Frontiers in Magnetism of Reduced Dimension Systems presents a definitive statement of our current knowledge and the state of the art in a field that has yet to achieve maturity, even though there are a number of potential applications of thin magnetic films and multilayers, such as magnetic sensors, data storage/retrieval media, actuators, etc. The book is organized into 13 chapters, each including a lecture and contributed papers on a similar subject. Five chapters deal with theoretical descriptions of electron transport phenomena, relaxation processes, nonlinear paramagnetic interactions, phase transitions and macroscopic quantum effects in magnetic films and particles. The description of different characterization techniques occupies an important place in the book. Separate chapters are dedicated to magnetic resonances (FMR, SWR, NMR), magneto-optical spectroscopy, controlling chaos, magnetoelastic phenomena and magnetic resonance force microscopy. A further chapter gives a detailed review, spread over a number of papers, of materials in current use in information storage devices.
This atlas is a comprehensive compendium of congeni- and two-dimensional echocardiographic examples. The tal cardiac morphology as depicted by tomographic two- examples and experience span all ages and may be used dimensional echocardiography. Anatomic specimens by both pediatric and adult cardiologists. The intended cut in planes of section corresponding to the echocar- emphasis is on tomographic morphology and not on diographic views help in the understanding of the echo- specialty applications such as fetal, contrast, or Dop- cardiographic sections. Composite photographs relate pler echocardiography. different planes of section or cardiac events. Still-frame The tomographic approach to congenital anomalies is photography cannot always adequately relate real-time the imaging modality of the 80s and is applicable to echocardiography, computerized tomography, and imaging events. However, the emphasis of this text is to demonstrate the tomographic morphology and no at- magnetic resonance imaging. It is the building block tempt is made to discuss in detail functional or physio- from which the expected three-dimensional imaging logic events. techniques of the 1990s will be developed. The wide- spread clinical application of these imaging modalities Those performing two-dimensional echocardiography should have a working knowledge of cardiac anatomy has rekindled interest in cardiac anatomy and pathol- and common congenital aberrations. This is an in-depth ogy, particularly in the evaluation of patients with con- tomographic atlas not only of the common congenital genital heart disease.
The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 [KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. The first attempts of such description were made at the end of 19th century by Jacobi [Ja890] who estimated the number of algebraically independent constants in the general solution of a system of linear ordinary differential equations. Later on, Jacobi's results were extended to some cases of nonlinear systems, but in general case the problem of such estimation (that is known as the problem of Jacobi's bound) remains open. There are some generalization of the problem of Jacobi's bound to the partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differenÂ tial equations were actively developed by F. Riquier [RiqlO] and M.