122 research outputs found

    Generalized metallic pseudo-Riemannian structures

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    We generalize the notion of metallic structure in the pseudo-Riemannian setting, define the metallic Norden structure and study its integrability. We construct a metallic natural connection recovering as particular case the Ganchev and Mihova connection, which we extend to a metallic natural connection on the generalized tangent bundle. Moreover, we construct metallic pseudo-Riemannian structures on the tangent and cotangent bundles.Comment: 16 page

    Generalized quasi-statistical structures

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    Given a non-degenerate (0,2)(0,2)-tensor field hh on a smooth manifold MM, we consider a natural generalized complex and a generalized product structure on the generalized tangent bundle TMTMTM\oplus T^*M of MM and we show that they are \nabla-integrable, for \nabla an affine connection on MM, if and only if (M,h,)(M,h,\nabla) is a quasi-statistical manifold. We introduce the notion of generalized quasi-statistical structure and we prove that any quasi-statistical structure on MM induces generalized quasi-statistical structures on TMTMTM\oplus T^*M. In this context, dual connections are considered and some of their properties are established. The results are described in terms of Patterson-Walker and Sasaki metrics on TMT^*M, horizontal lift and Sasaki metrics on TMTM and, when the connection \nabla is flat, we define prolongation of quasi-statistical structures on manifolds to their cotangent and tangent bundles via generalized geometry. Moreover, Norden and Para-Norden structures are defined on TMT^*M and TMTM.Comment: 28 page

    Generalized metallic structures

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    We study the properties of a generalized metallic, a generalized product and a generalized complex structure induced on the generalized tangent bundle of MM by a metallic Riemannian structure (J,g)(J,g) on MM, providing conditions for their integrability with respect to a suitable connection. Moreover, by using methods of generalized geometry, we lift (J,g)(J,g) to metallic Riemannian structures on the tangent and cotangent bundles of MM, underlying the relations between them.Comment: 19 page

    Harmonic metallic structures

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    The concept of harmonic metallic structure on a metallic pseudo-Riemannian manifold is introduced. In the case of compact manifolds we prove that harmonicity of a metallic structure JJ, with J2=pJ+qIJ^2=pJ+qI and p2+4q0p^2+4q\neq 0, is equivalent to dJ=0dJ=0. Conditions for a harmonic metallic structure to be preserved by harmonic maps are also given. Moreover, we consider harmonic metallic structures on the generalized tangent bundle, provide a Weitzenb\"{o}ck formula for the dual metallic structure and express the Hodge-Laplace operator on TMTMTM \oplus T^*M.Comment: 17 page

    α\alpha-connections in generalized geometry

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    We consider a family of α\alpha-connections defined by a pair of generalized dual quasi-statistical connections (^,^)(\hat{\nabla},\hat{\nabla}^*) on the generalized tangent bundle (TMTM,hˇ)(TM\oplus T^*M, \check{h}) and determine their curvature, Ricci curvature and scalar curvature. Moreover, we provide the necessary and sufficient condition for ^\hat \nabla^* to be an equiaffine connection and we prove that if hh is symmetric and h=0\nabla h=0, then (TMTM,hˇ,^(α),^(α))(TM\oplus T^*M, \check{h}, \hat{\nabla}^{(\alpha)}, \hat{\nabla}^{(-\alpha)}) is a conjugate Ricci-symmetric manifold. Also, we characterize the integrability of a generalized almost product, of a generalized almost complex and of a generalized metallic structure w.r.t. the bracket defined by the α\alpha-connection. Finally we study α\alpha-connections defined by the twin metric of a pseudo-Riemannian manifold, (M,g)(M,g), with a non-degenerate gg-symmetric (1,1)(1,1)-tensor field JJ such that dJ=0d^\nabla J=0, where \nabla is the Levi-Civita connection of gg.Comment: 29 page

    Distance Oracles for Time-Dependent Networks

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    We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes (1+ϵ)(1+\epsilon)-approximate distance summaries from selected landmark vertices to all other vertices in the network. Our oracle uses subquadratic space and time preprocessing, and provides two sublinear-time query algorithms that deliver constant and (1+σ)(1+\sigma)-approximate shortest-travel-times, respectively, for arbitrary origin-destination pairs in the network, for any constant σ>ϵ\sigma > \epsilon. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An extended abstract also appeared in the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014, track-A

    On invariants of almost symplectic connections

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    We study the irreducible decomposition under Sp(2n, R) of the space of torsion tensors of almost symplectic connections. Then a description of all symplectic quadratic invariants of torsion-like tensors is given. When applied to a manifold M with an almost symplectic structure, these instruments give preliminary insight for finding a preferred linear almost symplectic connection on M . We rediscover Ph. Tondeur's Theorem on almost symplectic connections. Properties of torsion of the vectorial kind are deduced

    On curvature tensors of Norden and metallic pseudo-Riemannian manifolds

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    AbstractWe study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ2n

    Effects of trinexapae-ethyl on stoloon development in potted Patriot bermudagrass

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    A recent technique developed for establishment of warm season turfgrasses is based on the transplant of single plug plantlets pre-rooted in the nursery. Plantlets are obtained from one-node sprigs about 2 cm long derived from stolon fragmentation. Usually, stolons must be cut several times to obtain sprigs of the right length because of overly long internodes. In the present study, potted plants of Patriot bermudagrass grown in the nursery were treated with trinexa-pac-ethyl (TE) at the rates 0.1, 0.2, 0.4 and 0.8 kg a.i. ha-1. TE application was aimed at obtaining internode shortening in order to facilitate the stolon division practice. In fact, TE-treated plants showed a decrease in the average length of internodes with respect to control at any applied rate. Nevertheless, the lowest rate applied (0.1 kg a.i. ha-1) did not assure a prolonged effect while the highest rate (0.8 kg a.i. ha-1) caused a decrease in the yield of sprigs. Therefore, our results suggest that TE may be advantageously used and at rates of 0.2-0.4 kg a.i. ha-1 to control stolon development of Patriot bermudagrass for nursery purposes

    Demonstration of quantum volume 64 on a superconducting quantum computing system

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    We improve the quality of quantum circuits on superconducting quantum computing systems, as measured by the quantum volume, with a combination of dynamical decoupling, compiler optimizations, shorter two-qubit gates, and excited state promoted readout. This result shows that the path to larger quantum volume systems requires the simultaneous increase of coherence, control gate fidelities, measurement fidelities, and smarter software which takes into account hardware details, thereby demonstrating the need to continue to co-design the software and hardware stack for the foreseeable future.Comment: Fixed typo in author list. Added references [38], [49] and [52
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