Mapping prior information onto LMI eigenvalue-regions for discrete-time subspace identification

In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding LMI regions. In this paper, first we argue on what kind of practical information can be extracted from historical data or step-response experiments to possibly improve the dynamical properties of the corresponding model and, also, on how to mitigate the effect of the uncertainty on such information. For instance, prior knowledge regarding the overshoot, the period between damped oscillations and settling time may be useful to constraint the possible locations of the eigenvalues of the discrete-time model. Then, we show how to map the prior information onto LMI regions and, when the obtaining regions are non-convex, to obtain convex approximations.Comment: Under revie

Proton and neutron polarized structure functions from low to high Q**2

Phenomenological parameterizations of proton and neutron polarized structure functions, g1p and g1n, are developed for x > 0.02 using deep inelastic data up to ~ 50 (GeV/c)**2 as well as available experimental results on photo- and electro-production of nucleon resonances. The generalized Drell-Hearn-Gerasimov sum rules are predicted from low to high values of Q**2 and compared with proton and neutron data. Furthermore, the main results of the power correction analysis carried out on the Q**2-behavior of the polarized proton Nachtmann moments, evaluated using our parameterization of g1p, are briefly summarized.Comment: Proceedings of the II International Symposium on the Gerasimov-Drell-Hearn sum rule and the spin structure of the nucleon, Genova (Italy), July 3-6, 200

Neutron structure function moments at leading twist

The experimental data on F2 structure functions of the proton and deuteron were used to construct their moments. In particular, recent measurements performed with CLAS detector at Jefferson Lab allowed to extend our knowledge of structure functions in the large-x region. The phenomenological analysis of these experimental moments in terms of the Operator Product Expansion permitted to separate the leading and higher twist contributions. Applying nuclear corrections to extracted deuteron moments we obtained the contribution of the neutron. Combining leading twist moments of the neutron and proton we found d/u ratio at x->1 approaching 0, although 1/5 value could not be excluded. The twist expansion analysis suggests that the contamination of higher twists influences the extraction of the d/u ratio at x->1 even at Q2-scale as large as 12 (GeV/c)^2.Comment: To appear in proceedings of Quark Confinement and the Hadron Spectrum VII Conference, Ponta Delgada, Portugal, 2-7 September 200

Possible evidence of extended objects inside the proton

Recent experimental determinations of the Nachtmann moments of the inelastic structure function of the proton F2p(x, Q**2), obtained at Jefferson Lab, are analyzed for values of the squared four-momentum transfer Q**2 ranging from ~ 0.1 to ~ 2 (GeV/c)**2. It is shown that such inelastic proton data exhibit a new type of scaling behavior and that the resulting scaling function can be interpreted as a constituent form factor consistent with the elastic nucleon data. These findings suggest that at low momentum transfer the inclusive proton structure function originates mainly from the elastic coupling with extended objects inside the proton. We obtain a constituent size of ~ 0.2 - 0.3 fm.Comment: 1 reference adde

Comment on "Nucleon elastic form factors and local duality"

We comment on the papers "Nucleon elastic form factors and local duality" [Phys. Rev. {\bf D62}, 073008 (2000)] and "Experimental verification of quark-hadron duality" [Phys. Rev. Lett. {\bf 85}, 1186 (2000)]. Our main comment is that the reconstruction of the proton magnetic form factor, claimed to be obtained from the inelastic scaling curve thanks to parton-hadron local duality, is affected by an artifact.Comment: to appear in Phys. Rev.

A necessary condition for extremality of solutions to autonomous obstacle problems with general growth

Let us consider the autonomous obstacle problemmin(v) integral(Omega) F(Dv(x)) dxon a specific class of admissible functions, where we suppose the Lagrangian satisfies proper hypotheses of convexity and superlinearity at infinity. Our aim is to find a necessary condition for the extremality of the solution, which exists and it is unique, thanks to a primal-dual formulation of the problem. The proof is based on classical arguments of Convex Analysis and on Calculus of Variations' techniques. (c) 2023 Elsevier Ltd. All rights reserved

Regularity for obstacle problems without structure conditions

This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurance of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap are needed. The main tool used here is a ingenious Lemma which reveals to be crucial because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions' regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients