We study the interplay between the classes of right quasi-euclidean rings and right K-Hermite rings, and relate them to projective-free rings and Cohn's GE(2)-rings using the method of noncommutative euclidean div...
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We study the interplay between the classes of right quasi-euclidean rings and right K-Hermite rings, and relate them to projective-free rings and Cohn's GE(2)-rings using the method of noncommutative euclidean divisions and matrix factorizations into idempotents. Right quasi-euclidean rings are closed under matrix extensions, and a left quasi-euclidean ring is right quasi-euclidean if and only if it is right Bezout. Singular matrices over left and right quasi-euclidean domains are shown to be products of idempotent matrices, generalizing an earlier result of Laffey for singular matrices over commutative euclidean domains. (C) 2014 Elsevier Inc. All rights reserved.
In the reconstruction problem of discrete tomography, projections are considered from a finite set. of lattice directions. Employing a limited number of projections implies that the injectivity of the Radon transform ...
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In the reconstruction problem of discrete tomography, projections are considered from a finite set. of lattice directions. Employing a limited number of projections implies that the injectivity of the Radon transform is lost, and, in general, images consistent with a given set of projections form a huge class. In order to lower the number of allowed solutions, one usually tries to include in the problem some a priori information. This suggests that modelling the tomographic reconstruction problem as a linear system of equations is preferable. In this paper we propose to restrict the usual notion of uniqueness, related to the solutions of the linear system, and to provide, for each set., a geometrical characterization of the shape of a lattice subset, say region of uniqueness (ROU), forming a partial, fast reconstructible, solution. Any selected set. intrinsically determines its ROU inside an arbitrary lattice grid. For instance, trivially, if vertical bar S vertical bar = 1, the ROU is represented by two rectangles having sizes equal to the absolute values of the entries of the unique direction in., and placed at two opposite corners of the chosen grid. Surprisingly, if vertical bar S vertical bar = 2, the problem becomes much more complicated. Our purpose is to provide a geometrical characterization of the ROU. This is based on a double euclidean division algorithm (DEDA), which runs in polynomial time. It turns out that the ROU is delimited by a zigzag profile obtained by means of numerical relations among the entries of the employed directions. According to different inputs in DEDA, the shape of the ROU can change consistently, as it can be easily observed from the provided examples. Moreover, after selecting a region of interest (ROI) from a given phantom, we exploit DEDA to reconstruct the part of the ROI which falls in the ROU and, with a few further a priori knowledge, even parts of the ROI which are outside the ROU.
The Wigner little group for massless particles is isomorphic to the euclidean group SE(2). Applied to momentum eigenstates, or to infinite plane waves, the euclidean “Wigner translations” act as the identity. We sho...
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The Wigner little group for massless particles is isomorphic to the euclidean group SE(2). Applied to momentum eigenstates, or to infinite plane waves, the euclidean “Wigner translations” act as the identity. We show that when applied to finite wave packets, the translation generators move the packet trajectory parallel to itself through a distance proportional to the particle’s helicity. We relate this effect to the spin Hall effect of light and to the Lorentz-frame dependence of the position of a massless spinning particle.
The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters, which becomes exact in the limit of large euclidean ...
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The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters, which becomes exact in the limit of large euclidean projection time. Previous studies have used the adiabatic projection method to extract scattering phase shifts from finite periodic-box energy levels using Lüscher's method. In this paper we demonstrate that scattering observables can be computed directly from asymptotic cluster wave functions. For a variety of examples in one and three spatial dimensions, we extract elastic phase shifts from asymptotic cluster standing waves corresponding to spherical wall boundary conditions. We find that this approach of extracting scattering wave functions from the adiabatic Hamiltonian to be less sensitive to small stochastic and systematic errors as compared with using periodic-box energy levels.
Over cosmic distances, astrophysical neutrino oscillations average out to a classical flavor propagation matrix P. Thus, flavor ratios injected at the cosmic source We,Wμ,Wτ evolve to flavor ratios at Earthly detect...
