Christianity arrived early in Egypt, brought according to tradition by Saint Mark the Evangelist, who became the first patriarch of Alexandria. The Coptic Orthodox Church has flourished ever since, with millions of adherents both in Egypt and in Coptic communities around the world. Since its split from the Byzantine Church in 451, the Coptic Church has proudly maintained its early traditions, and influence from outside has been minimal: the liturgy is still sung to unique rhythms in Coptic, a late stage of the same ancient Egyptian language that is inscribed in hieroglyphs on temple walls and papyri. Dr. Otto Meinardus, a leading authority on the history of the Coptic Church, here revises, updates, and combines his renowned studies Christian Egypt, Ancient and Modern (The American University in Cairo Press, 1965, 1977) and Christian Egypt, Faith and Life (The American University in Cairo Press, 1970) into a new, definitive, one-volume history for the Millennium, surveying the twenty centuries of existence of one of the oldest churches in the world.
Drawing on more than four decades of experience studying Christian communities in Egypt, Otto Meinardus offers here a sweeping overview of the principal Christian churches and organizations in Egypt today. For the first time, this wealth of information has been gathered into one volume, making it an ideal introduction to the contemporary scene of the various Orthodox, Catholic, and Protestant denominations that have a presence in Egypt. Looking at Maronite churches in Alexandria, Greek Orthodox congregations in Cairo, and new evangelical communities in Upper Egypt, among others, this book serves as an important reference work for anyone interested in the broad variety of Christian groups in Egypt, including the majority Coptic Orthodox Church. As one of the foremost scholars of the Christian history of Egypt and the wider Middle East, Dr. Meinardus brings an unparalleled wealth of expertise to this subject, while placing Christianity in the historical perspective of its relationship to the ancient pharaonic religion and medieval and modern Islam. A first of its kind, Christians in Egypt is an indispensable resource for both scholars and interested general readers.
Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald)
Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald)
Der vorliegende Band stellt Vortragsmanuskripte einer am Mathematischen Forschungsinstitut, Oberwolfach, in der Zeit vom 25. bis 31. Mai 1975 veran stalteten Tagung zusammen, die unter der Leitung der Unterzeichner stand. Die letzten dieser Tagungen über numerische Methoden der Approximations theorie fanden 1971 und 1973 statt - der Schwerpunkt lag bei Fragen der Numerik von Algorithmen zur Darstellung von Funktionen -, ließen aber bereits ein wachsendes Interesse an Anwendungen erkennen. Die diesjährige Tagung war gekennzeichnet durch die Behandlung praktischer AufgabensteI lungen sowie durch die Einbeziehung der Anwendungen aus Nachbargebie ten bzw. die Verwendung der Methoden dieser Gebiete in der Approxima tionstheorie, insbesondere wurde auch auf die Beziehungen von Optimierung und Kontrolltheorie zu speziellen approximationstheoretischen Aufgaben eingegangen. Der starke Einfluß auf die numerischen Methoden zur Behand lung von Differentialgleichungen wurde etwa bei der Methode der finiten Elemente oder bei Kollokationsaufgaben deutlich. So ist zu hoffen, daß auch diese Tagung dazu beigetragen hat, Theorie und Anwendungen wieder stärker zu verbinden. Die spezifische Atmosphäre des Forschungsinstituts stimulierte einen intensi ven, durch die breite internationale Streuung der Tagungsteilnehmer verstärk ten, fruchtbaren Gedankenaustausch. Zum Erfolg der Tagung trug - wie immer - die hervorragende Betreuung durch die Mitarbeiter und Angestellten des Forschungsinstituts und das verständnisvolle Entgegenkommen von Herrn Kollege Barner bei. Unser besonderer Dank gilt ferner dem Birkhäuser Verlag für die sehr gute Ausstattung des Buches. L. COLLATZ, G. MEINARDUS, H. WERNER Inhaltsverzeichnis ANSELONE, P.M., LEE, J.W. : Double Approximation Methods for the Solution of Fredholm Integral Equations ...
for example, the so-called Lp approximation, the Bernstein approxima tion problem (approximation on the real line by certain entire functions), and the highly interesting studies of J. L. WALSH on approximation in the complex plane. I would like to extend sincere thanks to Professor L. COLLATZ for his many encouragements for the writing of this book. Thanks are equally due to Springer-Verlag for their ready agreement to my wishes, and for the excellent and competent composition of the book. In addition, I would like to thank Dr. W. KRABS, Dr. A. -G. MEYER and D. SCHWEDT for their very careful reading of the manuscript. Hamburg, March 1964 GUNTER MEINARDUS Preface to the English Edition This English edition was translated by Dr. LARRY SCHUMAKER, Mathematics Research Center, United States Army, The University of Wisconsin, Madison, from a supplemented version of the German edition. Apart from a number of minor additions and corrections and a few new proofs (e. g. , the new proof of JACKSON'S Theorem), it differs in detail from the first edition by the inclusion of a discussion of new work on comparison theorems in the case of so-called regular Haar systems (§ 6) and on Segment Approximation (§ 11). I want to thank the many readers who provided comments and helpful suggestions. My special thanks are due to the translator, to Springer-Verlag for their ready compliance with all my wishes, to Mr.
