The book is an expanded autobiography of the famous theoretical physicist Isaak Khalatnikov. He worked together with L.D. Landau at the Institute for Physical Problems lead by P.L. Kapitza. He is the co-author of L.D. Landau in a number of important works. They worked together in the frame of the so-called Nuclear Bomb Project. After the death of L.D. Landau, I.M. Khalatnikov initiated the establishment of the Institute for Theoretical Physics, named in honour of L.D. Landau, within the USSR Academy of Sciences. He headed this institute from the beginning as its Director. The institute inherited almost all traditions of the Landau scientific school and played a prominent role in the development of theoretical physics. So, this is a story about how the institute was created, how it worked, and about the life of the physicists in the "golden age" of the Soviet science. A separate chapter is devoted to today ́s life of the institute and the young generation of physicists working now in science. It is an historically interesting book on the development of Soviet and Russian science and presents the background of the Soviet nuclear bomb program in the cold war age. In war times, Khalatnikov was a chief of the military staff of nuclear research. He writes about the internal conditions of Soviet society, the way of operating of the Soviet authorities and ways for scientists to interact with them. It gives many interesting insights into the development of superconductivity and superfluidity. The book is written by the most experienced and best informed person among the few living Russian scientists in the environment of Landau. Many stories of the book were never published before and considered as "top secret".

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"Jerusalem is the center of the universe, the hub of the three great monotheistic religions, yet how did a city located on the desert fringe, in the semi-arid southern highlands of Israel with little tillable land achieve such dominance? To provide answers to this enduring riddle, Israel Finkelstein has collected twenty-four of his best articles and essays covering the Middle Bronze Age to the late Hellenistic period. With critical and well-informed care, he analyzes archaeological evidence that often stands in tension with the biblical text. Topics of particular interest include the archaeology of the tenth century BCE; Saul, David, and Solomon in the Bible and archaeology; the first expansion of the city in the ninth century; its full growth in the late eighth to seventh centuries; Jerusalem and Judah under the Assyrian Empire; the days of King Josiah; and transormations in the Persian-Hellenistic era"--

I Hilbert Spaces.- 1.1 Complex n-Space.- 1.2 The Hilbert Space ?2.- 1.3 Definition of Hilbert Space and its Elementary Properties.- 1.4 Distance from a Point to a Finite Dimensional Space.- 1.5 The Gram Determinant.- 1.6 Incompatible Systems of Equations.- 1.7 Least Square Fit.- 1.8 Distance to a Convex Set and Projections onto Subspaces.- 1.9 Orthonormal Systems.- 1.10 Szegö Polynomials.- 1.11 Legendre Polynomials.- 1.12 Orthonormal Bases.- 1.13 Fourier Series.- 1.14 Completeness of the Legendre Polynomials.- 1.15 Bases for the Hilbert Space of Functions on a Square.- 1.16 Stability of Orthonormal Bases.- 1.17 Separable Spaces.- 1.18 Isometry of Hilbert Spaces.- 1.19 Example of a Non Separable Space.- Exercises.- II Bounded Linear Operators on Hilbert Spaces.- 2.1 Properties of Bounded Linear Operators.- 2.2 Examples of Bounded Linear Operators with Estimates of Norms.- 2.3 Continuity of a Linear Operator.- 2.4 Matrix Representations of Bounded Linear Operators.- 2.5 Bounded Linear Functionals.- 2.6 Operators of Finite Rank.- 2.7 Invertible Operators.- 2.8 Inversion of Operators by the Iterative Method.- 2.9 Infinite Systems of Linear Equations.- 2.10 Integral Equations of the Second Kind.- 2.11 Adjoint Operators.- 2.12 Self Adjoint Operators.- 2.13 Orthogonal Projections.- 2.14 Two Fundamental Theorems.- 2.15 Projections and One-Sided Invertibility of Operators.- 2.16 Compact Operators.- 2.17 The Projection Method for Inversion of Linear Operators.- 2.18 The Modified Projection Method.- 2.19 Invariant Subspaces.- 2.20 The Spectrum of an Operator.- Exercises.- III Laurent and Toeplitz Operators on Hilbert Spaces.- 3.1 Laurent Operators.- 3.2 Toeplitz Operators.- 3.3 Band Toeplitz operators.- 3.4 Toeplitz Operators with Continuous Symbols.- 3.5 Finite Section Method.- 3.6 The Finite Section Method for Laurent Operators.- Exercises.- IV Spectral Theory of Compact Self Adjoint Operators.- 4.1 Example of an Infinite Dimensional Generalization.- 4.2 The Problem of Existence of Eigenvalues and Eigenvectors.- 4.3 Eigenvalues and Eigenvectors of Operators of Finite Rank.- 4.4 Existence of Eigenvalues.- 4.5 Spectral Theorem.- 4.6 Basic Systems of Eigenvalues and Eigenvectors.- 4.7 Second Form of the Spectral Theorem.- 4.8 Formula for the Inverse Operator.- 4.9 Minimum-Maximum Properties of Eigenvalues.- Exercises.- V Spectral Theory of Integral Operators.- 5.1 Hilbert-Schmidt Theorem.- 5.2 Preliminaries for Mercer's Theorem.- 5.3 Mercer's Theorem.- 5.4 Trace Formula for Integral Operators.- Exercises.- VI Unbounded Operators on Hilbert Space.- 6.1 Closed Operators and First Examples.- 6.2 The Second Derivative as an Operator.- 6.3 The Graph Norm.- 6.4 Adjoint Operators.- 6.5 Sturm-Liouville Operators.- 6.6 Self Adjoint Operators with Compact Inverse.- Exercises.- VII Oscillations of an Elastic String.- 7.1 The Displacement Function.- 7.2 Basic Harmonic Oscillations.- 7.3 Harmonic Oscillations with an External Force.- VIII Operational Calculus with Applications.- 8.1 Functions of a Compact Self Adjoint Operator.- 8.2 Differential Equations in Hilbert Space.- 8.3 Infinite Systems of Differential Equations.- 8.4 Integro-Differential Equations.- Exercises.- IX Solving Linear Equations by Iterative Methods.- 9.1 The Main Theorem.- 9.2 Preliminaries for the Proof.- 9.3 Proof of the Main Theorem.- 9.4 Application to Integral Equations.- X Further Developments of the Spectral Theorem.- 10.1 Simultaneous Diagonalization.- 10.2 Compact Normal Operators.- 10.3 Unitary Operators.- 10.4 Singular Values.- 10.5 Trace Class and Hilbert Schmidt Operators.- Exercises.- XI Banach Spaces.- 11.1 Definitions and Examples.- 11.2 Finite Dimensional Normed Linear Spaces.- 11.3 Separable Banach Spaces and Schauder Bases.- 11.4 Conjugate Spaces.- 11.5 Hahn-Banach Theorem.- Exercises.- XII Linear Operators on a Banach Space.- 12.1 Description of Bounded Operators.- 12.2 Closed Linear Operators.- 12.3 Closed Graph Theorem.- 12.4 Applications of the Closed Grap