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Over cosmic distances, astrophysical neutrino oscillations average out to a classical flavor propagation matrix P. Thus, flavor ratios injected at the cosmic source We,Wμ,Wτ evolve to flavor ratios at Earthly detectors we,wμ,wτ according to w→=PW→. The unitary constraint reduces the euclidean octant to a “flavor triangle.” We prove a theorem that the area of the Earthly flavor triangle is proportional to Det(P). One more constraint would further reduce the dimensionality of the flavor triangle at Earth (two) to a line (one). We discuss four such constraints. The first is the possibility of a vanishing determinant for P. We give a formula for a unique δ(θij) that yields the vanishing determinant. Next, we consider the thinness of the Earthly flavor triangle. We relate this thinness to the small deviations of the two angles θ32 and θ13 from maximal mixing and zero, respectively. Then we consider the confusion resulting from the tau-neutrino decay topologies, which are showers at low energy, “double-bang” showers in the PeV range, and a mixture of showers and tracks at even higher energies. We examine the simple low-energy regime, where there are just two topologies: wshower=we+wτ and wtrack=wμ. We apply the statistical uncertainty to be expected from IceCube to this model. Finally, we consider ramifications of the expected lack of ντ injection at cosmic sources. In particular, this constraint reduces the Earthly triangle to a boundary line of the triangle. Some tests of this “no ντ injection” hypothesis are given.
The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces in the Minkowski spacetime, subject to an ...
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The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces in the Minkowski spacetime, subject to an additional convexity assumption. In a recent paper, Brendle and Wang A (Gibbons-Penrose inequality for surfaces in Schwarzschild Spacetime. arXiv:1303.1863, 2013) find a sufficient condition for the validity of this Penrose inequality in terms of the geometry of the orthogonal projection of onto a constant time hyperplane. In this work, we study the geometry of hypersurfaces in n-dimensional euclidean space which are normal graphs over other surfaces and relate the intrinsic and extrinsic geometry of the graph with that of the base hypersurface. These results are used to rewrite Brendle and Wang's condition explicitly in terms of the time height function of over a hyperplane and the geometry of the projection of along its past null cone onto this hyperplane. We also include, in Appendix, a self-contained summary of known and new results on the geometry of projections along the Killing direction of codimension two-spacelike surfaces in a strictly static spacetime.
We discuss the renormalization of higher-derivative gravity, both without and with matter fields, in terms of two primary coupling constants rather than three. A technique for determining the dependence of the Gauss-B...
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We discuss the renormalization of higher-derivative gravity, both without and with matter fields, in terms of two primary coupling constants rather than three. A technique for determining the dependence of the Gauss-Bonnet coupling constant on the remaining couplings is explained, and consistency with the local form of the Gauss-Bonnet relation in four dimensions is demonstrated to all orders in perturbation theory. A similar argument is outlined for the Hirzebruch signature and its coupling. We speculate upon the potential implications of instantons on the associated nonperturbative coupling constants.
We investigate the relation between the physical pion pole and screening masses and the mesonic fluctuation scale in low-energy QCD, which relates to the curvature of the mesonic effective potential. This relation is ...
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We investigate the relation between the physical pion pole and screening masses and the mesonic fluctuation scale in low-energy QCD, which relates to the curvature of the mesonic effective potential. This relation is important for the correct relative weight of quantum, thermal and density fluctuations. Hence, it governs the location of phase boundaries as well as the phase structure of QCD. The identification of the correct physics scales is also primarily important for the correct adjustment of the parameters of effective models for low-energy QCD. It is shown that subject to an appropriate definition of the latter, all these scales agree at vanishing temperature, while they deviate from each other at finite temperature.
A class of self-dual and geodesically complete spacetimes with maximally superintegrable geodesic flows is constructed by applying the Eisenhart lift to mechanics in pseudo-euclidean spacetime of signature (1,1). It i...
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A class of self-dual and geodesically complete spacetimes with maximally superintegrable geodesic flows is constructed by applying the Eisenhart lift to mechanics in pseudo-euclidean spacetime of signature (1,1). It is characterized by the presence of a second-rank Killing tensor. Spacetimes of the ultrahyperbolic signature (2,q) with q>2, which admit a second-rank Killing tensor and possess superintegrable geodesic flows, are built.
The Steiner and Gromov–Steiner ratios and Steiner subratio are fundamental characteristics of metric spaces. In this work, an attempt is made to find these ratios for the space of compacta in euclidean space with Hau...
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