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On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his P...
A Companion to Music at the Habsburgs Courts in the Sixteenth and Seventeenth Centuries, edited by Andrew H. Weaver, is the first in-depth survey of Habsburg musical patronage over a broad timeframe. Bringing together existing research and drawing upon primary sources, the authors, all established experts, provide overviews of the musical institutions, the functions of music, the styles and genres cultivated, and the historical, political, and cultural contexts for music at the Habsburg courts. The wide geographical scope includes the imperial courts in Vienna and Prague, the royal court in Madrid, the archducal courts in Graz and Innsbruck, and others. This broad view of Habsburg musical activities affirms the dynasty’s unique position in the cultural life of early modern Europe. Contributors are Lawrence Bennett, Charles E. Brewer, Drew Edward Davies, Paula Sutter Fichtner, Alexander J. Fisher, Christine Getz, Beth L. Glixon, Jeffrey Kurtzman, Virginia Christy Lamothe, Honey Meconi, Sara Pecknold, Jonas Pfohl, Pablo L. Rodríguez, Steven Saunders, Herbert Seifert, Louise K. Stein, and Andrew H. Weaver.
This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.
Readership: Graduate students and researchers in condensed matter physics.
Stem cells are the focus of intense interest from a growing, multidisciplinary community of investigators with new tools for isolating and characterizing these elusive cell types. This volume, which features contributions from many of the world's leading laboratories, provides a uniquely broad and authoritative basis for understanding the biology of stem cells and the current excitement about their potential for clinical exploitation. It is an essential work of reference for investigators in embryology, hematology, and neurobiology, and their potential for clinical exploitation. It is an essential work of reference for investigators in embryology, hematology, and neurobiology, and their collaborators in the emerging field of regenerative medicine.
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