A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Long Wavelength Peristaltic Transport of Non-Newton Fluids

Solutions are obtained for the stream function and the pressure field for the flow of non-Newtonian fluids in a tube by long peristaltic waves of arbitrary shape. The axial velocity profiles and stress distributions on the wall are discussed for particular waves of some practical interest. The effect of non- Newtonian character of the fluid is examined.

Self-love and self-liking in the moral and political philosophy of Bernard Mandeville and David Hume

This work offers a novel interpretation of David Hume’s (1711–1776) conception of the conjectural development of civil society and artificial moral institutions. It focuses on the social elements of Hume’s Treatise of human nature (1739–40) and the necessary connection between science of man and politeness, civilised monarchies, social distance and hierarchical structure of civil society. The study incorporates aspects of intellectual history, history of philosophy and book history. In order to understand David Hume’s thinking, the intellectual development of Bernard Mandeville (1670–1733) needs to be accounted for. When put into a historical perspective, the moral, political and social components of Treatise of human nature can be read in the context of a philosophical tradition, in which Mandeville plays a pivotal role. A distinctive character of Mandeville and Hume’s account of human nature and moral institutions was the introduction of a simple distinction between self-love and self-liking. The symmetric passions of self-interest and pride can only be controlled by the corresponding moral institutions. This is also the way in which we can say that moral institutions are drawn from human nature. In the case of self-love or self-interest, the corresponding moral institution is justice. Respectively, concerning self-liking or pride the moral institution is politeness. There is an explicit analogy between these moral institutions. If we do not understand this analogy, we do not understand the nature of either justice or politeness. The present work is divided into two parts. In the first part, ‘Intellectual development of Bernard Mandeville’, it is argued that the relevance of the paradigmatic change in Mandeville’s thinking has been missed. It draws a picture of Mandeville turning from the Hobbism of The Fable of the Bees to an original theory of civil society put forward in his later works. In order to make this change more apparent, Mandeville’s career and the publishing history of The Fable of the Bees are examined comprehensively. This interpretation, based partly on previously unknown sources, challenges F. B. Kaye’s influential decision to publish the two parts of The Fable of the Bees as a uniform work of two volumes. The main relevance, however, of the ‘Intellectual development of Mandeville’ is to function as the context for the young Hume. The second part of the work, ‘David Hume and Greatness of mind’, explores in philosophical detail the social theory of the Treatise and politics and the science of man in his Essays. This part will also reveal the relevance of Greatness of mind as a general concept for David Hume’s moral and political philosophy.

Tombstone of David Benjamin; Strangriede Cemetery (R 84.7); Hannover Cemeteries Tombs

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Tombstones of Frederike Benjamin nee Salamon and her husband David Benjamin; Strangriede Cemetery (R 84.6 and R 84.7); Hannover Cemeteries; Tombs

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Albert Einstein with David Ben Gurion; Princeton, New Jersey Portraits; Groups; Men

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Albert Einstein with David Ben Gurion and unidentified man; Princeton, New Jersey Portraits; Groups; Men

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Portrait of the family of David Stern and Bernice Stern nee Propper.

Seated: David Stern, Bernice Stern, and Jessica Agosti; left to right: Doreen Stern, her husband Michael Stern, Carol Richardson, her husband Blake Richardson, John Agosti. The baby is Katherine Stern

Ruth Weiss nee Stern with Annette, Meir, and David Weiss at Mortimer Hill Farm; Mortimer, England.

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Ruth Weiss nee Stern with Annette, Meir, and David Weiss at Mortimer Hill Farm; Mortimer, England..

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