Search results for "analytic function"
showing 10 items of 52 documents
Mode-superposition correction method for deterministic and stochastic analysis of structural systems
2001
The role played by the modal analysis in the framework of structural dynamics is fundamental from both deterministic and stochastic point of view. However the accuracy obtained by means of the classical modal analysis is not always satisfactory. Therefore it is clear the importance of methods able to correct the modal response in such a way to obtain the required accuracy. Many methods have been proposed in the last years but they are meaningful only when the forcing function is expressed by an analytical function. Moreover in stochastic analysis they fail for white noise excitation. In the paper a method able to give a very accurate response for both deterministic and stochastic input is p…
Vector-valued Hardy inequalities and B-convexity
2000
Inequalities of the form $$\sum\nolimits_{k = 0}^\infty {|\hat f(m_k )|/(k + 1) \leqslant C||f||_1 } $$ for allf∈H 1, where {m k } are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy's inequality and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms ff atoms and that they actually characterizeB-convexity. It is also shown that for 1<q<∞ and 0<α<∞ the spaceX=H(1,q,γa) consisting of analytic functions on the unit disc such that $$\int_0^1 {(1 - r)^{q\alpha - 1} M_1^q (f,r) dr< \infty } $$ satisfies the previous inequality for vector valued functions inH 1 (X), defined as the space ofX…
Mapping properties of weakly singular periodic volume potentials in Roumieu classes
2020
The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper, we focus on the mapping properties of the volume potentials with weakly singular periodic kernels. Our main result is to prove that the map which takes a density function and a periodic kernel to a (suitable restriction of the) volume potential is bilinear and continuous with values in a Roumieu class of analytic functions. This result extends to the periodic case of some previous results obtained by the authors for nonperiodic potentials, and it is motivated by the study of perturbation problems for the solut…
A new analytical solar cell I–V curve model
2011
Abstract A simple mathematical equation that can represent empirical I–V curves of individual solar cells, systems of solar cells and modules has been found. The basic model is determined by four parameters: the open circuit voltage, the short circuit current and two shape parameters. With the four parameters determined, the complete current–voltage curve, the fill factor and the maximum power point are given by simple analytical functions. The model is valid both in the positive and the negative (dark condition) voltage range. Several simple examples demonstrate some of the potential of the model. Due to its mathematical simplicity, it is suggested that the model will be suitable for analy…
Numerical solution of a class of nonlinear boundary value problems for analytic functions
1982
We analyse a numerical method for solving a nonlinear parameter-dependent boundary value problem for an analytic function on an annulus. The analytic function to be determined is expanded into its Laurent series. For the expansion coefficients we obtain an operator equation exhibiting bifurcation from a simple eigenvalue. We introduce a Galerkin approximation and analyse its convergence. A prominent problem falling into the class treated here is the computation of gravity waves of permanent type in a fluid. We present numerical examples for this case.
Singular integrals, analytic capacity and rectifiability
1997
In this survey we study some interplay between classical complex analysis (removable sets for bounded analytic functions), harmonic analysis (singular integrals), and geometric measure theory (rectifiability).
A note on the analytic solutions of the Camassa-Holm equation
2005
Abstract In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using the Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic, belongs to H s ( R ) with s > 3 / 2 , ‖ u 0 ‖ L 1 ∞ and u 0 − u 0 x x does not change sign, we prove that the solution stays analytic globally in time. To cite this article: M.C. Lombardo et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).
Parameterization-based tracking for the P2 experiment
2017
The P2 experiment in Mainz aims to determine the weak mixing angle θW at low momentum transfer by measuring the parity-violating asymmetry of elastic electronproton scattering. In order to achieve the intended precision of Δ(sin2 θW )/sin2 θW = 0:13% within the planned 10 000 hours of running the experiment has to operate at the rate of 1011 detected electrons per second. Although it is not required to measure the kinematic parameters of each individual electron, every attempt is made to achieve the highest possible throughput in the track reconstruction chain.In the present work a parameterization-based track reconstruction method is described. It is a variation of track following, where t…
The best fit for the observed galaxy Counts-in-Cell distribution function
2017
The Sloan Digital Sky Survey (SDSS) is the first dense redshift survey encompassing a volume large enough to find the best analytic probability density function that fits the galaxy Counts-in-Cells distribution $f_V(N)$, the frequency distribution of galaxy counts in a volume $V$. Different analytic functions have been previously proposed that can account for some of the observed features of the observed frequency counts, but fail to provide an overall good fit to this important statistical descriptor of the galaxy large-scale distribution. Our goal is to find the probability density function that better fits the observed Counts-in-Cells distribution $f_V(N)$. We have made a systematic stud…
Starlikeness Condition for a New Differential-Integral Operator
2020
A new differential-integral operator of the form I n f ( z ) = ( 1 &minus