Search results for " Mathematics"
showing 10 items of 10797 documents
Design aspects of rating scales in questionnaires
2018
Packing colorings of subcubic outerplanar graphs
2018
Given a graph $G$ and a nondecreasing sequence $S=(s_1,\ldots,s_k)$ of positive integers, the mapping $c:V(G)\longrightarrow \{1,\ldots,k\}$ is called an $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in $c^{-1}(i)$, the distance between $x$ and $y$ is greater than $s_i$. The smallest integer $k$ such that there exists a $(1,2,\ldots,k)$-packing coloring of a graph $G$ is called the packing chromatic number of $G$, denoted $\chi_{\rho}(G)$. The question of boundedness of the packing chromatic number in the class of subcubic (planar) graphs was investigated in several earlier papers; recently it was established that the invariant is unbounded in the class of all sub…
Inhomogeneous long-range percolation in the weak decay regime
2023
We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the transience of infinite clusters.
Miscellaneous Graph Preliminaries
2020
Summary This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library [2] to the best of the author’s knowledge. Most of them regard graph theory as formalized in the GLIB series (cf. [8]) and most of them are preliminaries needed in [7] or other forthcoming articles.
Propositions pour une littérature d’investigation
2017
Le temps semble a l’alliance de la litterature et des sciences sociales. Mais les modalites en sont encore incertaines. Au lieu de considerer l’anthropologie comme une forme de litterature, on peut envisager la litterature comme une enquete. Cette « litterature d’investigation » se donne notamment pour objectif de documenter des formes de vie et de monter des dispositifs rendant compte d’aspects inapercus de phenomenes sociaux. Elle occupe ainsi une position intermediaire : elle se menage a la fois une liberte et une creativite relatives vis-a-vis des protocoles d’enquete propres aux sciences sociales et une certaine mefiance pour un respect trop reverencieux envers la litterature.
A posteriori error majorants of the modeling errors for elliptic homogenization problems
2013
In this paper, we derive new two-sided a posteriori estimates of the modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non-oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity.
A posteriori modelling-discretization error estimate for elliptic problems with L ∞-Coefficients
2017
We consider elliptic problems with complicated, discontinuous diffusion tensor A0. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say Aϵ, and to use standard finite elements. In [19] a combined modelling-discretization strategy has been proposed which estimates the discretization and modelling errors by a posteriori estimates of functional type. This strategy allows to balance these two errors in a problem adapted way. However, the estimate of the modelling error was derived under the assumption that the difference A0 - Aϵ becomes small with respect to the L∞-norm. This implies in particular that interfaces/discontinui…
Modeling mass transfer in fracture flows with the time domain-random walk method
2019
The time domain-random walk method was developed further for simulating mass transfer in fracture flows together with matrix diffusion in surrounding porous media. Specifically, a time domain-random walk scheme was developed for numerically approximating solutions of the advection-diffusion equation when the diffusion coefficient exhibits significant spatial variation or even discontinuities. The proposed scheme relies on second-order accurate, central-difference approximations of the advective and diffusive fluxes. The scheme was verified by comparing simulated results against analytical solutions in flow configurations involving a rectangular channel connected on one side with a porous ma…
"Table 30" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow \nu b \bar{b}$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 41" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Endcap MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow \nu b \bar{b}$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.