Search results for "continuity"

On Generalizing Lipschitz Global Methods forMultiobjective Optimization

2015

Lipschitz global methods for single-objective optimization can represent the optimal solutions with desired accuracy. In this paper, we highlight some directions on how the Lipschitz global methods can be extended as faithfully as possible to multiobjective optimization problems. In particular, we present a multiobjective version of the Pijavskiǐ-Schubert algorithm.

A systematic review of animal models for experimental neuroma

2015

Summary Peripheral neuromas can result in an unbearable neuropathic pain and functional impairment. Their treatment is still challenging, and their optimal management is to be defined. Experimental research still plays a major role, but - although numerous neuroma models have been proposed on different animals - there is still no single model recognised as being the reference. Several models show advantages over the others in specific aspects of neuroma physiopathology, prevention or treatment, making it unlikely that a single model could be of reference. A reproducible and standardised model of peripheral neuroma would allow better comparison of results from different studies. We present a…

A beam element allowing multiple slope discontinuities for RC structures: An application

2018

A beam/column element allowing the formation of multiple plastic hinges in columns or beams of a reinforced concrete (RC) framed structure is used in this work to show, through an application, its advantages with respect to conventional lumped plasticity models. Slope discontinuities can be located at any position of an Euler-Bernoulli beam span and not at the two extremes only. The model is in fact written in the framework of a modified lumped plasticity theory, and respectful of a thermodynamic approach. Flow rules and state equations are derived invoking the Theorem of maximum dissipation and using a Bresler's type activation domain. The beam element has already been implemented in a res…

Nonlinear Analysis of Reinforced Concrete Frames: Safety Evaluation and Retrofitting Techniques

Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity

2011

In this article, we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems, we prove the existence of a random compact global attractor.

Non-Lipschitz Homogeneous Volterra Integral Equations

2018

In this chapter we introduce a class of nonlinear Volterra integral equations (VIEs) which have certain properties that deviate from the standard results in the field of integral equations. Such equations arise from various problems in shock wave propagation with nonlinear flux conditions. The basic equation we will consider is the nonlinear homogeneous Hammerstein–Volterra integral equation of convolution type $$\displaystyle u(t) = \int _0^t k(t-s) g(u(s))\,\mathrm {d}s. $$ When g(0) = 0, this equation has function u ≡ 0 as a solution (trivial solution). It is interesting to determine whether there exists a nontrivial solution or not. Classical results on integral equations are not to be …

Power ENO methods: a fifth-order accurate Weighted Power ENO method

2004

In this paper we introduce a new class of ENO reconstruction procedures, the Power ENO methods, to design high-order accurate shock capturing methods for hyperbolic conservation laws, based on an extended class of limiters, improving the behavior near discontinuities with respect to the classical ENO methods. Power ENO methods are defined as a correction of classical ENO methods [J. Comput. Phys. 71 (1987) 231], by applying the new limiters on second-order differences or higher. The new class of limiters includes as a particular case the minmod limiter and the harmonic limiter used for the design of the PHM methods [see SIAM J. Sci. Comput. 15 (1994) 892]. The main features of these new ENO…

Combined impacts of the Allee effect, delay and stochasticity: Persistence analysis

2020

Abstract We study a combined influence of the Allee effect, delay and stochasticity on the base of the phenomenological Hassell mathematical model of population dynamics. This bistable dynamical model possesses a wide variety of regimes, both regular and chaotic. In the persistence zone, these regimes coexist with the trivial equilibrium that corresponds to the extinction of the population. It is shown that borders of the persistence zone are defined by the crisis and saddle-node bifurcation points. Noise-induced transitions from the persistence to the extinction are studied both numerically and analytically. Using numerical modeling, we have found that the persistence zone can decrease and…

On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques

2020

Abstract We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally optimized shape parameter and in the combination of RBF interpolants. We examine the accuracy of the proposed reconstruction techniques in smooth regions and their ability to avoid Gibbs phenomena close to discontinuities. In this paper, we propose a true MQ-RBF–WENO method that does not revert to the classical polynomial WENO approximation near discontinuities, as opposed to what was pr…

On Ekeland's variational principle in partial metric spaces

2015

In this paper, lower semi-continuous functions are used to extend Ekeland's variational principle to the class of parti al metric spaces. As consequences of our results, we obtain some fixed p oint theorems of Caristi and Clarke types.