Homotheties and topology of tangent sphere bundles

We prove a Theorem on homotheties between two given tangent sphere bundles $S_rM$ of a Riemannian manifold $M,g$ of $\dim\geq 3$, assuming different variable radius functions $r$ and weighted Sasaki metrics induced by the conformal class of $g$. New examples are shown of manifolds with constant positive or with constant negative scalar curvature, which are not Einstein. Recalling results on the associated almost complex structure $I^G$ and symplectic structure ${\omega}^G$ on the manifold $TM$, generalizing the well-known structure of Sasaki by admitting weights and connections with torsion, we compute the Chern and the Stiefel-Whitney characteristic classes of the manifolds $TM$ and $S_rM$.Comment: 15 pages, to appear in Journal of Geometr

Nature of the X(5568) : a critical Laplace sum rule analysis at N2LO

We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)\bar(bd) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (\tau-sum rule variable, t_c continuum threshold and subtraction constant \mu). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results + the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173\sim 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavours (buds), do not support some previous interpretations of the D0 candidate[1], X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: sin 2\theta\approx 0.15. One can also scan the region (2327~ 2444) MeV (where the D*_{s0}(2317) might be a good candidate) and the one (5173~ 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or \pi+hadrons decays.Comment: Version matching with the publised version : some references added and updated, comments added, misprint corrected (51 pages, 66 figures, 7 tables

Heisenberg model in a random field: phase diagram and tricritical behavior

By using the differential operator technique and the effective field theory scheme we study the tricritical behavior of Heisenberg classical model of spin-1/2 in a random field. The phase diagram in the T-h plane on a square and simple cubic lattice for a cluster with two spins is obtained when the random field is bimodal distributed.Comment: 10 pages, 1 figur

Selection of cassava parents by morphological and agronomic TRAITS, and genetic divergence analysis.

Brazil has been suggested as the center of origin and domestication of cassava (Allem 1987, Olsen and Schaal 1999, 2001). In the Amazon region, cassava is mainly grown as a subsistence crop by small farmers, thanks to its ease of cultivation, cheap production and its ability to tolerate poor soils. Moreover it suffers from few serious pests and disease

Controle integrado da podridão mole das raízes de mandioca no trópico úmido.

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