An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Lack of fifth anchoring point and violation of the insertion of the rotator cuff during antegrade humeral nailing: pitfalls in straight antegrade humeral nailing.

Antegrade nailing of proximal humeral fractures using a straight nail can damage the bony insertion of the supraspinatus tendon and may lead to varus failure of the construct. In order to establish the ideal anatomical landmarks for insertion of the nail and their clinical relevance we analysed CT scans of bilateral proximal humeri in 200 patients (mean age 45.1 years (sd 19.6; 18 to 97) without humeral fractures. The entry point of the nail was defined by the point of intersection of the anteroposterior and lateral vertical axes with the cortex of the humeral head. The critical point was defined as the intersection of the sagittal axis with the medial limit of the insertion of the supraspinatus tendon on the greater tuberosity. The region of interest, i.e. the biggest entry hole that would not encroach on the insertion of the supraspinatus tendon, was calculated setting a 3 mm minimal distance from the critical point. This identified that 38.5% of the humeral heads were categorised as 'critical types', due to morphology in which the predicted offset of the entry point would encroach on the insertion of the supraspinatus tendon that may damage the tendon and reduce the stability of fixation. We therefore emphasise the need for 'fastidious' pre-operative planning to minimise this risk.

A Simple Statistical Test of Violation of the Weak Axiom of Cost Minimization

A problem with a practical application of Varian.s Weak Axiom of Cost Minimization is that an observed violation may be due to random variation in the output quantities produced by firms rather than due to inefficiency on the part of the firm. In this paper, unlike in Varian (1985), the output rather than the input quantities are treated as random and an alternative statistical test of the violation of WACM is proposed. We assume that there is no technical inefficiency and provide a test of the hypothesis that an observed violation of WACM is merely due to random variations in the output levels of the firms being compared.. We suggest an intuitive approach for specifying a value of the variance of the noise term that is needed for the test. The paper includes an illustrative example utilizing a data set relating to a number of U.S. airlines.

The violation of the neutrality of Belgium.

Preface by M. Paul Hymans.--Meeting of the Belgian parliament (4th August, 1914)--Proclamation by King Albert to the Belgian army (5th August, 1914)--Observations on Belgian neutrality.--Proclamation by the Belgian government at Ostend (13th October, 1914)--Correspondence of H.M. the King of Belgium and the Belgian government with the President of the French republic (12th-14th October, 1914)

Reports on the violation of the rights of nations and of the laws ans customs of war in Belgium.

[Vol. I] includes a preface by J. van den Heuvel, minister of state, reports 1-12, and extracts from the pastoral letter of Cardinal Mercier, archbishop of Malines; vol. II includes reports 13-22, with facsimiles of German soldiers' diaries, correspondence between Cardinal Mercier and the German authorities, the protest of Mgr. Heylen, bishop of Namur, etc., etc., appended.

Report of the case of the Steamship Meteor, libelled for alleged violation of the Neutrality Act ...

I. Procedeings [sic] in the District Court of the United States for the Southern District of New York.--II. Proceedings in the Circuit Court of the United States for the Southern District of New York in the Second Circuit, and in the Supreme Court of the United States.

The practical art of generating; a simple and practical analysis of the generating principle, together with numerous examples showing how it has been applied commercially in many industries to profitable advantage.

Mode of access: Internet.

Notes on the four Gospels and the Acts of the apostles ; Illustrations of the doctrine principle and practice of the Church of England.

Mode of access: Internet.

Of the moral principle of the atonement : also of faith and of its two sorts, conviction and confidence, and of the connexion between them /

Includes bibliographical references.

The original, and present state of man, briefly considered; : wherein is shewn, the nature of his fall, and the necessity, means, and manner of his restoration, through the sacrifice of Christ, and the sensible operation of the divine principle of grace and truth, held forth to the world by the people called Quakers. : To which are added, some remarks on the doctrine of predestination, the scriptures, worship, and the kingdom of heaven. /

Smith, J. Friends' books