Book by Scheffler, Israel

This book offers a personal account of scholars in philosophy and education with whom I have had the good fortune to interact during the course of my half century at Harvard University and elsewhere. My aim in writing this account is threefold: ?rst, to recapture for myself the pleasure of their memorable company for its own sake, secondly, to have occasion to re'ect on the educational impact of their teaching, and, ?nally, to counteract the prevalent amnesia of universities by recalling the conduct of scholars of past generations who still have things to teach us. Iowe thanks to many people who have helped me in this endeavor. Professor Harvey Siegel, Dr. Stefania Jha, and Dr. Rosalind Schef'er read initial versions of the manuscript and gave me the bene't of their criticisms, as did the publisher's anonymous readers. JoAnne Sorabella and Stefania Jha listened to my readings of a number of these chapters, and JoAnne Sorabella produced several typescripts of the whole with her usual matchless pro'ciency. I presented some portions of the manuscript to the Philosophy of Education Research Center at Harvard and pro'ted from these occasions. After I joined the Mandel Center at Brandeis University in the Fall of 2003, Avital Feuer assisted me ably in readying the ?nal version of the book. And I am grateful to Laurie Schef'er for her meticulous help with proofreading.

About the Contributor(s): Israel Scheffler is Victor S. Thomas Professor of Education and Philosophy Emeritus at Harvard University. He taught philosophy at Harvard from 1952 to 1992 and, from 1983 to 2003, was codirector, then director of the Philosophy of Education Research Center there. He is a Fellow of the American Academy of Arts and Sciences, a founding member of the National Academy of Education, and a past president of both the Philosophy of Science Association and the Charles S. Peirce Society. Among his previous books are ""The Anatomy of Inquiry""( 1963), ""Four Pragmatists""(1974), ""Of Human Potential""(1985), ""In Praise of the Cognitive Emotions""(1991), and ""Worlds of Truth""(2009). His main interests lie in the philosophical interpretation of language, symbolism, science, and education.

This book is an educational memoir, addressed in particular to aspects of his early Jewish education

Worlds of Truth: A Philosophy of Knowledge explicates and builds upon a half century of philosophical work by the noted philosopher Israel Scheffler. Propounds a new doctrine of plurealism which maintains the existence of multiple real worlds Offers a defense of absolute truth, which denies certainty and eschews absolutism, and defends systematic relativity, objectivity, and fallibilism Emphasizes a wide range of pragmatic interests: epistemology and scientific development, cognition and emotion, science and ethics, ritual and culture, and art and science

"Chosen Peoples", from Israel Zangwill. Israel Zangwil, british humorist and writer (1864-1926).