1,931 research outputs found
A wavefront tracking algorithm for N×N nongenuinely nonlinear conservation laws
No full textAbstractWe introduce a wavefront tracking algorithm for N×N hyperbolic systems of conservation lawsut+F(u)x=0, that admits characteristic fields that are neither genuinely nonlinear nor linearly degenerate in the sense of Lax. Instead we assume that, for any nongenuinely nonlinear ith characteristic family, the derivative of the ith eigenvalue λi(u) of DF(u) in the direction of the ith right eigenvector ri(u), vanishes on a single (N−1)-dimensional hypersurface in the u-space, transversal to the field ri(u). Systems that fulfill this type of assumptions are of particular interest in studying elastodynamic or rigid heat conductors at low temperature. The first proof of the existence of weak solutions for nongenuinely nonlinear systems was given by T. P. Liu (Mem. Amer. Math. Soc.30 (1981), no. 240), based on a Glimm scheme. Our construction here provides an alternative method for establishing the global existence of weak solutions for such systems. Moreover, relying on the stability analysis developed in Ancona and Marson, preprint S.I.S.S.A.-I.S.A.S. 27/99/11, 1999, and preprint, 2000, we show that these solutions are entropy admissible in the sense of Lax
Decomposition of homogeneous vector fields of degree one and representation of the flow
No full textSummary:
The paper gives a decomposition theorem for the elements of the nonsemisimple Lie algebra of the vector fields on that are homogeneous of degree one with respect to a dilation Each is proved to be equal to with and linear semisimple. As a consequence, the author proves that "in absence of esonance" the vector field is equivalent to its linear part. Finally, the above results are applied to obtain a representation formula for the trajectories of a vector field and those of the affine control system with constant of minimum degree
Le regole processuali dell'accertamento probatorio. Il dibattito contemporaneo al vaglio di un testo tommasiano
No full textThis essay deals with some procedural issues related
to the forensic pursuance of truth, especially
the latest law trends about the judge’s powers of
investigation and the prohibition of judge’s personal knowledge. In the second part the author
shows how the same problems are considered and
solved in an article of Aquinas’ Summa Theologiae
Homogeneous Tangent Vectors and High Order Necessary Conditions for Optimal Controls
No full textSummary:
The author introduces and analyzes "homogeneous" tangent vectors which provide high-order approximations to the attainable set for an affine control system of the form . Homogeneous tangent vectors are defined relative to one-parameter families of dilations on . Adjoint equations associated with the corresponding homogeneous variational equation are derived and used to transport homogeneous tangent vectors along the flow of a reference trajectory. These constructions are then used to derive a homogeneous high-order test for optimality of control problems in Mayer form without terminal constraints. Essentially, it is shown that if is a homogeneous tangent vector with respect to a dilation generated by a control variation, then it is a necessary condition for optimality that , where denotes the solution of the corresponding homogeneous adjoint equation
Studio dell'evoluzione microstrutturale in superleghe e ricoprimenti per palette di turbine e gas con la tecnica del Small Angle Neutron Scattering
No full textRelazione finale del contratto n. 2RTII0427 ENEL- Univ.di Ancona - Febbraio 1991, (Italia
An invariance property of predictors in kernel-induced hypothesis spaces
No full textWe consider kernel-based learning methods for regression and analyze
what happens to the risk minimizer when new variables, statistically
independent of input and target variables, are added to the set of input
variables. This problem arises, for example, in the detection of causality
relations between two time series. We find that the risk minimizer
remains unchanged if we constrain the risk minimization to hypothesis
spaces induced by suitable kernel functions. We show that not all
kernel-induced hypothesis spaces enjoy this property. We present sufficient
conditions ensuring that the risk minimizer does not change and
show that they hold for inhomogeneous polynomial and gaussian radial
basis function kernels. We also provide examples of kernel-induced hypothesis
spaces whose risk minimizer changes if independent variables
are added as input.We consider kernel-based learning methods for regression and analyze what happens to the risk minimizer when new variables, statistically independent of input and target variables, are added to the set of input variables. This problem arises, for example, in the detection of causality relations between two time series. We find that the risk minimizer remains unchanged if we constrain the risk minimization to hypothesis spaces induced by suitable kernel functions. We show that not all kernel-induced hypothesis spaces enjoy this property. We present sufficient conditions ensuring that the risk minimizer does not change and show that they hold for inhomogeneous polynomial and gaussian radial basis function kernels. We also provide examples of kernel-induced hypothesis spaces whose risk minimizer changes if independent variables are added as input. © 2006 Massachusetts Institute of Technology
Radial basis function approach to nonlinear Granger causality of time series
No full textWe consider an extension of Granger causality to nonlinear bivariate time series. In this frame, if the
prediction error of the first time series is reduced by including measurements from the second time series, then
the second time series is said to have a causal influence on the first one. Not all the nonlinear prediction
schemes are suitable to evaluate causality; indeed, not all of them allow one to quantify how much knowledge
of the other time series counts to improve prediction error. We present an approach with bivariate time series
modeled by a generalization of radial basis functions and show its application to a pair of unidirectionally
coupled chaotic maps and to physiological examples
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