The rapid evolution of technology and mathematical methods in this century has led to the recognition and accumulation of a large quantity of scientific facts. At the same time, however, in studying natural bodies, primary attention has not been paid to their total character; the body either ceased to be an individual, as in the case of mathematical methods, or has become a complex of separate, not always closely connected characteristics examined by laboratory analyses. The goniometric study of a crystal, for example, has developed into the determination of constants of the crystal lattice, but the examination of minerals from a specific deposit was concerned primarily with the chemical analysis of their admixtures. In geological sciences a thorough morphological investigation has preserved its original importance, particularly in geomorphology and paleontology. Even in petrography, the three-dimensional description of rocks was replaced by the study of thin sections, since the optical microscope does not permit examination of an uneven surface as a result of a restricted depth of observation field. The art of ancient naturalists of conceiving the object in its entirety, with all its particularities, has not developed with time, as would have been desirable.
One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.
Trade was a necessity in the ancient Greek world, yet the prevalent scholarly view is that Greek states intervened in foreign trade only rarely and sporadically. This book studies four necessary commodities, gold, silver, ship-building timber and grain, from production through export to import. Through the re-evaluation of known evidence and the presentation of new avenues of research, the book shows that Greek and non-Greek governments in the archaic and classical periods intervened and involved themselves greatly in foreign trade. The book offers the student of the Greek economy a fresh perspective on state intervention in trade and the ways in which intervention worked in the Greek world.
The book reflects the results of the study of sedimentation history, paleoclimatology, and paleoceanography of the Arctic and Subarctic during the last 130 ka. The main objects under consideration are marine basins of the West Subarctic (Iceland, Norwegian, and Greenland Seas), the Arctic Ocean (Barents, Pechora, Kara, Laptev, East Siberian, Chukchi Seas and deep-sea Arctic Ocean proper), East Subarctic (Bering and Okhotsk Seas). The modern environment and geological history of water- (ice-) sheds and marine basins have been studied for each region, using different sedimentological and geochemical proxies. Mainly results of the authors' own studies are represented, with special emphasis on glacial/interglacial variability and land-ocean interaction. The book is aimed at sedimentologists, quaternary and marine geologists, paleoclimatologists and paleoceanographers, as well as being of great interest to students in the related fields.
This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Calculation methods in the context of physics are emphasized. New materials drawn from the teaching and research experience of the author are included. The generalized Gel'fand's method is presented to calculate the matrices of irreducible representations of the simple Lie algebra and its Clebsch-Gordan coefficients. This book is for graduate students and young researchers in physics, especially theoretical physics. It is also for graduate students in theoretical chemistry.
This book contains 25 papers, most of which were presented, for the first time, at the International Workshop on Operator Theory and its Applications held in Groningen, the Netherlands, from June 30-July 3, 1998. The topics include dilation and interpolation problems, reproducing kernel spaces, numerical ranges of operators, Riccati equations, harmonic analysis, spectral theory of differential operators and analytic operator functions to scattering of waves. All papers deal with operators in Banach or Hilbert spaces, or in spaces with an indefinite metric. This volume is dedicated to Israel Gohberg, one of the founding fathers of the IWOTA worskhops and an outstanding leader in operator theory. His work had a deep influence on the field and its range of applications. The IWOTA Groningen 1998, the tenth in its series, was a good occasion for a pre-celebration of his 70th birthday. This book also contains the speeches held at the workshop dinner, a review of Israel Gohberg's contributions to mathematics and a complete list of his publications. The book is of interest to a wide audience of pure and applied mathematicians.
The rapid evolution of technology and mathematical methods in this century has led to the recognition and accumulation of a large quantity of scientific facts. At the same time, however, in studying natural bodies, primary attention has not been paid to their total character; the body either ceased to be an individual, as in the case of mathematical methods, or has become a complex of separate, not always closely connected characteristics examined by laboratory analyses. The goniometric study of a crystal, for example, has developed into the determination of constants of the crystal lattice, but the examination of minerals from a specific deposit was concerned primarily with the chemical analysis of their admixtures. In geological sciences a thorough morphological investigation has preserved its original importance, particularly in geomorphology and paleontology. Even in petrography, the three-dimensional description of rocks was replaced by the study of thin sections, since the optical microscope does not permit examination of an uneven surface as a result of a restricted depth of observation field. The art of ancient naturalists of conceiving the object in its entirety, with all its particularities, has not developed with time, as would have been desirable.
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