Search results for "Truncation"
showing 10 items of 56 documents
Comparison of free software platforms for the calculation of the 90% confidence interval of f2 similarity factor by bootstrap analysis
2020
Abstract Introduction The calculation of the 90% confidence interval of f2 based on the bootstrap methodology has been proposed and accepted by the main regulatory authorities when the dissolution data shows excessive variability. Different free software platforms allow the calculation of the 90% CI of f2 by means of bootstrapping. Their use in regulatory submissions is growing, but divergent results have been observed between the available software platforms. Therefore, the objective of this work is to analyze the characteristics of these software platforms and evaluate their results. Methods and materials Highly variable in vitro dissolution data from two products were selected. Three dif…
A Seven Mode Truncation of the Kolmogorov Flow with Drag: Analysis and Control
2009
The transition from laminar to chaotic motions in a viscous °uid °ow is in- vestigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov °ow with drag friction. An- alytical expressions of the Hopf bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynolds num- ber is increased for ¯xed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is ob- tained through a model reference approach which makes the control global. Finally, the e®ectiveness of this control strategy is numerically illustra…
The electron self-energy in QED at two loops revisited
2018
We reconsider the two-loop electron self-energy in quantum electrodynamics. We present a modern calculation, where all relevant two-loop integrals are expressed in terms of iterated integrals of modular forms. As boundary points of the iterated integrals we consider the four cases $p^2=0$, $p^2=m^2$, $p^2=9m^2$ and $p^2=\infty$. The iterated integrals have $q$-expansions, which can be used for the numerical evaluation. We show that a truncation of the $q$-series to order ${\mathcal O}(q^{30})$ gives numerically for the finite part of the self-energy a relative precision better than $10^{-20}$ for all real values $p^2/m^2$.
Axial behavior of diffractive lenses under Gaussian illumination: complex-argument spectral analysis
1999
We present a general procedure to analyze the axial-irradiance distribution generated by an unlimited diffractive lens under coherent, Gaussian illumination. The resulting on-axis diffraction pattern, which is evaluated in terms of the power complex spectrum of the Fresnel-zone transmittance, explicitly depends on the truncation parameter that we define, which evaluates the effective number of zones illuminated by the Gaussian beam. Depending on the value of this parameter, different kinds of axial behavior are observed. In particular, for moderate values a multiple-focal-shift phenomenon appears, and a simple formula for its evaluation is presented. Additionally, for low values of the trun…
Geometric operators in the asymptotic safety scenario for quantum gravity
2019
We consider geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the role of these operators from the Asymptotic Safety perspective, and compute their anomalous dimensions within the Einstein-Hilbert truncation. We also discuss certain subtleties arising in the definition of such geometric operators. Our results hint to an effective dimensional reduction of the considered geometric operators.
Unitary time-dependent superconvergent technique for pulse-driven quantum dynamics
2003
We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the KAM transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime.
Cyclical behaviour and disc truncation in the Be/X-ray binary A0535+26
2003
A0535+26 is shown to display quantised IR excess flux states, which are interpreted as the first observational verification of the resonant truncation scheme proposed by Okazaki and Negueruela (2001) for BeXRBs. The simultaneity of X-ray activity with transitions between these states strongly suggests a broad mechanism for outbursts, in which material lost from the disc during the reduction of truncation radius is accreted by the NS. Furthermore changes between states are shown to be governed by a 1500 day period, probably due to precession of the Be disc, which profoundly dictates the global behaviour of the system. Such a framework appears to be applicable to BeXRBs in general.
A real-space approach to the analysis of stacking faults in close-packed metals: G(r) modelling and Q-space feedback
2019
An R-space approach to the simulation and fitting of a structural model to the experimental pair distribution function is described, to investigate the structural disorder (distance distribution and stacking faults) in close-packed metals. This is carried out by transferring the Debye function analysis into R space and simulating the low-angle and high-angle truncation for the evaluation of the relevant Fourier transform. The strengths and weaknesses of the R-space approach with respect to the usual Q-space approach are discussed.
Principal polynomial analysis for remote sensing data processing
2011
Inspired by the concept of Principal Curves, in this paper, we define Principal Polynomials as a non-linear generalization of Principal Components to overcome the conditional mean independence restriction of PCA. Principal Polynomials deform the straight Principal Components by minimizing the regression error (or variance) in the corresponding orthogonal subspaces. We propose to use a projection on a series of these polynomials to set a new nonlinear data representation: the Principal Polynomial Analysis (PPA). We prove that the dimensionality reduction error in PPA is always lower than in PCA. Lower truncation error and increased independence suggest that unsupervised PPA features can be b…
Bifurcation phenomena for the positive solutions of semilinear elliptic problems with mixed boundary conditions
2016
We consider a parametric semilinear elliptic equation with a Cara-theodory reaction which exhibits competing nonlinearities. It is "concave" (sub-linear) near the origin and "convex" (superlinear) or linear near $+\infty$. Using variational methods based on the critical point theory, coupled with suitable truncation and comparison techniques, we prove a bifurcation-type theorem, describing the set of positive solutions as the parameter varies.