An asymptotic expansion is a series that provides a sequence of increasingly accurate approximations to a function in a particular limit. The formal definition, given by Poincare (1886, Acta Math. 8:295), is as follows. Given a function,

Sir Dominic Corrigan's classic monograph "On Permanent Patency of the Mouth of the Aorta, or Inadequacy of the Aortic Valves" was published in 1832. Descriptions of aortic regurgitation had previously been published by others, but Corrigan's contribution was so comprehensive that his name is still closely associated with this disorder. He described the physical findings and the underlying gross pathologic anatomy of aortic regurgitation. He recognized that sudden death was not characteristic of aortic regurgitation, as it was in aortic stenosis, and his therapeutic approach was based on firm physiologic principles. In the past 150 years we have expanded Corrigan's work, and we have developed a detailed appreciation of the natural history, pathophysiology, diagnostic methods, and treatment of chronic aortic regurgitation. Fifteen years ago, cardiac catheterization and angiography had already achieved widespread application in the evaluation of aortic regurgitation, but cardiac ultrasound, especially Doppler echocardiography, was in its infancy, and the utility of radionuclide ventriculography was not widely appreciated.

Cardiac anatomy had already been a subject of and its control in health and disease has been great interest for centuries when Harvey de- published. Studies of hypertrophy, heart failure, scribed the dynamic nature of blood flow, but ischemia, and infarction have been vigorously the concept of defining ventricular function was pursued in experimental animals and in human first introduced with the measurement of a subjects, and as a result new areas for study have emerged. These include the process of hypertro- mare's blood pressure by Steven Hales in 1733. Amidst the important contributions of a number phy as an adaptive mechanism, the coronary vas- of European physiologists, the primal relation- cular reserve in hypertrophy, the role of the ship between the mechanical energy of the heart microvasculature in myocardial failure, active and the length of a myocardial fiber was enun- relaxation and other diastolic mechanisms that contribute to the syndrome of congestive heart ciated by E. H. Starling in 1912; this became known as the "law of the heart. " Perhaps the failure, ventricular interaction and the role of the normal pericardium, ischemic-stunned- first major refinement of this law was suggested by Sarnoff and co-workers, who introduced the reperfused myocardium, and vasoactive drugs in concept of homeometric autoregulation to ex- the treatment of heart failure.

Sir Dominic Corrigan's classic monograph "On Permanent Patency of the Mouth of the Aorta, or Inadequacy of the Aortic Valves" was published in 1832. Descriptions of aortic regurgitation had previously been published by others, but Corrigan's contribution was so comprehensive that his name is still closely associated with this disorder. He described the physical findings and the underlying gross pathologic anatomy of aortic regurgitation. He recognized that sudden death was not characteristic of aortic regurgitation, as it was in aortic stenosis, and his therapeutic approach was based on firm physiologic principles. In the past 150 years we have expanded Corrigan's work, and we have developed a detailed appreciation of the natural history, pathophysiology, diagnostic methods, and treatment of chronic aortic regurgitation. Fifteen years ago, cardiac catheterization and angiography had already achieved widespread application in the evaluation of aortic regurgitation, but cardiac ultrasound, especially Doppler echocardiography, was in its infancy, and the utility of radionuclide ventriculography was not widely appreciated.

Cardiac anatomy had already been a subject of and its control in health and disease has been great interest for centuries when Harvey de- published. Studies of hypertrophy, heart failure, scribed the dynamic nature of blood flow, but ischemia, and infarction have been vigorously the concept of defining ventricular function was pursued in experimental animals and in human first introduced with the measurement of a subjects, and as a result new areas for study have emerged. These include the process of hypertro- mare's blood pressure by Steven Hales in 1733. Amidst the important contributions of a number phy as an adaptive mechanism, the coronary vas- of European physiologists, the primal relation- cular reserve in hypertrophy, the role of the ship between the mechanical energy of the heart microvasculature in myocardial failure, active and the length of a myocardial fiber was enun- relaxation and other diastolic mechanisms that contribute to the syndrome of congestive heart ciated by E. H. Starling in 1912; this became known as the "law of the heart. " Perhaps the failure, ventricular interaction and the role of the normal pericardium, ischemic-stunned- first major refinement of this law was suggested by Sarnoff and co-workers, who introduced the reperfused myocardium, and vasoactive drugs in concept of homeometric autoregulation to ex- the treatment of heart failure.

..". a] brilliant study... a valuable addition to the literature on the Psalms." Indiana University Jewish Studies Program

"A superbly interesting book on the Psalms. Levine understands the relationship between literary and religious questions and uses an impressive array of tools to get at them. His sophisticated methods of reading are presented in clear and often elegant writing." Arthur Green, Brandeis University

..". offers some remarkable new angles on familiar material. Literary and religious insights are not often woven together so closely as they are here." Theological Book Review

"The arrival of Herbert Levine s Sing Unto God a New Song came as both a surprise and a pleasure. It is full of absorbing insights.... This is a rich book which is concerned with not only the theory but also the practice of reading the same psalms in several different ways." Church Times

"This reading of the Psalms, from the twin perspectives of poetry and ritual, is quite an achievement: it is deeply Jewish and religious while, at the same time, profoundly scholarly." Journal for the Study of the Old Testament

Drawing on a variety of critical perspectives, Herbert Levine offers revelatory readings of one of the most familiar and best loved books of the Bible."

The proceedings of a January 1991 workshop in La Jolla, California, at which mathematicians, physicists, and engineers from 12 countries gathered to exchange information on the new problems in their various fields that require asymptotics beyond all orders, and the several apparently unrelated metho