A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Maritime intent estimation and the detection of unknown obstacles

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 195-196).The benefits of using Unmanned Undersea Vehicles (UUVs) in maritime operations are numerous. However, before these benefits can be realized, UUV capabilities must be expanded. This thesis focuses on improving certain aspects of the Maritime Reconnaissance and Undersea Search and Survey capabilities of a UUV. An algorithm is first presented which provides the UUV with the ability to estimate the intent of the contacts it is observing (intent estimation). This was accomplished by developing a probabilistic model of the contact's possible intents and then using those models to estimate the contact's actual intent. The results from that algorithm are used to analyze the contact's observed path to determine a probabilistic belief of the potential location of obstacles in the environment (obstacle detection) that the contact is avoiding. These values are recorded in an obstacle inference map, which is capable of incorporating the results from the analysis of any number of observed paths from multiple contacts. The laws of probability were used to develop the algorithms in this thesis-with an emphasis on Bayes' rule. Various scenarios are presented to demonstrate the capabilities and limitations of the intent estimation and obstacle detection algorithms.by Edward Hsiang Lung Fong.S.M

Mott-Kondo Insulator Behavior in the Iron Oxychalcogenides

We perform a combined experimental-theoretical study of the Fe-oxychalcogenides (FeO\emph{Ch}) series La$_{2}$O$_{2}$Fe$_{2}$O\emph{M}$_{2}$ (\emph{M}=S, Se), which is the latest among the Fe-based materials with the potential \ to show unconventional high-T$_{c}$ superconductivity (HTSC). A combination of incoherent Hubbard features in X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS) spectra, as well as resitivity data, reveal that the parent FeO\emph{Ch} are correlation-driven insulators. To uncover microscopics underlying these findings, we perform local density approximation-plus-dynamical mean field theory (LDA+DMFT) calculations that unravel a Mott-Kondo insulating state. Based upon good agreement between theory and a range of data, we propose that FeO\emph{Ch} may constitute a new, ideal testing ground to explore HTSC arising from a strange metal proximate to a novel selective-Mott quantum criticality

Auto and cross correlation of phases of the whole-sky CMB and foreground maps from the 1-year WMAP data

The issue of non-Gaussianity is not only related to distinguishing the theories of the origin of primordial fluctuations, but also crucial for the determination of cosmological parameters in the framework of inflation paradigm. We present an advenced method for testing non-Gaussianity on the whole-sky CMB anisotropies. This method is based on the Kuiper's statistic to probe the two-dimensional uniformity on a periodic mapping square associating phases: return mapping of phases of the derived CMB (similar to auto correlation) and cross correlations between phases of the derived CMB and foregrounds. Since phases reflect morphology, detection of cross correlation of phases signifies the contamination of foreground signals in the derived CMB map. The advantage of this method is that one can cross check the auto and cross correlation of phases of the derived CMB and foregrounds, and mark off those multipoles in which the non-Gaussianity results from the foreground contaminations. We apply this statistic on the derived signals from the 1-year WMAP data. The auto-correlations of phases from the ILC map shows the significance above 95% CL against the random phase hypothesis on 17 spherical harmonic multipoles, among which some have pronounced cross correlations with the foreground maps. We conclude that most of the non-Gaussianity found in the derived CMB maps are from foreground contaminations, except, among others, l=6. With this method we are better equipped to approach the issue of non-Gaussianity of primordial origin for the upcoming PLANCK mission.Comment: 2 figures added: new representation of reconstructed (from 1D Fourier composition) DT distribution for each multipole number el

Effect of recent R_p and R_n measurements on extended Gari-Krumpelmann model fits to nucleon electromagnetic form factors

The Gari-Krumpelmann (GK) models of nucleon electromagnetic form factors, in which the rho, omega, and phi vector meson pole contributions evolve at high momentum transfer to conform to the predictions of perturbative QCD (pQCD), was recently extended to include the width of the rho meson by substituting the result of dispersion relations for the pole and the addition of rho' (1450) isovector vector meson pole. This extended model was shown to produce a good overall fit to all the available nucleon electromagnetic form factor (emff) data. Since then new polarization data shows that the electric to magnetic ratios R_p and R_n obtained are not consistent with the older G_{Ep} and G_{En} data in their range of momentum transfer. The model is further extended to include the omega' (1419) isoscalar vector meson pole. It is found that while this GKex cannot simultaneously fit the new R_p and the old G_{En} data, it can fit the new R_p and R_n well simultaneously. An excellent fit to all the remaining data is obtained when the inconsistent G_{Ep} and G_{En} is omitted. The model predictions are shown up to momentum transfer squared, Q^2, of 8 GeV^2/c^2.Comment: 14 pages, 8 figures, using RevTeX4; email correspondence to [email protected] ; minor typos corrected, figures added, conclusions extende

Correlated Strength in Nuclear Spectral Function

We have carried out an (e,e'p) experiment at high momentum transfer and in parallel kinematics to measure the strength of the nuclear spectral function S(k,E) at high nucleon momenta k and large removal energies E. This strength is related to the presence of short-range and tensor correlations, and was known hitherto only indirectly and with considerable uncertainty from the lack of strength in the independent-particle region. This experiment confirms by direct measurement the correlated strength predicted by theory.Comment: 4 pages, 2 figures, accepted by Phys. Rev. Let

Extended Gari-Krumpelmann model fits to nucleon electromagnetic form factors

Nucleon electromagnetic form factor data (including recent data) is fitted with models that respect the confinement and asymptotic freedom properties of QCD. Gari-Krumpelmann (GK) type models, which include the major vector meson pole contributions and at high momentum transfer conform to the predictions of perturbative QCD, are combined with Hohler-Pietarinen (HP) models, which also include the width of the rho meson and the addition of higher mass vector meson exchanges, but do not evolve into the explicit form of PQCD at high momentum transfer. Different parameterizations of the GK model's hadronic form factors, the effect of including the width of the rho meson and the addition of the next (in mass) isospin 1 vector meson are considered. The quality of fit and the consistency of the parameters select three of the combined HP/GK type models. Projections are made to the higher momentum transfers which are relevant to electron-deuteron experiments. The projections vary little for the preferred models, removing much of the ambiguity in electron-nucleus scattering predictions.Comment: 18pp, 7 figures, using RevTeX with BoxedEPS macros; 1 new figure, minor textual changes; email correspondence to [email protected]

Phenomenology of the Deuteron Electromagnetic Form Factors

A rigorous extraction of the deuteron charge form factors from tensor polarization data in elastic electron-deuteron scattering, at given values of the 4-momentum transfer, is presented. Then the world data for elastic electron-deuteron scattering is used to parameterize, in three different ways, the three electromagnetic form factors of the deuteron in the 4-momentum transfer range 0-7 fm^-1. This procedure is made possible with the advent of recent polarization measurements. The parameterizations allow a phenomenological characterization of the deuteron electromagnetic structure. They can be used to remove ambiguities in the form factors extraction from future polarization data.Comment: 18 pages (LaTeX), 2 figures Feb. 25: minor changes of content and in Table