Search results for " partial D"

A Noncommutative Approach to Ordinary Differential Equations

2005

We adapt ideas coming from Quantum Mechanics to develop a non-commutative strategy for the analysis of some systems of ordinary differential equations. We show that the solution of such a system can be described by an unbounded, self-adjoint and densely defined operator H which we call, in analogy with Quantum Mechanics, the Hamiltonian of the system. We discuss the role of H in the analysis of the integrals of motion of the system. Finally, we apply this approach to several examples.

Existence results for $L^1$ data of some quasi-linear parabolic problems with a quadratic gradient term and source

2002

In this paper we deal with a Cauchy–Dirichlet quasilinear parabolic problem containing a gradient lower order term; namely, ut - Δu + |u|2 γ-2u |∇u|2 = |u|p-2u. We prove that if p ≥ 1, γ ≥ ½ and p < 2 γ + 2, then there exists a global weak solution for all initial data in L1 (Ω). We also see that there exists a non-negative solution if the initial datum is non-negative.

Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term

2006

We study existence and regularity of distributional solutions for possibly degenerate quasi-linear parabolic problems having a first order term which grows quadratically in the gradient. The model problem we refer to is the following (1){ut−div(α(u)∇u)=β(u)|∇u|2+f(x,t),in Ω×]0,T[;u(x,t)=0,on ∂Ω×]0,T[;u(x,0)=u0(x),in Ω. Here Ω is a bounded open set in RN, T>0. The unknown function u=u(x,t) depends on x∈Ω and t∈]0,T[. The symbol ∇u denotes the gradient of u with respect to x. The real functions α, β are continuous; moreover α is positive, bounded and may vanish at ±∞. As far as the data are concerned, we require the following assumptions: ∫ΩΦ(u0(x))dx<∞ where Φ is a convenient function which …

Evolution of oral cancer treatment in an andalusian population sample: Rehabilitation with prosthetic obturation and removable partial prosthesis

2017

BACKGROUND Radical surgical resection as a treatment modality for oral cancer often leads to an extensive deficit in both the maxillary and mandibular levels, where the use of a palatal obturator prosthesis (POP) or removable partial denture (RPP). The aim of this study was to evaluate the treatment with POP and RPP in patients treated for oral cancer in the Unit of Prosthetic Rehabilitation of the University Hospital Virgen del Rocio in a period of 20 years. MATERIAL AND METHODS Retrospective descriptive study during the years 1991 and 2011 analyzing oral cancer type, characteristics, treatment and follow-up. The sample consisted of patients whose tumor had previously been removed and who …

Weak D and partial D: our experience in daily activity

2011

Sur une classe d’equations du type parabolique lineaires

1996

The application of the variational method for the existence theorem, developped by J. L. Lions, for the evolution equations in Hilbert spaces to a considerably large class of systems of linear partial differential equations of parabolic type is studied by defining Hilbert spaces in relation to the elliptic operator of the system, and an example insired by the system of equations for a viscous gas is examined.

Performances of a PCB-based Loop Antenna Inductive Sensor for Partial Discharges Detection

2022

This paper presents the test results of an electrically small loop antenna sensor towards detecting the radiated magnetic field due to partial discharge (PD) activities. The loop antenna prototype was printed on an FR-4 substrate with a thickness of 1.6 mm, featuring a compact size of 20 mm times20 mm times1.7 mm. The proposed sensor, initially simulated with Ansys HFSS software, has a resonant frequency of about 100 MHz. Its detection capability for three types of partial discharges (i.e., corona, surface and internal PDs) has been evaluated. Laboratory experiments showed that the evaluated loop spiral antenna is appropriate for the detection of the three types of PDs. Indeed, the results …

Partial discharges characteristics during load transients in an HVDC model cable

2021

The occurrence of Partial Discharges (PD) in HVAC cables is widespread considered as one of the most important concerns for the stability of the insulation. To date, the role of PD in the ageing and definitive fault of HVDC cables has been poorly investigated. This is mainly due to some practical difficulties in the performing of the measurements. Compared to the PDs occurring under AC stress, the higher inception voltages and the lower repetition rates, obtainable under DC voltage, make the exclusion of the measurement noise more difficult. This paper is focused on the study of the characteristics of the PDs occurring in an artificial defect located in proximity of the outer dielectric' su…

Characteristics of partial discharges in an experimental setup reproducing HVDC cable insulation operating conditions

2021

The occurrence of Partial Discharge (PD) inside a cavity subjected to HVDC voltage can be considered as one of the most likely sources of insulation ageing and failure. In practical applications, the recognition of PD under HVDC is more difficult than under AC stress because of the lower repetition rates and the impossibility to obtain a PD pattern synchronized with the waveform of the applied voltage. In this paper, the relationship between conduction phenomena in dielectrics and the occurrence of PD is investigated by means of a novel experimental setup. A couple of dielectric cells connected in series is subjected to various HVDC stress levels. The applied voltage is divided between the …

Investigation of PCB-based Inductive Sensors Orientation for Corona Partial Discharge Detection

2022

This paper presents an experimental investigation of two different printed circuit board (PCB) inductive sensors, with meander and non-spiral shapes, to assess their capabilities and best orientation for corona partial discharge (PD) detection. First, simulations with the Ansys HFSS software are performed in order to evaluate the equivalent electrical circuit of the two sensors and their 2d radiation patterns. The meander sensors presented a resonant frequency of 600 MHz, while it was around 1.1 GHz for the non-spiral. The 2d radiation pattern showed that better sensitivity is achieved when the inductive sensor is oriented 90 degrees with respect to the PD source. Experimental tests showed …