Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Antecedents of travellers' electronic word-of-mouth communication

Electronic word-of-mouth (eWOM) is recognised as a means of interpersonal communication and a powerful marketing tool. However, previous studies have focussed on related motivations, and limited attention has been given to understanding the antecedents of eWOM communication behaviour in the travel industry. This study proposes a full and partial mediation model, which brings together for the first time three key antecedents: adoption of electronic communication technology, consumer dis/satisfaction with travel consumption experience, and subjective norm. The model aims to understand the impact of these antecedents on travellers' attitude towards eWOM communication and intention to use eWOM communication media. The data were collected from international travellers (n = 524), and structural equation modelling is used to test the conceptual framework. The findings of the study suggest that overall attitude towards eWOM communication partially mediates the impact of the traveller's adoption of electronic communication technology and subjective norm, and fully mediates the impact of consumer dis/satisfaction with travel consumption experience on travellers' intention to use eWOM communication media.

Symbolic consumption of tourism destination brands

Electronic word-of-mouth (eWOM) is recognised as a means of interpersonal communication and a powerful marketing tool. However, previous studies have focussed on related motivations, and limited attention has been given to understanding the antecedents of eWOM communication behaviour in the travel industry. This study proposes a full and partial mediation model, which brings together for the first time three key antecedents: adoption of electronic communication technology, consumer dis/satisfaction with travel consumption experience, and subjective norm. The model aims to understand the impact of these antecedents on travellers' attitude towards eWOM communication and intention to use eWOM communication media. The data were collected from international travellers (n = 524), and structural equation modelling is used to test the conceptual framework. The findings of the study suggest that overall attitude towards eWOM communication partially mediates the impact of the traveller's adoption of electronic communication technology and subjective norm, and fully mediates the impact of consumer dis/satisfaction with travel consumption experience on travellers' intention to use eWOM communication media.

Zero attracting recursive least squares algorithms

The l1-norm sparsity constraint is a widely used technique for constructing sparse models. In this contribution, two zero-attracting recursive least squares algorithms, referred to as ZA-RLS-I and ZA-RLS-II, are derived by employing the l1-norm of parameter vector constraint to facilitate the model sparsity. In order to achieve a closed-form solution, the l1-norm of the parameter vector is approximated by an adaptively weighted l2-norm, in which the weighting factors are set as the inversion of the associated l1-norm of parameter estimates that are readily available in the adaptive learning environment. ZA-RLS-II is computationally more efficient than ZA-RLS-I by exploiting the known results from linear algebra as well as the sparsity of the system. The proposed algorithms are proven to converge, and adaptive sparse channel estimation is used to demonstrate the effectiveness of the proposed approach.

A constrained recursive least squares algorithm for adaptive combination of multiple models

In this paper, we develop a novel constrained recursive least squares algorithm for adaptively combining a set of given multiple models. With data available in an online fashion, the linear combination coefficients of submodels are adapted via the proposed algorithm.We propose to minimize the mean square error with a forgetting factor, and apply the sum to one constraint to the combination parameters. Moreover an l1-norm constraint to the combination parameters is also applied with the aim to achieve sparsity of multiple models so that only a subset of models may be selected into the final model. Then a weighted l2-norm is applied as an approximation to the l1-norm term. As such at each time step, a closed solution of the model combination parameters is available. The contribution of this paper is to derive the proposed constrained recursive least squares algorithm that is computational efficient by exploiting matrix theory. The effectiveness of the approach has been demonstrated using both simulated and real time series examples.