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

Shuttle flight pressure instrumentation: Experience and lessons for the future

Flight data obtained from the Space Transportation System orbiter entries are processed and analyzed to assess the accuracy and performance of the Development Flight Instrumentation (DFI) pressure measurement system. Selected pressure measurements are compared with available wind tunnel and computational data and are further used to perform air data analyses using the Shuttle Entry Air Data System (SEADS) computation technique. The results are compared to air data from other sources. These comparisons isolate and demonstrate the effects of the various limitations of the DFI pressure measurement system. The effects of these limitations on orbiter performance analyses are addressed, and instrumentation modifications are recommended to improve the accuracy of similar fight data systems in the future

Pressure distributions obtained on a 0.04-scale and 0.02-scale model of the Space Shuttle Orbiter's forward fuselage in the Langley 20-inch Mach 6 air tunnel

Results from pressure distribution tests on 0.04-scale and 0.02-scale models of the forward fuselage of the Space Shuttle Orbier are presented without analysis. The tests were completed in the Langley 20-Inch Mach 6 Tunnel. The 0.04-scale model was tested at angles of attack from 0 to 35 and angles of sideslip from 0 to -4. The 0.02-scale model was tested at angles of attack from -10 to 45 and angles of sideslip from 0 to -4. The tests were conducted in support of the development of the Shuttle Entry Air Data System (SEADS). In addition to modeling the 20 SEADS pressure orifices, the wind-tunnel to models were also instrumented with orifices to match Development Flight Instrumentation (DFI) port locations currently existing on the Space Shuttle Orbiter Columbia (OV-102). This DFI simulation had provided a means for comparisons between reentry flight pressure data and wind-tunnel data

Pressure distributions obtained on a 0.04-scale and 0.02-scale model of the Space Shuttle Orbiter's forward fuselage in the Langley continuous flow hypersonic tunnel

Results from pressure distribution tests on 0.04-scale and 0.02-scale models of the forward fuselage of the Space Shuttle Orbiter are presented without analysis. The tests wre completed in the Langley Continuous Flow Hypersonic Tunnel (CFHT). The 0.04-scale model was tested at angles of attack from -5 deg to 45 deg and angles of sideslip from -3 deg to 3 deg. The 0.02-scale model was tested at angles of attack from -10 deg to 45 deg and angles of sideslip from -5 deg to 5 deg. The tests were conducted in support of the development of the Shuttle Entry Air Data System (SEADS). In addition to modeling the 20 SEADS pressure orifices, the wind-tunnel models were also instrumented with orifices to match Development Flight Instrumentation (DFI) port locations currently existing on the Space Shuttle Orbiter Columbia (OV-102). This DFI simulation has provided a means for comparisons between reentry flight pressure data and wind-tunnel data

Pressure distributions on a 0.04-scale model of the Space Shuttle Orbiter's forward fuselage in the Langley unitary plan wind tunnel

Pressure distribution tests on a 0.04-scale model of the forward fuselage of the Space Shuttle Orbiter are presented without analysis. The tests were completed in the Langley Unitary Plan Wind Tunnel (UPWT). The UPWT has two different test sections operating in the continuous mode. Each test section has its own Mach number range. The model was tested at angles of attack from -2.5 deg to 30 deg and angles of sideslip from -5 deg to 5 deg in both test sections. The test Reynolds number was 6.6 x 10 to the 6th power per meter. The tests were conducted in support of the development of the Shuttle Entry Air Data System (SEADS). In addition to modeling the 20 SEADS pressure orifices, the wind-tunnel model was also instrumented with orifices to match Development Flight Instrumentation (DFI) port locations currently existing on the Space Shuttle Orbiter Columbia (OV-102). This DFI simulation has provided a means for comparisons between reentry flight pressure data and wind-tunnel data

Normal origamis of Mumford curves

An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichm\"uller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer

An experimental investigation to determine the effect of window cooling by mass injection for the Shuttle Infrared Leeside Temperature Sensing (SILTS) experiment

The effect of mass injection on the shuttle infrared leeside temperature sensing (SILTS) pod window surfaces in reducing window heating and minimizing window lens radiation during the reentry data taking period is investigated. Heat transfer coefficients on and around the simulated windows and window cavities are determined. Heat transfer rates and window coolant flow rates are reported for the SILTS configuration. A comparison of two windows' geometries and their effects on the heat transfer rate is discussed and oil flow photographs are presented to indicate how mass injection affects the flow field near the SILTS window

A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Wide QRS Complex Tachycardia in a Patient with Wolff-Parkinson-White Syndrome and Cardiomyopathy: What is the Mechanism?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75406/1/j.1540-8167.2000.tb01767.x.pd

Reliable low-cost fabrication of low-loss Al2O3:Er3+Al_2O_3:Er^{3+} waveguides with 5.4-dB optical gain

A reliable and reproducible deposition process for the fabrication of $Al_2O_3$ waveguides with losses as low as 0.1 dB/cm has been developed. The thin films are grown at ~ 5 nm/min deposition rate and exhibit excellent thickness uniformity within 1% over 50times50 mm2 area and no detectable $OH^{-}$ incorporation. For applications of the $Al_2O_3$ films in compact, integrated optical devices, a high-quality channel waveguide fabrication process is utilized. Planar and channel propagation losses as low as 0.1 and 0.2 dB/cm, respectively, are demonstrated. For the development of active integrated optical functions, the implementation of rare-earth-ion doping is investigated by cosputtering of erbium during the $Al_2O_3$ layer growth. Dopant levels between 0.2-5times $1020 cm^{-3}$ are studied. At $Er^{3+}$ concentrations of interest for optical amplification, a lifetime of the 4I13/2 level as long as 7 ms is measured. Gain measurements over 6.4-cm propagation length in a 700-nm-thick $Al_2O_3:Er^{3+}$ channel waveguide result in net optical gain over a 41-nm-wide wavelength range between 1526-1567 nm with a maximum of 5.4 dB at 1533 n