Search results for "heat kernel"
showing 10 items of 12 documents
Geometry and analysis of Dirichlet forms
2012
Let $ \mathscr E $ be a regular, strongly local Dirichlet form on $L^2(X, m)$ and $d$ the associated intrinsic distance. Assume that the topology induced by $d$ coincides with the original topology on $ X$, and that $X$ is compact, satisfies a doubling property and supports a weak $(1, 2)$-Poincar\'e inequality. We first discuss the (non-)coincidence of the intrinsic length structure and the gradient structure. Under the further assumption that the Ricci curvature of $X$ is bounded from below in the sense of Lott-Sturm-Villani, the following are shown to be equivalent: (i) the heat flow of $\mathscr E$ gives the unique gradient flow of $\mathscr U_\infty$, (ii) $\mathscr E$ satisfies the Ne…
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.
Microbial dynamics in durum wheat kernels during aging
2020
In the present work the microbial dynamics in wheat kernels were evaluated over time. The main aim of this research was to study the resistance of lactic acid bacteria (LAB) and yeasts associated to unprocessed cereals used for bread making during long term conservation. To this purpose four Triticum durum Desf. genotypes including two modern varieties (Claudio and Simeto) and two Sicilian wheat landraces (Russello and Timilia) were analysed by a combined culture-independent and -dependent microbiological approach after one, two or three years from cultivation and threshing. DNA based MiSeq Illumina technology was applied to reveal the entire bacterial composition of all semolina samples. T…
Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces
2003
Abstract We use the heat equation to establish the Lipschitz continuity of Cheeger-harmonic functions in certain metric spaces. The metric spaces under consideration are those that are endowed with a doubling measure supporting a (1,2)-Poincare inequality and in addition supporting a corresponding Sobolev–Poincare-type inequality for the modification of the measure obtained via the heat kernel. Examples are given to illustrate the necessity of our assumptions on these spaces. We also provide an example to show that in the general setting the best possible regularity for the Cheeger-harmonic functions is Lipschitz continuity.
Heat Kernel Measure on Central Extension of Current Groups in any Dimension
2006
We define measures on central extension of current groups in any dimension by using infinite dimensional Brownian motion.
Ecology of yeasts associated with kernels of several durum wheat genotypes and their role in co-culture with Saccharomyces cerevisiae during dough le…
2021
International audience; This work was performed to investigate on the yeast ecology of durum wheat to evaluate the interaction between kernel yeasts and the commercial baker's yeast Saccharomyces cerevisiae during dough leavening. Yeast populations were studied in 39 genotypes of durum wheat cultivated in Sicily. The highest level of kernel yeasts was 2.9 Log CFU/g. A total of 413 isolates was collected and subjected to phenotypic and genotypic characterization. Twenty-three yeast species belonging to 11 genera have been identified. Filobasidium oeirense, Sporobolomyces roseus and Aureobasidium pullulans were the species most commonly found in durum wheat kernels. Doughs were co-inoculated …
Malliavin Calculus of Bismut Type for Fractional Powers of Laplacians in Semi-Group Theory
2011
We translate into the language of semi-group theory Bismut's Calculus on boundary processes (Bismut (1983), Lèandre (1989)) which gives regularity result on the heat kernel associated with fractional powers of degenerated Laplacian. We translate into the language of semi-group theory the marriage of Bismut (1983) between the Malliavin Calculus of Bismut type on the underlying diffusion process and the Malliavin Calculus of Bismut type on the subordinator which is a jump process.
A more distinctive representation for 3D shape descriptors using principal component analysis
2015
Many researchers have used the Heat Kernel Signature (or HKS) for characterizing points on non-rigid three-dimensional shapes and Classical Multidimensional Scaling (Classical MDS) method in object classification which we quote, in particular, the example of Jian Sun et al. (2009) [1]. However, in this paper, the main focuses on classification that we propose a concise and provably factorial method by invoking Principal Component Analysis (PCA) as a classifier to improve the scheme of 3D shape classification. To avoid losing or disordering information after extracting features from the mesh, PCA is used instead of the Classical MDS to discriminate-as much as possible-feature points for each…
Gradient estimates for heat kernels and harmonic functions
2020
Let $(X,d,\mu)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carr\'e du champ". Assume that $(X,d,\mu,\E)$ supports a scale-invariant $L^2$-Poincar\'e inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for $p\in (2,\infty]$: (i) $(G_p)$: $L^p$-estimate for the gradient of the associated heat semigroup; (ii) $(RH_p)$: $L^p$-reverse H\"older inequality for the gradients of harmonic functions; (iii) $(R_p)$: $L^p$-boundedness of the Riesz transform ($p<\infty$); (iv) $(GBE)$: a generalised Bakry-\'Emery condition. We show that, for $p\in (2,\infty)$, (i), (ii) (iii) are equivalent, wh…
A nonlocal problem arising from heat radiation on non-convex surfaces
1997
We consider both stationary and time-dependent heat equations for a non-convex body or a collection of disjoint conducting bodies with Stefan-Boltzmann radiation conditions on the surface. The main novelty of the resulting problem is the non-locality of the boundary condition due to self-illuminating radiation on the surface. Moreover, the problem is nonlinear and in the general case also non-coercive. We show that the non-local boundary value problem admits a maximum principle. Hence, we can prove the existence of a weak solution assuming the existence of upper and lower solutions. This result is then applied to prove existence under some hypotheses that guarantee the existence of sub- and…