Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz (...) particle system and other mathematical structures with which fun ... (shrink)

In their rare comments on Existentialism, contemporary British philosophers, with a few notable exceptions, frequently ridicule the use of “nothing” by such writers as Sartre and Heidegger. And when it is discovered that these writers maintain that the contemplation of nothingness gives rise to anguish, this ridicule is expressed even more strongly. What may be taken as a typical example of this tendency are Professor Ayer's remarks in his Horizon articles on Sartre. A characteristic quotation runs as follows: “In particular, (...) Sartre's reasoning on the subject of le néant seems to me exactly on a par with that of the King in Alice through the Looking-Glass … The point is that words like ‘nothing” and ‘nobody” are not used as the names of something insubstantial and mysterious; they are not used to name anything at all”;. (shrink)

INTRODUCTION Max Scheler's Wesen und Formen der Sympathie, which appeared in 1923, is an essentially altered and extended second edition of a book published ...

Human fibroblasts express five tropomyosin‐like proteins, three of which have been shown to be structurally related to each other and to tropomyoins from muscle sources. These cytoskeletal tropomyosins are transcribed from three separate, non‐overlapping structural genes. However, each of these structural genes can also produce additional tropomyosin isoforms by a tissue‐specific alternative mRNA splicing mechanism.

Bradley is often described as an Anglo-Hegelian, and hence it is assumed that his doctrines derive from Hegel. It is true that his first two works ‘The Presuppositions of Critical History’ and Ethical Studies are heavily influenced by Hegel. The Principles of Logic is much less so: it certainly contains a number of both laudatory and critical references to Hegel, but the whole design of the book is completely unrelated to his treatment of logic. Appearance and Reality seems to me (...) not to be Hegelian at all. The interesting logical discussions occur in the Principles , and it is here that we can find points of comparison between Bradley and Frege and Russell. This is in part because all three were agreed that it was impossible to account for logic by reference to psychology. Bradley's doctrine of internal relations first emerges in this context, though it is given a more metaphysical interpretation in the subsequent Appearance and Reality . However, most who have talked of internal relations have taken their view from the latter work, and have found the doctrine either confused or silly. This quotation from Appearance and Reality seems to bring out all that is objectionable in the view: And if you could have a perfect relational knowledge of the world, you could go on from the nature of red-hairedness to these other characters which qualify it, and you could from the nature of red-hairedness reconstruct all the red-haired men. In such perfect knowledge you could start internally from any one character in the Universe, and you could from that pass to the rest…For example, a red-haired man who knew himself utterly would and must, starting from within, go on to know everyone else who had red hair, and he would not know himself until he knew them. But, as things are, he does not know how or why he himself has red hair, nor how and why a different man is also the same in that point, and therefore, because he does not know the ground, the how and why, of his relation to other men, it remains for him relatively external, contingent, and fortuitous. But there is really no mere externality except in his ignorance. (shrink)

Bradley is often described as an Anglo-Hegelian, and hence it is assumed that his doctrines derive from Hegel. It is true that his first two works ‘The Presuppositions of Critical History’ and Ethical Studies are heavily influenced by Hegel. The Principles of Logic is much less so: it certainly contains a number of both laudatory and critical references to Hegel, but the whole design of the book is completely unrelated to his treatment of logic. Appearance and Reality seems to me (...) not to be Hegelian at all. The interesting logical discussions occur in the Principles, and it is here that we can find points of comparison between Bradley and Frege and Russell. This is in part because all three were agreed that it was impossible to account for logic by reference to psychology. Bradley's doctrine of internal relations first emerges in this context, though it is given a more metaphysical interpretation in the subsequent Appearance and Reality. However, most who have talked of internal relations have taken their view from the latter work, and have found the doctrine either confused or silly. This quotation from Appearance and Reality seems to bring out all that is objectionable in the view:And if you could have a perfect relational knowledge of the world, you could go on from the nature of red-hairedness to these other characters which qualify it, and you could from the nature of red-hairedness reconstruct all the red-haired men. In such perfect knowledge you could start internally from any one character in the Universe, and you could from that pass to the rest…For example, a red-haired man who knew himself utterly would and must, starting from within, go on to know everyone else who had red hair, and he would not know himself until he knew them. But, as things are, he does not know how or why he himself has red hair, nor how and why a different man is also the same in that point, and therefore, because he does not know the ground, the how and why, of his relation to other men, it remains for him relatively external, contingent, and fortuitous. But there is really no mere externality except in his ignorance. (shrink)

Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new generalizations of (...) Shannon entropy and Kullback–Leibler relative entropy and called them U-entropy and U-relative entropy. In this article, a utility-based criterion for independence of two random variables is defined. Then, Markov’s inequality for probabilities is extended from the U-entropy viewpoint. Moreover, a lower bound for the U-relative entropy is obtained. Finally, a link between conditional U-entropy and conditional Renyi entropy is derived. (shrink)