Search results for "Operator"

On ( p ( x ),  q ( x ))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

2021

In the present work, we consider a (p(x), q(x))-elliptic equation describing the behavior of a double-phase anisotropic problem which has relevance in electrorheological fluid applications. The analysis leads to the existence of weak (nonnegative) solutions in the special case of potential terms with critical frequency and a superlinear reaction term. In order to prove the existence result, we combine critical point theory of mountain pass type with related topological and variational methods. Basically, the approach is variational, but we do not impose any Ambrosetti-Rabinowitz type condition for the superlinearity of the reaction. More specifically, we apply the Euler-Lagrange functional …

Abstract Estimates of the Rate of Convergence for Optimal Control Problems

1997

A method for solving optimal control problems with general elliptic operators is presented and analyzed. Especially, estimates of the rate of convergence for the control problems with the proposed approach are derived independently of the underlying approximation method. Some numerical experiments with the proposed method are included.

Boundary accessibility and elliptic harmonic measures

1988

Suppose G is a bounded domain in R n such that the complement of G satisfies a capacity dcnsity condition. It is shown that all elliptic measures in G have a support set with Moreover, the capacity density condition cannot be removed. A nonlinear version of the result is also given.

Form-perturbation theory for higher-order elliptic operators and systems by singular potentials

2020

We give a form-perturbation theory by singular potentials for scalar elliptic operators onL2(Rd)of order 2mwith Hölder continuous coefficients. The form-bounds are obtained from anL1functional analytic approach which takes advantage of both the existence ofm-gaussian kernel estimates and the holomorphy of the semigroup inL1(Rd).We also explore the (local) Kato class potentials in terms of (local) weak compactness properties. Finally, we extend the results to elliptic systems and singular matrix potentials.This article is part of the theme issue ‘Semigroup applications everywhere’.

Lp-uniqueness for elliptic operators with unbounded coefficients in RN

AbstractLet A be an elliptic operator with unbounded and sufficiently smooth coefficients and let μ be a (sub)-invariant measure of the operator A. In this paper we give sufficient conditions guaranteeing that the closure of the operator (A,Cc∞(RN)) generates a sub-Markovian strongly continuous semigroup of contractions in Lp(RN,μ). Applications are given in the case when A is a generalized Schrödinger operator.

Control Design for Discrete-Time Fuzzy Systems with Disturbance Inputs via Delta Operator Approach

2013

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher: http://dx.doi.org/10.1155/2013/724918 Open Access This paper is concerned with the problem of passive control design for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay and disturbance input via delta operator approach. The discrete-time passive performance index is established in this paper for the control design problem. By constructing a new type ofLyapunov-Krasovskii function (LKF) in delta domain, and utilizing some fuzzy weighing matrices, a new passive performance condition is proposed for the system under consideration. Based on the condition, a st…

Determination of Technological Forces in the Incremental Forming Process

2013

The paper presents a joint theoretical and experimental approach to determine the technological forces within the asymmetric single point incremental forming ASPIF process, based upon a theoretical model, image processing and data acquisition. The first step of this approach was to develop a theoretical model of the forces within the process, based upon the model of a mechanical feed drive of a CNC milling machine. By means of this model, relationships between the resistant torque at the motor spindle level and the technological force on the movement axis could be determined. Using an image processing method, which allowed the user to extract information within the machines operator panel a…

Single thermal zone balance solved by Transfer Function Method

2005

We present an algorithm that uses the Z-transform operator to face the problem of heat transmission in a single thermal zone composed by multilayered walls. The method is very flexible and could be adopted to calculate the transfer function coefficients able to simulate the thermal behaviour of a room in free floating. Knowing the transfer function coefficients, it is possible to simulate the dynamic profile of each inner surfaces temperature and furthermore of the inner air temperature. The proposed algorithm is fully described granting maximum clarity. The explicitness of all steps of the calculus make possible the definition of a method that is able to vary all of the calculus parameters…

Health & safety 4.0: A digital twin reference model to support the smart operator at the workplace

2020

In the Industry 4.0 era, Cyber-Physical Systems (CPS) and the Internet of Things are the enabling technologies for a new tool, the Digital Twin, that allows a streamlined communication, automation and interoperability among all the production assets. Even if there has been a great deal of efforts toward digital twin engineering, little attention has been paid to the correct integration of humans in the emerging context of smart factories and, in particular, to the potential contribution of digital twins for supporting a health and safety 4.0 at the workplace. This paper sets the stage for a discussion over health and safety aspects for the Smart Operator and proposes a renewed approach to t…

A characterization of the n-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem

2018

A theorem of single-sorted algebra states that, for a closure space (A, J ) and a natural number n, the closure operator J on the set A is n-ary if and only if there exists a single-sorted signature Σ and a Σ-algebra A such that every operation of A is of an arity ≤ n and J = SgA, where SgA is the subalgebra generating operator on A determined by A. On the other hand, a theorem of Tarski asserts that if J is an n-ary closure operator on a set A with n ≥ 2, then, for every i, j ∈ IrB(A, J ), where IrB(A, J ) is the set of all natural numbers which have the property of being the cardinality of an irredundant basis (≡ minimal generating set) of A with respect to J , if i < j and {i + 1, . . . …