Systems of conservation laws with third-order Hamiltonian structures

We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in $\mathbb{P}^{n+2}$ satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space $W$ of dimension $n+2$, classify $n$-tuples of skew-symmetric 2-forms $A^{\alpha} \in \Lambda^2(W)$ such that $$\phi_{\beta \gamma}A^{\beta}\wedge A^{\gamma}=0,$$ for some non-degenerate symmetric $\phi$.Comment: 31 page

Extreme value laws in dynamical systems under physical observables

Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by large values attained by the observable along orbits of the system. Based on this theory, the so-called block maximum method is often used in applications for statistical prediction of large value occurrences. In this method, one performs inference for the parameters of the Generalised Extreme Value (GEV) distribution, using maxima over blocks of regularly sampled observations along an orbit of the system. The observables studied so far in the theory are expressed as functions of the distance with respect to a point, which is assumed to be a density point of the system's invariant measure. However, this is not the structure of the observables typically encountered in physical applications, such as windspeed or vorticity in atmospheric models. In this paper we consider extreme value limit laws for observables which are not functions of the distance from a density point of the dynamical system. In such cases, the limit laws are no longer determined by the functional form of the observable and the dimension of the invariant measure: they also depend on the specific geometry of the underlying attractor and of the observable's level sets. We present a collection of analytical and numerical results, starting with a toral hyperbolic automorphism as a simple template to illustrate the main ideas. We then formulate our main results for a uniformly hyperbolic system, the solenoid map. We also discuss non-uniformly hyperbolic examples of maps (H\'enon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models). Our purpose is to outline the main ideas and to highlight several serious problems found in the numerical estimation of the limit laws

On the uniqueness of blow-up solutions of fully nonlinear elliptic equations

This paper contains new uniqueness results of the boundary blow-up viscosity solutions of second order elliptic equations, generalizing a well known result of Marcus-Veron for the Laplace operato

Automatic adjustment of tire inflation pressure through an intelligent CTIS: Effects on the vehicle lateral dynamic behavior

The paper investigates the effect of tire inflation pressure on the lateral dynamics of a passenger car, and presents a possible control-oriented methodology aimed at adapting tire pressure to the current vehicle loading condition targeting a reference characteristic. Starting from the tire characteristics at several inflation pressure levels, the paper investigates the effect of changing selectively tire pressure on each of the two axles, through theoretical calculation of the curvature gain based on the computation of the derivatives of stability, and compares the obtained sensitivity to the results of a multibody simulation model validated through on-track tests. Finally, the work presents a possible algorithm that could be implemented on-board vehicle ECU to provide, for the current loading condition of the vehicle, a tire pressure combination that targets a specific lateral dynamics characteristic. The algorithm is intended as part of the control logic of an intelligent Central Tire Inflation System (CTIS) able to adjust automatically tire pressure according to the actual vehicle working conditions

Lagrangian reductive structures on gauge-natural bundles

A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a variational sequence such that the generalized Jacobi morphism is naturally self-adjoint. As a consequence, its kernel defines a reductive split structure on the relevant underlying principal bundle.Comment: 11 pages, remarks and comments added, this version published in ROM

Metabolic and Hormonal Determinants of Glomerular Filtration Rate and Renal Hemodynamics in Severely Obese Individuals.

OBJECTIVE: Renal function is often compromised in severe obesity. A true measurement of glomerular filtration rate (GFR) is unusual, and how estimation formulae (EstForm) perform in such individuals is unclear. We characterized renal function and hemodynamics in severely obese individuals, assessing the reliability of EstForm. METHODS: We measured GFR (mGFR) by iohexol plasma clearance, renal plasma flow (RPF) by 123I-ortho-iodo-hippurate, basal and stimulated vascular renal indices, endothelium-dependent and -independent vasodilation using flow-mediated dilation (FMD) as well as metabolic and hormonal profile in morbid, otherwise healthy, obese subjects. RESULTS: Compared with mGFR, the better performing EstForm was CKD-EPI (5.3 ml/min/1.73 m2 bias by Bland-Altman analysis). mGFR was directly related with RPF, total and incremental glucose AUC, and inversely with PTH and h8 cortisol. Patients with mGFR below the median shown significantly higher PTH and lower vitamin D3. Basal or dynamic renal resistive index, FMD, pulse wave velocity were not related with mGFR. In an adjusted regression model, renal diameter and plasma flow remained related with mGFR (R2 = 0.67), accounting for 15% and 21% of mGFR variance, respectively. CONCLUSIONS: CKD-EPI formula should be preferred in morbid obesity; glucose increments during oral glucose tolerance test correlate with hyperfiltration; RPF and diameter are independent determinants of mGFR; slightly high PTH values, frequent in obesity, might influence mGFR

An approach to map geography mark-up language data to resource description framework schema

GML serves as premier modeling language used to represent data of geographic information related to geography locations. However, a problem of GML is its ability to integrate with a variety of geographical and GPS applications. Since, GML saves data in coordinates and in topology for the purpose to integrate data with variety of applications on semantic web, data be mapped to Resource Description Framework (RDF) and Resource Description Framework Schema (RDFS). An approach of mapping GML metadata to RDFS is presented in this paper. This study focuses on the methodology to convert GML data in semantics to represent in extended and enriched form such as RDFS as representation in RDF is not sufficient over semantic web. Firstly, we have GML script from case study and parse it using GML parser and get XML file. XML file parse using Java and get text file to extract GML features and then get a graph form of these features. After that we designed methodology of prototype tool to map GML features to RDFS. Tool performed features by features mapping and extracted results are represented in the tabular form of mapping GML metadata to RDFS. © 2020, Springer Nature Singapore Pte Ltd.E

Covariant gauge-natural conservation laws

When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equations for the gauge-natural invariant Lagrangian. {\em Vice versa} all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms which are in the kernel of generalized Jacobi morphisms are generators of canonical covariant currents and superpotentials. In particular, only a few gauge-natural lifts can be considered as {\em canonical} generators of covariant gauge-natural physical charges.Comment: 16 pages; presented at XXXVI Symposium on Math. Phys., Torun 09/06-12/06/04; the last paragraph of Section 3 has been reformulated, in particular a mistake in the equation governing the vertical part of gauge-natural lifts with respect to prolongations of principal connections (appearing e.g. in the vertical superpotential) has been correcte