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The development of many important directions of mathematics and physics owes a major debt to the concepts and methods which evolved during the investigation of such simple objects as the Sturm-Liouville equation 2 2 y" ] q(x)y = zy and the allied Sturm-Liouville operator L = - d /dx + q(x) (lately Land q(x) are often termed the one-dimensional Schrodinger operator and the potential). These provided a constant source of new ideas and problems in the spectral theory of operators and kindred areas of analysis. This sourse goes back to the first studies of D. Bernoulli and L. Euler on the...

Alexei Fedorovich Losev (1893-1988) was among the greatest Russian philosophers, thinkers and classicists of the twentieth century. A contemporary of Mikhail Bakhtin, and a scholar of astonishing erudition with a love of the ancient world, his work remained almost unknown to the public until the fall of communism in 1990. The Dialectics of Myth, published here for the first time in the English language, remains his foremost achievement. Setting out a provocative and spiritually informed account of the way that myth informs secular and religious ideologies, it challenges limited...

Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrodinger operators and for their finite-difference analogues, Jacobi matrices. This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the...

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches....