Search results for "MULTIPLICITY"
showing 10 items of 296 documents
Absolute continuity of mappings with finite geometric distortion
2015
Suppose that ⊂ R n is a domain with n ≥ 2. We show that a continuous, sense-preserving, open and discrete mapping of finite geometric outer distortion with KO(·,f) ∈ L 1/(n 1) loc () is absolutely continuous on almost every line parallel to the coordinate axes. Moreover, if U ⊂ is an open set with N(f,U) 0 depends only on n and on the maximum multiplicity N(f,U).
The rate of multiplicity of the roots of nonlinear equations and its application to iterative methods
2015
Nonsimple roots of nonlinear equations present some challenges for classic iterative methods, such as instability or slow, if any, convergence. As a consequence, they require a greater computational cost, depending on the knowledge of the order of multiplicity of the roots. In this paper, we introduce dimensionless function, called rate of multiplicity, which estimates the order of multiplicity of the roots, as a dynamic global concept, in order to accelerate iterative processes. This rate works not only with integer but also fractional order of multiplicity and even with poles (negative order of multiplicity).
Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
1970
If, for each zero of a polynomial, an approximation is known, estimates for the errors of these approximations are given, based on the evaluation of the polynomial at these points. The procedure can be carried over to the case of multiple roots and root clusters using derivatives up to the orderk - 1, wherek is the multiplicity of the cluster.
Multiple solutions with sign information for semilinear Neumann problems with convection
2019
We consider a semilinear Neumann problem with convection. We assume that the drift coefficient is indefinite. Using the theory of nonlinear operators of monotone type, together with truncation and comparison techniques and flow invariance arguments, we prove a multiplicity theorem producing three nontrivial smooth solutions (positive, negative and nodal).
Multiplicity of fixed points and growth of ε-neighborhoods of orbits
2012
We study the relationship between the multiplicity of a fixed point of a function g, and the dependence on epsilon of the length of epsilon-neighborhood of any orbit of g, tending to the fixed point. The relationship between these two notions was discovered before (Elezovic, Zubrinic, Zupanovic) in the differentiable case, and related to the box dimension of the orbit. Here, we generalize these results to non-differentiable cases introducing a new notion of critical Minkowski order. We study the space of functions having a development in a Chebyshev scale and use multiplicity with respect to this space of functions. With the new definition, we recover the relationship between multiplicity o…
Predictions for 5.023 TeV Pb + Pb collisions at the CERN Large Hadron Collider
2016
We compute predictions for various low-transverse-momentum bulk observables in √sNN = 5.023 TeV Pb+Pb collisions at the CERN Large Hadron Collider (LHC) from the event-by-event next-to-leading-order perturbative-QCD + saturation + viscous hydrodynamics (“EKRT”) model. In particular, we consider the centrality dependence of charged hadron multiplicity, flow coefficients of the azimuth-angle asymmetries, and correlations of event-plane angles. The centrality dependencies of the studied observables are predicted to be very similar to those at 2.76 TeV, and the magnitudes of the flow coefficients and event-plane angle correlations are predicted to be close to those at 2.76 TeV. The flow coeffic…
Study of high-multiplicity three-prong and five-prong τ decays at BABAR
2012
We present measurements of the branching fractions of three-prong and five-prong tau decay modes using a sample of 430 million tau lepton pairs, corresponding to an integrated luminosity of 468 fb(-1), collected with the BABAR detector at the PEP-II asymmetric-energy e_e storage rings at SLAC National Accelerator Laboratory. The tau(-) -> (3 pi)(-) eta nu(tau), tau(-) -> (3 pi)(-) omega nu(tau), and tau(-) f(1) (1285)nu(tau) branching fractions are presented, as well as a new limit on the branching fraction of the second-class current decay tau(-) -> pi(-) eta'(958)nu(tau). We search for the decay mode tau(-) -> K- eta'(958)nu(tau) and for five-prong decay modes with kaons, and place the fi…
Radial solutions of Dirichlet problems with concave-convex nonlinearities
2011
Abstract We prove the existence of a double infinite sequence of radial solutions for a Dirichlet concave–convex problem associated with an elliptic equation in a ball of R n . We are interested in relaxing the classical positivity condition on the weights, by allowing the weights to vanish. The idea is to develop a topological method and to use the concept of rotation number. The solutions are characterized by their nodal properties.
Multiple positive solutions for singularly perturbed elliptic problems in exterior domains
2003
Abstract The equation − e 2 Δ u + a e ( x ) u = u p −1 with boundary Dirichlet zero data is considered in an exterior domain Ω = R N ⧹ ω ( ω bounded and N ⩾2). Under the assumption that a e ⩾ a 0 >0 concentrates round a point of Ω as e →0, that p >2 and p N /( N −2) when N ⩾3, the existence of at least three positive distinct solutions is proved.
An extension of the Burrows-Wheeler Transform and applications to sequence comparison and data compression
2005
We introduce a generalization of the Burrows-Wheeler Transform (BWT) that can be applied to a multiset of words. The extended transformation, denoted by E, is reversible, but, differently from BWT, it is also surjective. The E transformation allows to give a definition of distance between two sequences, that we apply here to the problem of the whole mitochondrial genome phylogeny. Moreover we give some consideration about compressing a set of words by using the E transformation as preprocessing.