The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

Development of advanced fuel cell system (phase 4)

For abstract, see N76-23686

Dark Matter Annihilation Signatures from Electroweak Bremsstrahlung

We examine observational signatures of dark matter annihilation in the Milky Way arising from electroweak bremsstrahlung contributions to the annihilation cross section. It has been known for some time that photon bremsstrahlung may significantly boost DM annihilation yields. Recently, we have shown that electroweak bremsstrahlung of W and Z gauge bosons can be the dominant annihilation channel in some popular models with helicity-suppressed 2 --> 2 annihilation. W/Z-bremsstrahlung is particularly interesting because the gauge bosons produced via annihilation subsequently decay to produce large correlated fluxes of electrons, positrons, neutrinos, hadrons (including antiprotons) and gamma rays, which are all of importance in indirect dark matter searches. Here we calculate the spectra of stable annihilation products produced via gamma/W/Z-bremsstrahlung. After modifying the fluxes to account for the propagation through the Galaxy, we set upper bounds on the annihilation cross section via a comparison with observational data. We show that stringent cosmic ray antiproton limits preclude a sizable dark matter contribution to observed cosmic ray positron fluxes in the class of models for which the bremsstrahlung processes dominate.Comment: 11 pages, 6 figures. Updated to match PRD versio

Development of advanced fuel cell system, phase 3

A multiple task research and development program was performed to improve the weight, life, and performance characteristics of hydrogen-oxygen alkaline fuel cells for advanced power systems. Gradual wetting of the anode structure and subsequent long-term performance loss was determined to be caused by deposition of a silicon-containing material on the anode. This deposit was attributed to degradation of the asbestos matrix, and attention was therefore placed on development of a substitute matrix of potassium titanate. An 80 percent gold 20 percent platinum catalyst cathode was developed which has the same performance and stability as the standard 90 percent gold - 10 percent platinum cathode but at half the loading. A hybrid polysulfone/epoxy-glass fiber frame was developed which combines the resistance to the cell environment of pure polysulfone with the fabricating ease of epoxy-glass fiber laminate. These cell components were evaluated in various configurations of full-size cells. The ways in which the baseline engineering model system would be modified to accommodate the requirements of the space tug application are identified

Development of advanced fuel cell system, phase 2

A multiple task research and development program was performed to improve the weight, life, and performance characteristics of hydrogen-oxygen alkaline fuel cells for advanced power systems. Development and characterization of a very stable gold alloy catalyst was continued from Phase I of the program. A polymer material for fabrication of cell structural components was identified and its long term compatibility with the fuel cell environment was demonstrated in cell tests. Full scale partial cell stacks, with advanced design closed cycle evaporative coolers, were tested. The characteristics demonstrated in these tests verified the feasibility of developing the engineering model system concept into an advanced lightweight long life powerplant

The orbital poles of Milky Way satellite galaxies: a rotationally supported disc-of-satellites

Available proper motion measurements of Milky Way (MW) satellite galaxies are used to calculate their orbital poles and projected uncertainties. These are compared to a set of recent cold dark-matter (CDM) simulations, tailored specifically to solve the MW satellite problem. We show that the CDM satellite orbital poles are fully consistent with being drawn from a random distribution, while the MW satellite orbital poles indicate that the disc-of-satellites of the Milky Way is rotationally supported. Furthermore, the bootstrapping analysis of the spatial distribution of theoretical CDM satellites also shows that they are consistent with being randomly drawn. The theoretical CDM satellite population thus shows a significantly different orbital and spatial distribution than the MW satellites, most probably indicating that the majority of the latter are of tidal origin rather than being DM dominated sub-structures. A statistic is presented that can be used to test a possible correlation of satellite galaxy orbits with their spatial distribution.Comment: Accepted for publication in Ap

Quantum Correlation Bounds for Quantum Information Experiments Optimization: the Wigner Inequality Case

Violation of modified Wigner inequality by means binary bipartite quantum system allows the discrimination between the quantum world and the classical local-realistic one, and also ensures the security of Ekert-like quantum key distribution protocol. In this paper we study both theoretically and experimentally the bounds of quantum correlation associated to the modified Wigner's inequality finding the optimal experimental configuration for its maximal violation. We also extend this analysis to the implementation of Ekert's protocol

Bell's Theorem and Nonlinear Systems

For all Einstein-Podolsky-Rosen-type experiments on deterministic systems the Bell inequality holds, unless non-local interactions exist between certain parts of the setup. Here we show that in nonlinear systems the Bell inequality can be violated by non-local effects that are arbitrarily weak. Then we show that the quantum result of the existing Einstein-Podolsky-Rosen-type experiments can be reproduced within deterministic models that include arbitrarily weak non-local effects.Comment: Accepted for publication in Europhysics Letters. 14 pages, no figures. In the Appendix (not included in the EPL version) the author says what he really thinks about the subjec