Search results for "Linear"
showing 10 items of 7165 documents
A class of quasi-Newton generalized Steffensen methods on Banach spaces
2002
AbstractWe consider a class of generalized Steffensen iterations procedure for solving nonlinear equations on Banach spaces without any derivative. We establish the convergence under the Kantarovich–Ostrowski's conditions. The majorizing sequence will be a Newton's type sequence, thus the convergence can have better properties. Finally, a numerical comparation with the classical methods is presented.
A sequence of positive solutions for sixth-order ordinary nonlinear differential problems
2021
Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
Space of signatures as inverse limits of Carnot groups
2021
We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.
The space H(Ω,(zj)) of holomorphic functions
2008
Abstract Let Ω be a domain in C n . Let H ( Ω ) be the linear space over C of the holomorphic functions in Ω, endowed with the compact-open topology. Let ( z j ) be a sequence in Ω without adherent points in Ω. In this paper, we define the space H ( Ω , ( z j ) ) and some of its linear topological properties are studied. We also show that, for some domains of holomorphy Ω and some sequences ( z j ) , the non-zero elements of H ( Ω , ( z j ) ) cannot be extended holomorphically outside Ω. As a consequence, we obtain some characterizations of the domains of holomorphy in C n .
Extraction of ERP from EEG data
2007
In this article, a simple but novel technique for extracting a linear subspace related to event related potentials (ERPs) from ElectroEncephaloGraphy (EEG) data is introduced. The technique consists of a sequence of basic linear operations applied to multidimensional EEG data in a problem-specific manner. The derivation of the proposed technique is given and results with real data are described together with overall conclusions.
A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates
2019
Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thicknes…
The vertical spectrum of H2CO revisited: (SC)2-CI and CC calculations
2003
The vertical electronic spectrum of formaldehyde has been studied by means of (SC)2-MR-SDCI and CCLR methods. Two basis sets of atomic natural orbitals (ANOs) complemented with a one-centre series of Rydberg orbitals were used. The first was taken from the CASPT2 study by Merchan, M., and Roos, B. O., 1995, Theoret. Chim. Acta, 92, 221, and may be described as C,O[4s3pld]/H[2slp] with a lslpld Rydberg series centred in the charge centroid of the 2B2 state of the cation. The second was a larger basis set that may be described as C,O[6s5p3d2f]/H[4s3p2d] + 3s3p3d in the same centre. The (SC)2 dressing may be applied efficiently to an MR-SDCI method and comparison with the dressed CAS-SDCI is s…
Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: Comparison among different strategie…
2008
We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of $k$-nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application d…
Quantifying the complexity of short-term heart period variability through K nearest neighbor local linear prediction
2008
The complexity of short-term heart period (HP) variability was quantified exploiting the paradigm that associates the degree of unpredictability of a time series to its dynamical complexity. Complexity was assessed through k-nearest neighbor local linear prediction. A proper selection of the parameter k allowed us to perform either linear or nonlinear prediction, and the comparison of the two approaches to infer the presence of nonlinear dynamics. The method was validated on simulations reproducing linear and nonlinear time series with varying levels of predictability. It was then applied to HP variability series measured from healthy subjects during head-up tilt test, showing that short-te…
A new approach to fuzzy sets: Application to the design of nonlinear time series, symmetry-breaking patterns, and non-sinusoidal limit-cycle oscillat…
2019
Abstract It is shown that characteristic functions of sets can be made fuzzy by means of the B κ -function, recently introduced by the author, where the fuzziness parameter κ ∈ R controls how much a fuzzy set deviates from the crisp set obtained in the limit κ → 0. As applications, we present first a general expression for a switching function that may be of interest in electrical engineering and in the design of nonlinear time series. We then introduce another general expression that allows wallpaper and frieze patterns for every possible planar symmetry group (besides patterns typical of quasicrystals) to be designed. We show how the fuzziness parameter κ plays an analogous role to temper…