This paper provides explicit pointwise formulas for the heat kernel on compact metric measure spaces that belong to a (
N
×
N
)
-parameter family of fractals, which are regarded as projective limits ...of metric measure graphs and do not satisfy the volume doubling property. The formulas are applied to obtain uniform continuity estimates of the heat kernel and to derive an expression of the fundamental solution of the free Schrödinger equation. The results also open up the possibility to approach infinite dimensional spaces based on this model.
With a view towards Riemannian or sub-Riemannian manifolds, RCD metric spaces and specially fractals, this paper proves Sobolev embedding theorems in the general framework of Dirichlet spaces. Under ...suitable assumptions that are verified in a variety of settings, we obtain the whole family of Gagliardo-Nirenberg and Trudinger-Moser inequalities with optimal exponents. These turn out to depend not only on the Hausdorff and walk dimensions of the space but also on other invariants. In addition, we prove Morrey type inequalities and apply them to study the infimum of the exponents that ensure continuity of Sobolev functions. The results are illustrated in the case of fractals with the Vicsek set, whereas several conjectures are made for general nested fractals and the Sierpinski carpet.
Heat kernel analysis on diamond fractals Alonso Ruiz, Patricia
Stochastic processes and their applications,
January 2021, 2021-01-00, Letnik:
131
Journal Article
Recenzirano
Odprti dostop
This paper presents a detailed analysis of the heat kernel on an (N×N)-parameter family of compact metric measure spaces which do not satisfy the volume doubling property. In particular, uniform ...bounds of the heat kernel, its Lipschitz continuity and the continuity of the corresponding heat semigroup are studied; a specific example is presented revealing a logarithmic correction. The estimates are applied to derive functional inequalities of interest in describing the convergence to equilibrium of the diffusion process.
Networking at any time and any place paves the way for a large number of possible applications in ad hoc networks, from disaster relief in remote areas to network extension. Thus, for the past ...decades, many works have been proposed trying to make ad hoc networks a reality. The importance of broadcasting in networking and the broadcast nature of the wireless medium have encouraged researchers to join their efforts on designing efficient dissemination algorithms for Mobile Ad Hoc Networks (MANETs). The many different challenges that MANETs face, such as limited network resources, network partitions, or energy restrictions, gave rise to many different approaches to overcome one or more of those problems. Therefore, literature reveals a huge variety of techniques that have been proposed for efficient message dissemination. In this article, we make an in-depth review of the existing state-of-the-art techniques, as well as propose a new taxonomy that provides a global overview of the most relevant existing algorithms.
Abstract
This paper studies the size of the minimal gap between any two consecutive eigenvalues in the Dirichlet and in the Neumann spectrum of the standard Laplace operator on the Sierpiński gasket. ...The main result shows the remarkable fact that this minimal gap is achieved and coincides with the spectral gap. The Dirichlet case is more challenging and requires some key observations in the behavior of the dynamical system that describes the spectrum.
Mitochondrial prohibitins (PHB) are highly conserved proteins with a peculiar effect on lifespan. While PHB depletion shortens lifespan of wild‐type animals, it enhances longevity of a plethora of ...metabolically compromised mutants, including target of rapamycin complex 2 (TORC2) mutants sgk‐1 and rict‐1. Here, we show that sgk‐1 mutants have impaired mitochondrial homeostasis, lipogenesis and yolk formation, plausibly due to alterations in membrane lipid and sterol homeostasis. Remarkably, all these features are suppressed by PHB depletion. Our analysis shows the requirement of SRBP1/SBP‐1 for the lifespan extension of sgk‐1 mutants and the further extension conferred by PHB depletion. Moreover, although the mitochondrial unfolded protein response (UPRmt) and autophagy are induced in sgk‐1 mutants and upon PHB depletion, they are dispensable for lifespan. However, the enhanced longevity caused by PHB depletion in sgk‐1 mutants requires both, the UPRmt and autophagy, but not mitophagy. We hypothesize that UPRmt induction upon PHB depletion extends lifespan of sgk‐1 mutants through autophagy and probably modulation of lipid metabolism.
TORC2/SGK‐1 mutants have impaired mitochondrial homeostasis, lipogenesis and yolk formation plausibly due to alterations in membrane lipid homeostasis. Depletion of the mitochondrial prohibitin complex suppresses sgk‐1 mutant defects, extending lifespan through autophagy and the mitochondrial UPR.
The transport and logistics sector is of vital importance for the stimulation of trade and hence the economic development of nations. However, over the last few years, this sector has taken central ...stage in the green agenda due to the negative environmental effects derived from its operations. Several disciplines including operations research and sub-areas of supply chain management such as green supply chains, green logistics and reverse logistics have tried to address this problem. However, despite the work undertaken through these disciplines, theoretical or empirical research into the sequential or simultaneous deployment of the lean and green paradigms, particularly, in the road transport and logistics sector is limited. This paper presents a case study where both paradigms have been combined to improve the transport operations of a world leader logistics organisation in the metropolitan area of Monterrey, Mexico. To do this, a systematic methodology and a novel tool called Sustainable Transportation Value Stream Map (STVSM) were proposed. The results obtained from the case study indicate that the concurrent deployment of the green and lean paradigms through such methodology and the STVSM tool is an effective approach to improve both operational efficiency and environmental performance of road transport operations. The paper can be used as a guiding reference for transport and logistics organisations to undertake improvement projects similar to the one presented in this paper. Additionally, this research also intends to stimulate scholarly research into the application of lean and green paradigms in the transport and logistics sector to expand the limited research pursued in this area.
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