Search results for "Manifold"
showing 10 items of 415 documents
Long-Time Behaviour for the Brownian Heat Kernel on a Compact Riemannian Manifold and Bismut’s Integration-by-Parts Formula
2007
We give a probabilistic proof of the classical long-time behaviour of the heat kernel on a compact manifold by using Bismut’s integration-by-parts formula.
Verification of IRRILAB Software Application for the Hydraulic Design of a Micro-Irrigation System by Using IRRIPRO for an Apple Farm in Sicily
2021
In recent years, many studies have been performed to develop simple and accurate methods to design micro-irrigation systems. However, most of these studies are based on numerical solutions that require a high number of iterations and attempts, without ensuring to maximize water use efficiency and energy-saving. Recently, the IRRILAB software, which is based on an analytical approach to optimally design rectangular micro-irrigation units, has been developed, providing the solution corresponding to the maximum energy-saving condition, for any slope of the laterals and of the manifold. One IRRILAB limitation is that, according to its theoretical basis, the rectangular planform geometry and uni…
Recent Progress in the WCLL Breeding Blanket Design for the DEMO Fusion Reactor
2018
The water-cooled lithium-lead (PbLi) breeding blanket is one of the candidate systems considered for the implementation in the European Demonstration Power Plant (DEMO) nuclear fusion reactor. This concept employs PbLi liquid metal as tritium breeder and neutron multiplier, water pressurized at 15.5 MPa as the coolant, and EUROFER as the structural material. The current design is based on the single module segment approach and follows the requirements of the DEMO-2015 baseline design. The module is constituted by a basic toroidal-radial cell that is recursively repeated along the poloidal direction where the liquid metal flows along a radial-poloidal path. The heat generated by the fusion r…
A blow-up result for a nonlinear wave equation on manifolds: the critical case
2021
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.
4-Manifold topology II: Dwyer's filtration and surgery kernels
1995
Even when the fundamental group is intractable (i.e. not "good") many interesting 4-dimensional surgery problems have topological solutions. We unify and extend the known examples and show how they compare to the (presumed) counterexamples by reference to Dwyer's filtration on second homology. The development brings together many basic results on the nilpotent theory of links. As a special case, a class of links only slightly smaller than "homotopically trivial links" is shown to have (free) slices on their Whitehead doubles.
On one-dimensionality of metric measure spaces
2019
In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to an arbitrary measure, is a one-dimensional manifold (possibly with boundary). As an immediate corollary we obtain that if a metric measure space is a very strict $CD(K,N)$ -space or an essentially non-branching $MCP(K,N)$-space with some open set isometric to an interval, then it is a one-dimensional manifold. We also obtain the same conclusion for a metric measure space which has a point in which the Gromov-Hausdorff tangent is unique and isometric to the real line, and fo…
Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type
2018
Let $\mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of Mihlin--H\"ormander type and wave propagator estimates of Miyachi--Peral type for $\mathscr{L}$ cannot be wider than the corresponding ranges for the Laplace operator on $\mathbb{R}^n$. The result applies to all sub-Laplacians on Carnot groups and more general sub-Riemannian manifolds, without restrictions on the step. The proof hinges on a Fourier integral representation for the wave propagator associated with $\mathscr{L}$ and nondegeneracy properties of the sub…
Broglie and Young, visionaries who shed light in the polar topology that grounds our reality: a hypothesis
2020
Una observación matemática que relaciona los patrones fractales y la operación de convolución en el contexto del procesamiento de imágenes digitales interrumpió una investigación que nos lleva a plantear la hipótesis de que el concepto de onda de materia (o dualidad onda-partícula) se encuentra en la dicotomía entre el par débil y un topología fuerte en el ámbito del marco de atractores singulares continuos en ninguna parte diferenciables y el concepto de fotón-solitón de Vigier. Tal inferencia parece ser más evidente en la interpretación de Broglie-Bohm de la mecánica cuántica en el cruce de características locales x globales. De esto se deduce también que la relación de los fenómenos natu…
Champs de vecteurs analytiques commutants, en dimension 3 ou 4: existence de zeros communs
1992
One proves the existence of a common zero for any two ℝ-analytic commuting vector fields on a 4-dimensional manifold with not zero Euler characteristic. A local version of this result remains true on 3-manifolds.