Search results for "SETS"

Games without repetitions on graphs with vertex disjoint cycles

1997

Games without repetitions on graphs with vertex disjoint cycles are considered. We show that the problem finding of the game partition in this class reduces to this problem for trees. A method of finding of the game partition for trees have been given in [2].

Hierarchical modeling for rare event detection and cell subset alignment across flow cytometry samples.

2013

Flow cytometry is the prototypical assay for multi-parameter single cell analysis, and is essential in vaccine and biomarker research for the enumeration of antigen-specific lymphocytes that are often found in extremely low frequencies (0.1% or less). Standard analysis of flow cytometry data relies on visual identification of cell subsets by experts, a process that is subjective and often difficult to reproduce. An alternative and more objective approach is the use of statistical models to identify cell subsets of interest in an automated fashion. Two specific challenges for automated analysis are to detect extremely low frequency event subsets without biasing the estimate by pre-processing…

Vagueness and Roughness

2008

The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak's rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent's point of view. Some algebraic operations on…

The Kuratowski convergence and connected components

2012

International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.

Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets

2014

The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to …

A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter

2021

The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalueλβwith negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer forλβand the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.

On dependence of sets of functions on the mean value of their elements

2009

The paper considers, for a given closed bounded set M ⊂ R m and K = (0,1) n ⊂ R n , the set M = {h ϵ L2 (K;R m ) | h(x) ϵ M a.e.x ϵ K} and its subsets It is shown that, if a sequence {hk } ⊂ coM converges to an element hk ϵ M(hk ) there is h‘k ϵ M(ho ) such that h'k - hk → 0 as k → ∞ . If, in addition, the set M is finite or M is the convex hull of a finite set of elements, then the multivalued mapping h → M(h) is lower semicontinuous on coM. First published online: 14 Oct 2010

Syntheses, Structures, Magnetic Properties, and Density Functional Theory Magneto-Structural Correlations of Bis(μ-phenoxo) and Bis(μ-phenoxo)-μ-acet…

2013

The bis(mu-phenoxo) (FeNiIII)-Ni-II compound [Fe-III(N-3)(2)LNiII(H2O)(CH3CN)](ClO4) (1) and the bis(mu-phenoxo)-mu-acetate/bis(mu-phenoxo)-bis(mu-acetate) (FeNiII)-Ni-III compound {[Fe-III(OAc)LNiII(H2O)(mu-OAc)](0.6)center dot[(FeLNiII)-L-III(mu-OAc)(2)](0.4)}(ClO4)center dot 1.1H(2)O (2) have been synthesized from the Robson type tetraiminodiphenol macrocyclic ligand H2L, which is the [2 + 2] condensation product of 4-methyl-2,6-diformylphenol and 2,2'-dimethy1-1,3-diaminopropane. Single-crystal X-ray structures of both compounds have been determined. The cationic part of the dinuclear compound 2 is a cocrystal of the two species [Fe-III(OAc)LNiII(H2O)(mu-OAc)](+) (2A) and [(FeLNiII)-L-I…

Sigma-fragmentability and the property SLD in C(K) spaces

AbstractWe characterize two topological properties in Banach spaces of type C(K), namely, being σ-fragmented by the norm metric and having a countable cover by sets of small local norm-diameter (briefly, the property norm-SLD). We apply our results to deduce that Cp(K) is σ-fragmented by the norm metric when K belongs to a certain class of Rosenthal compacta as well as to characterize the property norm-SLD in Cp(K) in case K is scattered.

Machine learning risk prediction of mortality for patients undergoing surgery with perioperative SARS-CoV-2: the COVIDSurg mortality score

2021

The British journal of surgery 108(11), 1274-1292 (2021). doi:10.1093/bjs/znab183