and real interest rates of 0.13,2.78,7.00, and 10.00 percent. Per acre combined labor and equipment cost was $116.07. Cost per tree to prune to a height of 25 feet was$0.61. Break-even values were found to range from $118.82 to$645.34 per acre depending on interest rate. Profit increase by utilizing low density management combined with pruning was found to range from $491.43 to$88,093.04 per acre over traditional management for a perpetual series of full rotations

Preparation of ingots of uranium-niobium alloy

A study was made of the preparation of a uranium - 10 w/o niobium alloy by the bomb reduction of a suitable form of niobium and uranium tetrafluoride with calcium. A compound with a probable formula of Na2NbOF5 proved to be most satisfactory as the source of niobium. High yields and good metal-slag separations were obtained. Chemical analysis and density determinations showed the composition to be 10 ± 0.5 w/o niobium. Fifteen pounds of alloy were melted in BeO and cast into a graphite mold

Heating mechanisms in radio frequency driven ultracold plasmas

Several mechanisms by which an external electromagnetic field influences the temperature of a plasma are studied analytically and specialized to the system of an ultracold plasma (UCP) driven by a uniform radio frequency (RF) field. Heating through collisional absorption is reviewed and applied to UCPs. Furthermore, it is shown that the RF field modifies the three body recombination process by ionizing electrons from intermediate high-lying Rydberg states and upshifting the continuum threshold, resulting in a suppression of three body recombination. Heating through collisionless absorption associated with the finite plasma size is calculated in detail, revealing a temperature threshold below which collisionless absorption is ineffective.Comment: 14 pages, 7 figure

Microwave Spectroscopy

Contains reports on five research projects