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

The Late Time Light Curve of SN 1998bw Associated with GRB980425

We report 139 photometric observations through the B, V, and I filters of the supernova SN 1998bw, an object which is associated with the Gamma-Ray Burst GRB 980425. Detailed light curves of this unique supernova can be compared to theoretical models, so we report here our light curve for 123 days between 27 June 1998 and 28 October 1998. The light curve of SN 1988bw is consistent with those of the Type Ic class. We find that the magnitude-versus-time relation for this supernova is linear to within 0.05 mags in all colors over the entire duration of our study. Our measured uniform decline rates are $0.0141 \pm 0.0002$, $0.0184 \pm 0.0003$, and $0.0181 \pm 0.0003$ magnitudes per day in the B, V, and I bands. The linear decline and the rate of that decline suggest that late time light curve is powered by the radioactive decay of cobalt with some leakage of the gamma rays.Comment: 15 pages, 1 figure, 1 table, Accepted for publication in PAS

Design-to-cost

Attempts made to design to costs equipment, vehicles and subsystems for various space projects are discussed. A systematic approach, based on mission requirement analysis, definition of a mission baseline design, benefit and cost analysis, and a benefit-cost analysis was proposed for implementing the cost control program

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

Estate Tax Planning And Marketing Oppor-tunities Of The Economic Growth And Tax Relief Reconciliation Act Of 2001

The best advice tax practitioners can give clients after the 2001 Tax Relief Act, is that the optimal time to die in the next decade will be 2010!  What has been touted as a repeal of the Federal estate tax, has actually resulted in increasing the importance of estate tax planning.   This is due to several factors.  First, the rate reduction is phased in so slowly that in 2009, the top estate rate will still be 45% and the exemption amount only $3.5 million.  In 2010, repeal is actually achieved, but for one year only.  The “repeal” sunsets in 2011 when the estate tax comes back in full, using a maximum 55$1 million exemption.   Basis of inherited property may prove to be a nightmare.  Some property will get a stepped up basis, other property will not.  Further complicating the picture is that the gift tax has not been repealed. The estate tax planner will be faced with a host of issues to consider.  Which estate planning strategies are still valid?  What new planning tools will be developed?  Many wills will include obsolete provisions and will need to be redrafted.  Health of the client will become more important in the planning process.  Marketing issues of planning under such uncertainty abound.  This paper examines the new estate and gift tax provisions; offers strategies for navigating the sea of complexity and uncertainty; and explores the marketing opportunities for financial planners created by the new law

Conceptual design of an orbital propellant transfer experiment. Volume 2: Study results

The OTV configurations, operations and requirements planned for the period from the 1980's to the 1990's were reviewed and a propellant transfer experiment was designed that would support the needs of these advanced OTV operational concepts. An overall integrated propellant management technology plan for all NASA centers was developed. The preliminary cost estimate (for planning purposes only) is $56.7 M, of which approximately$31.8 M is for shuttle user costs

Over-Sampling for Accurate Masking Threshold Calculation in Wavelet Packet Audio Coders

Many existing audio coders use a critically sampled discrete wavelet transform (DWT) for the decomposition of audio signals. While the aliasing present in the wavelet coefficients is cancelled in the decoder, these coders normally perform calculation of the simultaneous masking threshold directly on these aliased coefficients. This paper uses over-sampling in the wavelet packet decomposition in order to provide alias-free coefficients for accurate simultaneous masking threshold calculation. The proposed technique is compared with masking threshold calculation based upon the FFT and critically-sampled wavelet coefficients, and the results show that a bit rate saving of up to 16 kbit/s can be achieved using over-sampling

Debris/ice/TPS assessment and integrated photographic analysis for Shuttle Mission STS-56

The Debris Team developed and implemented measures to control damage from debris in the Shuttle operational environment and to make the control measures a part of routine launch flows. These measures include engineering surveillance during vehicle processing and closeout operations, facility and flight hardware inspections before and after launch, and photographic analysis of mission events. Photographic analyses of mission imagery from launch, on-orbit, and landing provide significant data in verifying proper operation of systems and evaluating anomalies. In addition to the Kennedy Space Center (KSC) Photo/Video Analysis, reports from JSC, MSFC, and Rockwell International--Downey are also included in this document to provide an integrated assessment of the mission