The international symposium held in October 1984 at the Uni versity of Mannheim was the first with the special aim to expose the connection of the Theory of Delay Eauations and Approximation Theory with the emphasis on constructive methods and applications. Although the separate character of both domains is reflected by their historical development, the latest research shows that the numerical treatment of Delay Equations leads to various appro ximation and optimization problems. An introductory survey of this circle of problems written by the editors is included at the beginning of the book. Delay Equations have their origin in domains of applications, such as physics, engineering, biology, medicine and economics. They appear in connection with the fundamental problem to analyse a retarded process from the real world, to develop a corresponding mathematical model and to determine the future behavior. Thirty mathematicians attended the conference coming from Germany, West- and Eastern Europe and the United States- more than twenty of them presented a research talk. The lectures about Delay Equations were mainly oriented on the following subjects: single-step, multi-step and spline methods; monotonicity methods for error estimations; asymptotic behavior 10 and periodicity of solutions. The topics of the talks on Approxi mation Theory covered different aspects of approximation by poly nomials, splines and rational functions and their numerical rea lization. Additionally included in the scientific program was a special session on Open Problems, where several suggestions were made for further research concerning both fields.
Workshop on Numerical Methods of Approximation Theory Oberwolfach, March 20–26, 1983 / Tagung über Numerische Methoden der Approximationstheorie Oberwolfach, 20.–26. März 1983
Workshop on Numerical Methods of Approximation Theory Oberwolfach, March 20–26, 1983 / Tagung über Numerische Methoden der Approximationstheorie Oberwolfach, 20.–26. März 1983
This book, first published in 1963, is the classica ccount of the traditions surrounding the flight of the Holy Family into and through Egypt. It has been compiles from both Eastern and Western sources, including bothe Muslim and Christian traditions, written and oral. The author has included an attempted reconstruction of the route taken by the Holy Family and retells the stories of their encounters along the way.
Workshop on Numerical Methods of Approximation Theory Oberwolfach, January 18–24, 1981 \ Tagung über Numerische Methoden der Approximationstheorie Oberwolfach, 18.–24.Januar 1981
Workshop on Numerical Methods of Approximation Theory Oberwolfach, January 18–24, 1981 \ Tagung über Numerische Methoden der Approximationstheorie Oberwolfach, 18.–24.Januar 1981
Der Band enthalt Manuskripte zu Vortragen, die auf einer von den Herausgebern geleiteten Tagung tiber "Numerische Methoden der Approximationstheorie" am Mathematischen Forschungsinstitut Ober wolfach in der Zeit vom 18. -24. Januar 1981 gehalten wurden. Das Spektrum der Vortrage reichte von der klassischen Approximations theorie tiber mehrdimensionale Approximationsverfahren bis hin zu praxisbezogenen Fragestellungen. Zu den zuerst genannten Gebieten gehorten z. B. die Verfeinerung von Fehlerabschatzungen bei der Polynominterpolation, Fragen zur Eindeutigkeit, Charakterisierung optimaler Interpolationsprozesse und Algorithmen zur rationalen Interpolation. Bei den weiteren genannten Gebieten spiegel ten zahlreiche Vortrage das steigende Interesse an der mehrdimensio nalen Interpolation, insbesondere mit verschiedenen Arten von Splines wider. Hier standen u. a. Probleme der Parameterschatzung in der Medizin und Flugtechnik, Fragen der Approximationstheorie bei der Konstruktion von Plottern und stabile Algorithmen beim Arbeiten mit mehrdimensionalen B-Splines im Mittelpunkt des Interesses. Die Tagung lieferte einen reprasentativen Ueberblick tiber die aktuellen Trends in der Approximationstheorie. Zum guten Erfolg der Tagung trug wie immer die hervorragende Be treuung durch die Mitarbeiter und Angestellten des Instituts so-' wie das verstandnisvolle Entgegenkommen des Institutsdirektors, Herrn Professor Dr. Barner, bei. Un serer besonderer Dank gilt dem Birkhauser Verlag ftir die wie stets sehr gute Ausstattung. Helmut Werner Lothar Collatz Gtinther Meinardus Hamburg Mannheim Bonn 7 INDEX Blatt, H. -P. Strenge Eindeutigkeitskonstanten und Fehlerabschatzungen bei linearer Tschebyscheff-Approximation 9 Bohmer, K. Polynom- und Spline-Interpolation (Ein Farbfilm) 26 Brannigan, M. A Multivariate Adaptive Data Fitting Algorithm 30 Brass, H. Zur numerischen Berechnung konjugierter Funktionen 43 Bultheel, A.
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