Search results for " partial D"

Two theorems of N. Wiener for solutions of quasilinear elliptic equations

1985

Relatively little is known about boundary behavior of solutions of quasilinear elliptic partial differential equations as compared to that of harmonic functions. In this paper two results, which in the harmonic case are due to N. Wiener, are generalized to a nonlinear situation. Suppose that G is a bounded domain in R n. We consider functions u: G--~R which are free extremals of the variational integral

A framework for assessing frequency domain causality in physiological time series with instantaneous effects.

2013

We present an approach for the quantification of directional relations in multiple time series exhibiting significant zero-lag interactions. To overcome the limitations of the traditional multivariate autoregressive (MVAR) modelling of multiple series, we introduce an extended MVAR (eMVAR) framework allowing either exclusive consideration of time-lagged effects according to the classic notion of Granger causality, or consideration of combined instantaneous and lagged effects according to an extended causality definition. The spectral representation of the eMVAR model is exploited to derive novel frequency domain causality measures that generalize to the case of instantaneous effects the kno…

Recovery of time-dependent coefficients from boundary data for hyperbolic equations

2019

We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.

Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms

2017

In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to $\varepsilon$-form.

High-Speed Machines: Typologies, Standards, and Operation under PWM Supply

2018

This paper presents an overview of the most recent state of the art in the field of high-speed electric machines fed through high-frequency converters. This type of systems is rapidly wide spreading in aeronautical and automotive applications, as well as microturbines. Each typology has its own advantages and downsides, which are analytically presented in this paper. Some types of high-speed electric machines require high-frequency voltage supply, highly stressing the dielectric materials of the winding insulation system. For this reason, in high-speed electric drives, premature failure may occur and a reduction of the total system reliability has been observed in the past years. Such issue…

A new result on impulsive differential equations involving non-absolutely convergent integrals

2009

AbstractIn this paper we obtain, as an application of a Darbo-type theorem, global solutions for differential equations with impulse effects, under the assumption that the function on the right-hand side is integrable in the Henstock sense. We thus generalize several previously given results in literature, for ordinary or impulsive equations.

Direct Derivation of Corrective Terms in SDE Through Nonlinear Transformation on Fokker–Planck Equation

2004

This paper examines the problem of probabilistic characterization of nonlinear systems driven by normal and Poissonian white noise. By means of classical nonlinear transformation the stochastic differential equation driven by external input is transformed into a parametric-type stochastic differential equation. Such equations are commonly handled with Ito-type stochastic differential equations and Ito's rule is used to find the response statistics. Here a different approach is proposed, which mainly consists in transforming the Fokker–Planck equation for the original system driven by external input, in the transformed probability density function of the new state variable. It will be shown …

A theorem of Radò’s type for the solutions of a quasi-linear equation

2004

A remark on infinite initial values for quasilinear parabolic equations

2020

Abstract We study the possibility of prescribing infinite initial values for solutions of the Evolutionary p -Laplace Equation in the fast diffusion case p > 2 . This expository note has been extracted from our previous work. When infinite values are prescribed on the whole initial surface, such solutions can exist only if the domain is a space–time cylinder.

Rhinitis as a risk factor for depressive mood in pre-adolescents: a new approach to this relationship

2014

Background Respiratory allergic symptoms impact on social life and school activities, influencing the patient's mood states. We evaluated the relationships between allergic respiratory diseases and depressive/anxious mood in a large sample of Italian middle school students, using the partial directed acyclic graph (P-DAG). Methods We studied 1283 subjects aged 10–13. A health respiratory questionnaire including questions relevant to socioeconomic status (HCI) and a test for depression and anxiety were administered. All subjects performed spirometry and skin prick tests. Results A causal role of rhinitis on depression was found: the likelihood of being depressed increased from 11.2 to 17.7%,…