Search results for "Truncation"
showing 10 items of 56 documents
Sharp inequalities via truncation
2003
Abstract We show that Sobolev–Poincare and Trudinger inequalities improve to inequalities on Lorentz-type scales provided they are stable under truncations.
Continuous numerical solutions of coupled mixed partial differential systems using Fer's factorization
1999
In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut A(t)uxx B(t)u=0; 0 0, u(0;t)=u(p;t)=0; u(x;0)=f(x);06 x6p. After truncation of an exact series solution, the numerical solution is constructed using Fer’s factorization. Given >0 and t0;t1; with 0<t0<t1 and D(t0;t1)=f(x;t); 06x6p; t06t6t1g the error of the approximated solution with respect to the exact series solution is less than uniformly in D(t0;t1). An algorithm is also included. c 1999 Elsevier Science B.V. All rights reserved. AMS classication: 65M15, 34A50, 35C10, 35A50
Multiple solutions for nonlinear nonhomogeneous resonant coercive problems
2018
We consider a nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a \begin{document}$p$\end{document} -Laplacian ( \begin{document}$2 ) and a Laplacian. The reaction term is a Caratheodory function \begin{document}$f(z,x)$\end{document} which is resonant with respect to the principal eigenvalue of ( \begin{document}$-\Delta_p,\, W^{1,p}_0(\Omega)$\end{document} ). Using variational methods combined with truncation and comparison techniques and Morse theory (critical groups) we prove the existence of three nontrivial smooth solutions all with sign information and under three different conditions concerning the behavior of \begin{document}$f(z,\cdot)$\end{document} near zero. By …
Scrutinizing the Green's functions of QCD: Lattice meets Schwinger-Dyson
2009
Proceedings of the International Workshop Light Cone 2009 (LC2009): Relativistic Hadronic and Particle Physics. Sao Jose dos Campos, Brazil, July 8-13, 2009.
PARETO OR LOG-NORMAL? BEST FIT AND TRUNCATION IN THE DISTRIBUTION OF ALL CITIES*
2015
In the literature, the distribution of city size is a controversial issue with two common contenders: the Pareto and the log-normal. While the first is most accredited when the distribution is truncated above a certain threshold, the latter is usually considered a better representation for the untruncated distribution of all cities. In this paper, we reassess the empirical evidence on the best-fitting distribution in relation to the truncation point issue. Specifically, we provide a comparison among four recently proposed approaches and alternative definitions of U.S. cities. Our results highlight the importance to look at issue of the best-fitting distribution together with the truncation …
A correction method for dynamic analysis of linear continuous systems
2005
A method to improve the dynamic response analysis of continuous classically damped linear system is proposed. As in fact usually, following a classical approach, a reduced number of eigenfunctions are accounted for and the response is evaluated by integrating the uncoupled differential equations of motion in modal space, neglecting the contribution of high frequency modes (truncation procedure). Here, starting from the given system, it is proposed to set up two differential equations governing the motion of two new continuous systems: the first one contains only the first m non-zero eigenvalues of the given system and the second one contains the remainder non-zero infinity - m eigenvalues. …
TSVD as a Statistical Estimator in the Latent Semantic Analysis Paradigm
2015
The aim of this paper is to present a new point of view that makes it possible to give a statistical interpretation of the traditional latent semantic analysis (LSA) paradigm based on the truncated singular value decomposition (TSVD) technique. We show how the TSVD can be interpreted as a statistical estimator derived from the LSA co-occurrence relationship matrix by mapping probability distributions on Riemanian manifolds. Besides, the quality of the estimator model can be expressed by introducing a figure of merit arising from the Solomonoff approach. This figure of merit takes into account both the adherence to the sample data and the simplicity of the model. In our model, the simplicity…
High-accuracy approximation of piecewise smooth functions using the Truncation and Encode approach
2017
Abstract In the present work, we analyze a technique designed by Geraci et al. in [1,11] named the Truncate and Encode (TE) strategy. It was presented as a non-intrusive method for steady and non-steady Partial Differential Equations (PDEs) in Uncertainty Quantification (UQ), and as a weakly intrusive method in the unsteady case. We analyze the TE algorithm applied to the approximation of functions, and in particular its performance for piecewise smooth functions. We carry out some numerical experiments, comparing the performance of the algorithm when using different linear and non-linear interpolation techniques and provide some recommendations that we find useful in order to achieve a hig…
Singular Neumann (p, q)-equations
2019
We consider a nonlinear parametric Neumann problem driven by the sum of a p-Laplacian and of a q-Laplacian and exhibiting in the reaction the competing effects of a singular term and of a resonant term. Using variational methods together with suitable truncation and comparison techniques, we show that for small values of the parameter the problem has at least two positive smooth solutions.
Multiple solutions for (p,2)-equations at resonance
2019
We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian and a reaction term which is (p− 1)-linear near ±∞ and resonant with respect to any nonprincipal variational eigenvalue of (−∆p, W01,p(Ω)). Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them.