An extension of the concept of gradient semigroups which is stable under perturbation

In this article we introduce the concept of a gradient-like nonlinear semigroup as an intermediate concept between a gradient nonlinear semigroup (those possessing a Lyapunov function, see [J.K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25, Amer. Math. Soc., 1989]) and a nonlinear semigroup possessing a gradient-like attractor. We prove that a perturbation of a gradient-like nonlinear semigroup remains a gradient-like nonlinear semigroup. Moreover, for non-autonomous dynamical systems we introduce the concept of a gradient-like evolution process and prove that a non-autonomous perturbation of a gradient-like nonlinear semigroup is a gradient-like evolution process. For gradient-like nonlinear semigroups and evolution processes, we prove continuity, characterization and (pullback and forwards) exponential attraction of their attractors under perturbation extending the results of [A.N. Carvalho, J.A. Langa, J.C. Robinson, A. Suarez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations 236 (2007) 570-603] on characterization and of [A.V. Babin, M.I. Vishik, Attractors in Evolutionary Equations, Stud. Math. Appl.. vol. 25, North-Holland, Amsterdam, 1992] on exponential attraction. (C) 2009 Elsevier Inc. All rights reserved.

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].

Inference for a skew extension of the Grubbs model

In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265-281, 2005b). Maximum likelihood parameter estimates are computed via the EM-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.

An extension of the generalized Birnbaum-Saunders distribution

In this paper we present an extension of the generalized Birnbaum-Saunders distribution family introduced in [Diaz-Garcia, J.A., Leiva-Sanchez, V., 2005. A new family of life distributions based on the contoured elliptically distributions. Journal of Statistical Planning and Inference 128 (2), 445-457] with a view to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied for some special members of this family such as the slash Birnbaum-Saunders and slash-t Birnbaum-Saunders. Simulation studies for some particular cases and a real data analysis are also reported, illustrating the usefulness of the extension considered. (C) 2008 Elsevier B.V. All rights reserved.

Influence Diagnostics for a Skew Extension of the Grubbs Measurement Error Model

Influence diagnostics methods are extended in this article to the Grubbs model when the unknown quantity x (latent variable) follows a skew-normal distribution. Diagnostic measures are derived from the case-deletion approach and the local influence approach under several perturbation schemes. The observed information matrix to the postulated model and Delta matrices to the corresponding perturbed models are derived. Results obtained for one real data set are reported, illustrating the usefulness of the proposed methodology.

Enforcement of arbitral awards where the seat of the arbitration is Australia, how the Eisenwerk decision might still be a sleeping assassin

This article examines the enforcement of foreign awards in Australia. It identifies and explains the difference between a “foreign award” and “international arbitration award,” observing it is a somewhat surprising but potentially significant distinction. The article then moves to consider the consequences of the distinction with particular reference to the Australian arbitral landscape. Australia has dual arbitration regimes operating at the state and federal level. Particular attention is given to the still controversial Queensland Supreme Court of Appeal decision in Australian Granites Ltd. v. Eisenwerk Hensel Bayreyth Dipl-Ing Burkhardt GmbH. The article concludes by promoting a line of interpretation that will effectively allow subsequent courts to avoid the potentially disastrous effects the Eisenwerk decision may yet still wreak.

The Strider Years: An Extension of the History of Colby College

Beloved Colby historian Ernest Cummings Marriner '13 documents Robert E. Lee Strider's nineteen years as president of Colby College. Marriner is also the author of the definitive History of Colby, which covers the period up to the Strider presidency.

Cause-related marketing : an extension of the congruity concept

This paper considers the concept of congruity or 'fit' in a cause-related marketing (CRM) context. At present, there is a gap in the literature that explores how nonprofit-forprofit pairings affect a consumer's response to and evaluation of CRM campaigns. This paper develops the concept of 'fit' with particular attention being paid to three dimensions, namely, cognitive, emotional and behavioural congruity and the role these concepts play in determining consumers’ perception of the 'relatedness' of products and causes.

Range extension of the Millewa Skink Hemiergis millewae in the Murray-Sunset National Park, Victoria

This article reports a range extension for the critically endangered Millewa Skink Hemiergis millewae in Victoria. An individual H. millewae was found approximately 85 km east of its former known range in mature mallee vegetation, near the eastern edge of the Murray-Sunset National Park on 27 March 2007. Site characteristics are described, and a list of other reptile species found at the same site is provided. Further research into the habitat associations and distribution of H. millewae is recommended in order to guide the management of this species.

Plane wave scattering by a spherical di-electric particle in motion : a relativistic extension of the Mie theory

Light scattering from small spherical particles has applications in a vast number of disciplines including astrophysics, meteorology optics and particle sizing. Mie theory provides an exact analytical characterization of plane wave scattering from spherical dielectric objects. There exist many variants of the Mie theory where fundamental assumptions of the theory has been relaxed to make generalizations. Notable such extensions are generalized Mie theory where plane waves are replaced by optical beams, scattering from lossy particles, scattering from layered particles or shells and scattering of partially coherent (non-classical) light. However, no work has yet been reported in the literature on modifications required to account for scattering when the particle or the source is in motion relative to each other. This is an important problem where many applications can be found in disciplines involving moving particle size characterization. In this paper we propose a novel approach, using special relativity, to address this problem by extending the standard Mie theory for scattering by a particle in motion with a constant speed, which may be very low, moderate or comparable to the speed of light. The proposed technique involves transforming the scattering problem to a reference frame co-moving with the particle, then applying the Mie theory in that frame and transforming the scattered field back to the reference frame of the observer.

An extension of the flower pattern diagram for roll forming

The initial process design of a roll forming system is often based on the traditional ‘flower pattern diagram’. In this diagram, the cross sections of the strip at each roll stand are superimposed on a single plane; the diagram is a 2D representation of the 3D process. In the present work, the flower pattern is extended into three dimensions. To demonstrate the method, the forming path or trajectory of a point at the edge of the strip during forming a V-section is considered. The forming path is a surface curve that lies on a cylindrical surface having its axis along the machine axis. This surface is unwrapped to give its plane development and important features of the forming process can be determined and are readily interpreted from this plane curve. It is shown that at any stage in the process, the axial strain and the curvature of the sheet adjacent to the point are dependent on the slope of the trajectory in this plane projection. This new diagram, which apparently has not been used previously, provides a useful initial method of examining the roll forming process and optimising the flower pattern. The model is purely geometric, as is the original flower pattern approach, and does not include the effect of material behaviour. The concept is applied to several cases available in the literature. It shows that the lowest level of shape defect in the part is achieved when the trajectory of the strip edge follows the shortest line length between the start and finish of forming, leading to the least longitudinal strain introduced in the flange. This trend is in agreement with previous experimental observations, suggesting that the analytical model proposed may be applied for early process design and optimisation before time-consuming numerical analysis is performed.

On the zeros of polynomials: An extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier B.V. All rights reserved.