A note on the moment map on compact K\"ahler manifolds

We consider compact K\"ahler manifolds acted on by a connected compact Lie group $K$ of isometries in Hamiltonian fashion. We prove that the squared moment map $\|\mu\|^2$ is constant if and only if the manifold is biholomorphically and $K$-equivariantly isometric to a product of a flag manifold and a compact K\"ahler manifold which is acted on trivially by $K$. The authors do not know whether the compactness of $M$ is essential in the main theorem; more generally it would be interesting to have a similar result for (compact) symplectic manifolds.Comment: 4 page

Homogeneous Hypercomplex Structures and the Joyce's Construction

We prove that any invariant hypercomplex structure on a homogeneous space $M = G/L$ where $G$ is a compact Lie group is obtained via the Joyce's construction, provided that there exists a hyper-Hermitian naturally reductive invariant metric on $M$.Comment: 11 page

Numerical solution of three-dimensional rectangular submerged jets with the evidence of the undisturbed region of flow

The evolution of turbulent rectangular submerged free jets has been investigated numerically with a two-dimensional (2D) approach by the present authors and, by using the large eddy simulations (LES) at several Reynolds numbers. The average numerical results confirmed the presence of the undisturbed region of flow (URF) located between the slot exit and the beginning of the potential core region (PCR) previously observed experimentally at the University of Rome “Tor Vergata” by Gori and coworkers. The 2D study of the present authors carried out under the conditions previously investigated in the literature, showed that the URF has a self-similar behavior, and proposed a new law for the evolution of the momentum. The present paper extends the LES to three-dimensional (3D) rectangular submerged free jets, in the range from Re =5,000 to Re =40,000, showing that the self-similar behavior of URF is also present in the 3D numerical simulations, as well as in the PCR and in the fully developed region (FDR)

Herbal Medicine Today: Clinical and Research Issues

Herbal medicine is the use of medicinal plants for prevention and treatment of diseases: it ranges from traditional and popular medicines of every country to the use of standardized and tritated herbal extracts. Generally cultural rootedness enduring and widespread use in a Traditional Medical System may indicate safety, but not efficacy of treatments, especially in herbal medicine where tradition is almost completely based on remedies containing active principles at very low and ultra low concentrations, or relying on magical-energetic principles

A 2d-Numerical Study on Slot Jet Applied to a Wind Turbine as a Circulation Control Technique

The file attached to this record is the author's final peer reviewed version.A study on the feasibility of the Circulation Control (CC) technique for wind turbines is proposed. The CC was born in aeronautic field to improve the lift force on the wings, allowing the short take-off and landing of aircraft. It consists in blowing air at a relatively high speed over a rounded trailing edge. The thin jet of air remains attached to the convex curved surface, imposing a certain curvature to the outer streamlines, and, hence, increasing the lift force of the airfoil. Aim of this study is to numerically investigate the advantages on a wind turbine, based on the S809 airfoil, taking into account the energy related considerations, as the cost of the jet production. The paper, after a thorough evaluation of the increase of the generated power, finds that this technique could be promising in the energy harvesting aim

Thermophysical parameter estimation of multi-layer walls with stochastic optimization methods

The problem of the estimation of thermal conductivities of multi-layer walls is studied using genetic algorithms and simulated annealing. Parameter estimation is shown for the cases of three- and five- layer walls, comparing the two stochastic approaches and also contrasting them with deterministic gradient-based methods. It is shown how stochastic methods permit better performances than classical ones when initial estimations of parameter values are not available or when the problem becomes complex

On a Criterion of Local Invertibility and Conformality for Slice Regular Quaternionic Functions

A new criterion for local invertibility of slice regular quaternionic functions is obtained. This paper is motivated by the need to find a geometrical interpretation for analytic conditions on the real Jacobian associated with a slice regular function f. The criterion involves spherical and Cullen derivatives of f and gives rise to several geometric implications, including an application to related conformality properties