Note on the classification theorems of gg-natural metrics on the tangent bundle of a Riemannian manifold (M,g)(M,g)

summary:In [7], it is proved that all $g$-natural metrics on tangent bundles of $m$-dimen\-sional Riemannian manifolds depend on arbitrary smooth functions on positive real numbers, whose number depends on $m$ and on the assumption that the base manifold is oriented, or non-oriented, respectively. The result was originally stated in [8] for the oriented case, but the smoothness was assumed and not explicitly proved. In this note, we shall prove that, both in the oriented and non-oriented cases, the functions generating the $g$-natural metrics are, in fact, smooth on the set of all nonnegative real numbers

On the completeness of total spaces of horizontally conformal submersions

summary:In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of $g$\HH natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem

On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds

AbstractIt is well known that if the tangent bundle TM of a Riemannian manifold (M,g) is endowed with the Sasaki metric gs, then the flatness property on TM is inherited by the base manifold [Kowalski, J. Reine Angew. Math. 250 (1971) 124–129]. This motivates us to the general question if the flatness and also other simple geometrical properties remain “hereditary” if we replace gs by the most general Riemannian “g-natural metric” on TM (see [Kowalski and Sekizawa, Bull. Tokyo Gakugei Univ. (4) 40 (1988) 1–29; Abbassi and Sarih, Arch. Math. (Brno), submitted for publication]). In this direction, we prove that if (TM,G) is flat, or locally symmetric, or of constant sectional curvature, or of constant scalar curvature, or an Einstein manifold, respectively, then (M,g) possesses the same property, respectively. We also give explicit examples of g-natural metrics of arbitrary constant scalar curvature on TM

Radiation heat transfer effect in solid oxide fuel cell: Application of the Lattice Boltzmann Method

the radiation effect within the solid anode, electrolyte, and cathode SOFC layers problem has been investigated in this paper. Energy equation is solved by the Lattice Boltzmann method (LBM). The Rosseland method is used to model the radiative transfer in the electrodes. The Schuster-Schwarzschild method is used to model the radiative transfer in the electrolyte. Without radiatve effect, the found results are in good agreement with those published. The obtained results show that the radiative effect can be neglected

A New Algorithm For Solving Isothermal Carbonization Of Wood Particle

A new algorithm based on the lattice Boltzmann method (LBM) is proposed as a potential solver for one-dimensional heat and mass transfer for isothermal carbonization of thick wood particles. To check the validity of this algorithm, computational results have been compared with the published data and a good agreement is obtained. Then, the model is used to study the effect of reactor temperature and particle size on the evolution of the local temperature and mass loss inside the wood particle

Occurrence of High-Risk Clonal Lineages ST58, ST69, ST224, and ST410 among Extended-Spectrum-Lactamase-Producing Escherichia coli Isolated from Healthy Free-Range Chickens (Gallus gallus domesticus) in a Rural Region in Tunisia

Antimicrobial-resistant Escherichia coli isolates have emerged in various ecologic compartments and evolved to spread globally. We sought to (1.) investigate the occurrence of ESBL-producing E. coli (ESBL-Ec) in feces from free-range chickens in a rural region and (2.) characterize the genetic background of antimicrobial resistance and the genetic relatedness of collected isolates. Ninety-five feces swabs from free-range chickens associated with two households (House 1/House 2) in a rural region in northern Tunisia were collected. Samples were screened to recover ESBL-Ec, and collected isolates were characterized for phenotype/genotype of antimicrobial resistance, integrons, and molecular typing (pulsed-field gel electrophoresis (PFGE) and multilocus sequence typing (MLST)). Overall, 47 ESBL-Ec were identified, with the following genes detected: 35 blaCTX-M-1, 5 blaCTX-M-55, 5 blaCTX-M-15, 1 blaSHV-2, and 1 blaSHV-12. Resistance to fluoroquinolones, tetracycline, sulfonamides, and colistin was encoded by aac(60)-Ib-cr (n = 21), qnrB (n = 1), and qnrS (n = 2); tetA (n = 17)/tetB (n = 26); sul1 (n = 29)/sul2 (n = 18); and mcr-2 (n = 2) genes, respectively. PFGE and MLST identified genetic homogeneity of isolates in House 1; however, isolates from House 2 were heterogeneous. Notably, among nine identified sequence types, ST58, ST69, ST224, and ST410 belong to pandemic high-risk clonal lineages associated with extrapathogenic E. coli. Minor clones belonging to ST410 and ST471 were shared by chickens from both households. The virulence genes fyuA, fimH, papGIII, and iutA were detected in 35, 47, 17, and 23 isolates, respectively. Findings indicate a high occurrence of ESBL-Ec in free-range chickens and highlight the occurrence of pandemic zoonotic clones

WSN for Event Detection Applications: Deployment, Routing, and Data Mapping Using AI

In the 20th century, computers were senseless brains, but today, thanks to sensor networks, they can feel things for themselves. This major trend has given rise to many wireless sensor networks with the ability to sense the environment, deliver findings and process those data appropriately. Within this trend, this chapter outlines deployment and routing strategies as well as data handling practices. For convenience, the most encompassing application to consider is that of event detection