Compact-like abelian groups without non-trivial quasi-convex null sequences

In this paper, we study precompact abelian groups G that contain no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0. We characterize groups with this property in the following classes of groups: (a) bounded precompact abelian groups; (b) minimal abelian groups; (c) totally minimal abelian groups; (d) \omega-bounded abelian groups. We also provide examples of minimal abelian groups with this property, and show that there exists a minimal pseudocompact abelian group with the same property; furthermore, under Martin's Axiom, the group may be chosen to be countably compact minimal abelian.Comment: Final versio

Truth-value semantics and functional extensions for classical logic of partial terms based on equality

We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and partial selection functions, independently of any strictness assumption.Comment: 15 pages, to appear in the Notre Dame Journal of Formal Logi

Interval orders and reverse mathematics

We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain $2 \oplus 2$. We also study proper interval orders and their characterization theorem: a partial order is a proper interval order if and only if it contains neither $2 \oplus 2$ nor $3 \oplus 1$.Comment: 21 pages; to appear in Notre Dame Journal of Formal Logic; minor changes from the previous versio

Effective dynamics of self-gravitating extended objects

We introduce an effective Lagrangian which describes the classical and semiclassical dynamics of spherically symmetric, self-gravitating objects that may populate the Universe at large and small (Planck) scale. These include wormholes, black holes and inflationary bubbles. We speculate that such objects represent some possible modes of fluctuation in the primordial spacetime foam out of which our universe was born. Several results obtained by different methods are encompassed and reinterpreted by our effective approach. As an example, we discuss: i) the gravitational nucleation coefficient for a pair of Minkowski bubbles, and ii) the nucleation coefficient of an inflationary vacuum bubble in a Minkowski backgroundComment: 13 pages, no figures, ReVTe

Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime

We discuss the relation between string quantization based on the Schild path integral and the Nambu-Goto path integral. The equivalence between the two approaches at the classical level is extended to the quantum level by a saddle--point evaluation of the corresponding path integrals. A possible relationship between M-Theory and the quantum mechanics of string loops is pointed out. Then, within the framework of ``loop quantum mechanics'', we confront the difficult question as to what exactly gives rise to the structure of spacetime. We argue that the large scale properties of the string condensate are responsible for the effective Riemannian geometry of classical spacetime. On the other hand, near the Planck scale the condensate ``evaporates'', and what is left behind is a ``vacuum'' characterized by an effective fractal geometry.Comment: 19pag. ReVTeX, 1fig. Invited paper to appear in the special issue of {\it Chaos, Solitons and Fractals} on ``Super strings, M,F,S,...Theory'' (M.S. El Naschie and C.Castro, ed

Hausdorff dimension of a quantum string

In the path integral formulation of quantum mechanics, Feynman and Hibbs noted that the trajectory of a particle is continuous but nowhere differentiable. We extend this result to the quantum mechanical path of a relativistic string and find that the ``trajectory'', in this case, is a fractal surface with Hausdorff dimension three. Depending on the resolution of the detecting apparatus, the extra dimension is perceived as ``fuzziness'' of the string world-surface. We give an interpretation of this phenomenon in terms of a new form of the uncertainty principle for strings, and study the transition from the smooth to the fractal phase.Comment: 18 pages, non figures, ReVTeX 3.0, in print on Phys.Rev.

Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI

Search for Chargino-Neutralino Associated Production at the Fermilab Tevatron Collider

We have searched in $p \bar{p}$ collisions at $\sqrt{s}$ = 1.8 TeV for events with three charged leptons and missing transverse energy. In the Minimal Supersymmetric Standard Model, we expect trilepton events from chargino-neutralino (\chione \chitwo) pair production, with subsequent decay into leptons. We observe no candidate $e^+e^-e^\pm$, $e^+e^-\mu^\pm$, $e^\pm\mu^+\mu^-$ or $\mu^+\mu^-\mu^\pm$ events in 106 pb$^{-1}$ integrated luminosity. We present limits on the sum of the branching ratios times cross section for the four channels: \sigma_{\chione\chitwo}\cdot BR(\chione\chitwo\to 3\ell+X) 81.5 \mgev\sp and M_\chitwo > 82.2 \mgev\sp for $\tan\beta=2$, $\mu =-600$~\mgev\sp and M_\squark= M_\gluino.Comment: 9 pages and 3 figure

PAMELA's measurements of geomagnetic cutoff variations during solar energetic particle events

Data from the PAMELA satellite experiment were used to measure the geomagnetic cutoff for high-energy ($\gtrsim$ 80 MeV) protons during the solar particle events on 2006 December 13 and 14. The variations of the cutoff latitude as a function of rigidity were studied on relatively short timescales, corresponding to single spacecraft orbits (about 94 minutes). Estimated cutoff values were cross-checked with those obtained by means of a trajectory tracing approach based on dynamical empirical modeling of the Earth's magnetosphere. We find significant variations in the cutoff latitude, with a maximum suppression of about 6 deg for $\sim$80 MeV protons during the main phase of the storm. The observed reduction in the geomagnetic shielding and its temporal evolution were compared with the changes in the magnetosphere configuration, investigating the role of IMF, solar wind and geomagnetic (Kp, Dst and Sym-H indexes) variables and their correlation with PAMELA cutoff results.Comment: Conference: The 34th International Cosmic Ray Conference (ICRC2015), 30 July - 6 August, 2015, The Hague, The Netherlands, Volume: PoS(ICRC2015)28

Premelting of Thin Wires

Recent work has raised considerable interest on the nature of thin metallic wires. We have investigated the melting behavior of thin cylindrical Pb wires with the axis along a (110) direction, using molecular dynamics and a well-tested many-body potential. We find that---in analogy with cluster melting---the melting temperature $T_m (R)$ of a wire with radius $R$ is lower than that of a bulk solid, $T_m^b$, by $T_m (R) = T_m^b -c/R$. Surface melting effects, with formation of a thin skin of highly diffusive atoms at the wire surface, is observed. The diffusivity is lower where the wire surface has a flat, local (111) orientation, and higher at (110) and (100) rounded areas. The possible relevance to recent results on non-rupturing thin necks between an STM tip and a warm surface is addressed.Comment: 10 pages, 4 postscript figures are appended, RevTeX, SISSA Ref. 131/94/CM/S