Search results for "Weighted"
showing 10 items of 190 documents
Characterisation of upper gradients on the weighted Euclidean space and applications
2020
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz functions.
Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift
2015
Abstract This paper deals with the eigenvalue problem for the operator L = − Δ − x ⋅ ∇ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue λ k of L under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any c > 0 and k ∈ N the following minimization problem min { λ k ( Ω ) : Ω quasi-open set , ∫ Ω e | x | 2 / 2 d x ≤ c } has a solution.
Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space
2020
This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains …
The annular decay property and capacity estimates for thin annuli
2016
We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted $\mathbf{R}^n$ and in metric spaces, primarily under the assumptions of an annular decay property and a Poincar\'e inequality. In particular, if the measure has the $1$-annular decay property at $x_0$ and the metric space supports a pointwise $1$-Poincar\'e inequality at $x_0$, then the upper and lower bounds are comparable and we get a two-sided estimate for thin annuli centred at $x_0$, which generalizes the known estimate for the usual variational capacity in unweighted $\mathbf{R}^n$. Most of our estimates are sharp, which we show by supplying several key counterexamples. We also character…
Traces of weighted function spaces: dyadic norms and Whitney extensions
2017
The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.
Analytic Bergman operators in the semiclassical limit
2018
Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.
Comparison and analysis of the revenue-based adaptive queuing models
2006
This paper presents several adaptive resource sharing models that use a revenue criterion to allocate bandwidth in an optimal way. The models ensure QoS requirements of data flows and, at the same time, maximize the total revenue by adjusting parameters of the underlying schedulers. Besides, the adaptive models eliminate the need to find the optimal static weight values because they are calculated dynamically. The simulation consists of several cases that analyse the models and the way they provide the required QoS guarantees. The simulation reveals that the installation of the adaptive model increases the total revenue and ensures the QoS requirements for all service classes. The paper als…
Random Early Detection for Congestion Avoidance in Wired Networks: A Discretized Pursuit Learning-Automata-Like Solution
2010
Published version of an article in the journal: IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works In this paper, we present a learning-automata-like (LAL) mechanism for congestion avoidance in wired networks. Our algorithm, named as LAL random early detection (LALRED), is founded on the principles of the operations of existing RED con…
EFFICIENT MACHINE LEARNING FRAMEWORK FOR COMPUTER-AIDED DETECTION OF CEREBRAL MICROBLEEDS USING THE RADON TRANSFORM
2014
International audience; Recent developments of susceptibility weighted MR techniques have improved visualization of venous vasculature and underlying pathologies such as cerebral microbleed (CMB). CMBs are small round hypointense lesions on MRI images that are emerging as a potential biomarker for cerebrovascular disease. CMB manual rating has limited reliability, is time-consuming and is prone to errors as small CMBs can be easily missed or mistaken for venous crosssections. This paper presents a computer-aided detection technique that utilizes a novel cascade of random forest classifiers which are trained on robust Radon-based features with an unbalanced sample distribution. The training …