Search results for " set"
showing 10 items of 2095 documents
Ab initio simulations on AgCl(111) surface and AgCl(111)/α-Al2O3(0001) interface
2005
The defect chemistry and ionic transport properties of the AgCl(111)/α-Al 2 O 3 (0001) interface were consid by using ab initio slab calculations. These calculations were performed in the framework of plane-wave basis combined with the density functional theory (DFT), as implemented into the VASP computer code, and Gaus basis set combined with the Hartree-Fock method (CRYSTAL-98 code). We analyze the electron density distribu on the interface and the electrostatic potential distribution near the AgCl surface. The size of the silver ion is great to enter the corundum surface layer and to create excess silver ions in this way. This is in agreement the experiments on heterogeneous doping of Ag…
Finite Alphabet Control of Logistic Networks with Discrete Uncertainty
2014
We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative exampl…
HyperLabelMe : A Web Platform for Benchmarking Remote-Sensing Image Classifiers
2017
HyperLabelMe is a web platform that allows the automatic benchmarking of remote-sensing image classifiers. To demonstrate this platform's attributes, we collected and harmonized a large data set of labeled multispectral and hyperspectral images with different numbers of classes, dimensionality, noise sources, and levels. The registered user can download training data pairs (spectra and land cover/use labels) and submit the predictions for unseen testing spectra. The system then evaluates the accuracy and robustness of the classifier, and it reports different scores as well as a ranked list of the best methods and users. The system is modular, scalable, and ever-growing in data sets and clas…
Word assembly through minimal forbidden words
2006
AbstractWe give a linear-time algorithm to reconstruct a finite word w over a finite alphabet A of constant size starting from a finite set of factors of w verifying a suitable hypothesis. We use combinatorics techniques based on the minimal forbidden words, which have been introduced in previous papers. This improves a previous algorithm which worked under the assumption of stronger hypothesis.
Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes
2006
A multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infi…
The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities
2015
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal everywhere to the original function. Thus, the method is specially suited for constructing families of fractal objects arising from a conserved physical quantity, the decomposition yielding an exact partition of the quantity in question. Most prominent classes of examples are provided by Hamiltonians and partition functions of statistical ensembles: By using this method, any such function can be decomposed in the ordinary sum of a specified number of terms (g…
Weak separation condition, Assouad dimension, and Furstenberg homogeneity
2015
We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine sets. In addition to dimension results for the limit set, we manage to express the Assouad dimension of any closed subset of a self-conformal set by means of the Hausdorff dimension. As an interesting consequence of this, we show that a Furstenberg homogeneous self-similar set in the real line satisfies the weak separation condition. We also exhibit a self-similar set which satisfies the open set condition but fails to be Furstenberg homogeneous.
Dimension estimates on circular (s,t)-Furstenberg sets
2023
In this paper, we show that circular $(s,t)$-Furstenberg sets in $\mathbb R^2$ have Hausdorff dimension at least $$\max\{\frac{t}3+s,(2t+1)s-t\} \text{ for all $0<s,t\le 1$}.$$ This result extends the previous dimension estimates on circular Kakeya sets by Wolff.
Curve packing and modulus estimates
2018
A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c > 0$. We strengthen Marstrand's result by showing that for $p > 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} > 0$.
Removable singularities for div v=f in weighted Lebesgue spaces
2018
International audience; Let $w\in L^1_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p_{1/w}$, $1<p<+\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author.