Search results for "interpolation."
showing 10 items of 253 documents
Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data
2013
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression techniques, particularly when the goal is the estimation of simple quantities such as means or totals. We extend, in this functional framework, model-assisted estimators with linear regression models that can take account of auxiliary variables whose totals over the population are known. We first show, under weak hypotheses on the sampling design and the regularity of the trajectories, that the estimator of the mean function as well as its variance estimator …
A note on Malliavin smoothness on the Lévy space
2017
We consider Malliavin calculus based on the Itô chaos decomposition of square integrable random variables on the Lévy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and fractional differentiability can be determined by weighted Lebesgue spaces. The measurability condition is satisfied for all random variables if the underlying Lévy process is a compound Poisson process on a finite time interval. peerReviewed
Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements
2019
In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivativ…
Geometric deformation measurement and correction applied to dynamic streak camera images
2002
The complete procedure of measuring and correcting geometric deformations encountered with dynamic streak camera images in the picosecond range is presented and discussed. First, we describe the experimental setup derived from the well known spacing calibration grid method. The implemented measurement bench, adapted to time-resolved 1D imaging, notably exhibits a great accuracy and repeatability both in space and time thanks to a three-axis motorized translation stage and programmable delay lines. Second, we examine image restoration by two different analytical transform means (local versus global): results and performances of both are compared. Then we deal with final image reconstruction …
Verification of linear hybrid systems with large discrete state spaces using counterexample-guided abstraction refinement
2017
Abstract We present a counterexample-guided abstraction refinement ( CEGAR) approach for the verification of safety properties of linear hybrid automata with large discrete state spaces, such as naturally arising when incorporating health state monitoring and degradation levels into the controller design. Such models can – in contrast to purely functional controller models – not be analyzed with hybrid verification engines relying on explicit representations of modes, but require fully symbolic representations for both the continuous and discrete part of the state space. The presented abstraction methods directly work on a symbolic representation of arbitrary non-convex combinations of line…
Spline Algorithms for Deconvolution and Inversion of Heat Equation
2014
In this chapter, we present algorithms based on Tikhonov regularization for solving two related problems: deconvolution and inversion of heat equation. The algorithms, which utilize the SHA technique, provide explicit solutions to the problems in one and two dimensions.
Evolution semigroups and time operators on Banach spaces
2010
AbstractWe present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces.
Geometric mean and triangles inscribed in a semicircle in Banach spaces
2008
AbstractWe consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces.
p-VARIATION OF VECTOR MEASURES WITH RESPECT TO BILINEAR MAPS
2008
AbstractWe introduce the spaces Vℬp(X) (respectively 𝒱ℬp(X)) of the vector measures ℱ:Σ→X of bounded (p,ℬ)-variation (respectively of bounded (p,ℬ)-semivariation) with respect to a bounded bilinear map ℬ:X×Y →Z and show that the spaces Lℬp(X) consisting of functions which are p-integrable with respect to ℬ, defined in by Blasco and Calabuig [‘Vector-valued functions integrable with respect to bilinear maps’, Taiwanese Math. J. to appear], are isometrically embedded in Vℬp(X). We characterize 𝒱ℬp(X) in terms of bilinear maps from Lp′×Y into Z and Vℬp(X) as a subspace of operators from Lp′(Z*) into Y*. Also we define the notion of cone absolutely summing bilinear maps in order to describe t…
In silicoAntibacterial Activity Modeling Based on the TOMOCOMD-CARDD Approach
2015
In the recent times, the race to cope with the increasing multidrug resistance of pathogenic bacteria has lost much of its momentum and health professionals are grasping for solutions to deal with the unprecedented resistance levels. As a result, there is an urgent need for a concerted effort towards the development of new antimicrobial drugs to stay ahead in the fight against the ever adapting bacteria. In the present report, antibacterial classification functions (models) based on the topological molecular computational design-computer aided >rational> drug design (TOMOCOMD-CARDD) atom-based non-stochastic and stochastic bilinear indices are presented. These models were built using the li…