sarily include the original publication in which the use of a particular protective group was first proposed. Despite these reservations, the book can be recommended as an excellent and very useful source of information for all chemists concerned with the synthesis of polyfunctional compounds. Its coverage has been extended from that of the first edition to include N-protecting groups for five-membered heterocycles and amides, but the latest developments in the use of protective groups that can be removed enzymically were, of course, too recent to be included (H. Waldmann, Kontakte (Merck) 1991 (3), 33). The second edition of “Protective Groups in Organic Synthesis” should be available at all times in every organic preparative laboratory. Hovst Kunz Institut fur Organische Chemie der Universitat Mainz (FRG) Elementary Introduction to Spatial and Temporal Fractals. (Series: Lecture Notes in Chemistry, Vol. 55.) By L. T Fan, D. Neogi and M . Yashima. Springer, Berlin, 1991. IX, 168 pp., paperback DM 44.00.--ISBN 3-540-54212-4 The importance of fractals for describing complex structures and complicated phenomena is now generally recognized, and in the last few years quite a number of books explaining the basic concepts of fractals in an easily understandable way have appeared. The book reviewed here is such a one; it gives an introduction to spatial and temporal fractals, and is intended particularly for students and research scientists working in the area of chemistry. The main emphasis is on definitions, methods and applications; detailed mathematical derivations are kept to a minimum. It is roughly 150 pages in length, and is clearly divided into four parts followed by a detailed appendix. In the first part the concepts and definitions of fractals are explained. Topological and Hausdorff-Besicovitch fractals and Euclidean dimensions are compared. Line, surface, and volume fractals are also explained. The second part contains examples that the reader can easily understand using the knowledge gained from the first part. The reader progresses via Cantor sets and Koch curves to coastal perimeters. Particular attention is devoted to methods for determining the fractal dimensions of irregular surfaces. The concept of multifractals is also touched on briefly, and it is shown that complex objects cannot always be fully characterized by a single exponent; instead this may require a distribution of exponents. The justification for this procedure in terms of information theory is not gone into here. Almost every book on fractals has to include a discussion of growth models; here the authors confine their attention to the best known of these, namely the Eden model and the diffusion-generated aggregation model. Transport and dynamic processes in fractal structures are not treated, and accordingly only those characteristic exponents that are of importance for structural analysis are discussed. The third part of the book deals with temporal fractals. These are also taken to include time series arising from measurements as a function of time, for example, data on the prices of commodities as these vary with time. Such price variations often do not show a normal (Gaussian) distribution. Fluctuations of this sort can be analyzed in terms of stable distributions and fractional Brownian motions. Here a distinction is also made between the properties of selfaffinity and self-similarity. The Hurst method for determining the characteristic exponents of discrete time series is deAngew. Chem. Inr. Ed. Engl. 3i (1992) No. S 0 VCH Verlagsgesellschaft mbH, scribed. Only in the final section of this part do the authors deal with “real” time fractals. These include stochastic processes in which the intervals between successive events have a distribution characterized by a divergent average interval. However, the fundamental importance of temporal fractals for the interpretation of dispersive transport processes and slow relaxation phenomena is scarcely mentioned. The last part is devoted to chaos phenomena. The authors clearly explain the role of the strange attractor in characterizing chaos in deterministic nonlinear systems, and that of the Liapunov exponents in predicting trajectories. The relationship between fractals and chaos is made clear by a consideration of the fractal dimensions of the strange attractor. The appendix should prove useful for readers interested in practical applications. Here the fractal properties for three particular cases are examined, by determining the fractal dimensions for the perimeter of coal particles, for the surface of rice hulls, and for the pressure fluctuations in multiphase flow systems. Each case study begins with a theoretical introduction, which is followed by a description of the experimental arrangement, and finally a discussion of the results with the help of figures and tables. This book serves very well the needs of the reader who has no previous knowledge of the subject, and wishes to acquire the necessary background for an understanding of fractals, especially for applications to chemistry, in a way that does not make exacting demands. The price of DM 44.00 is appropriate for a book at this level. Gerd Zumofen Laboratorium fur Physikalische Chemie der Eidgenossischen Technischen Hochschule, Zurich (Switzerland) Molecular Mechanism for Sensory Signals. By E. M . Kosower. Princeton University Press, Princeton NJ (USA), 1991. XVI, 438 pp., hardcover $79.50.-ISBN 0-69108553-6 The elucidation of the molecular mechanisms of sensory perception, signal transduction, and the processing and storage of the information thus obtained is one of the most fascinating research areas of modern biology and biochemistry. Many different approaches are being followed, involving a very wide variety of disciplines ranging from molecular biology to neurobiology, and from molecular structure determination to the study of neuronal networks. E. M. Kosower has performed a valuable service in bringing together in a single publication a survey of the current knowledge on this complex subject. At the beginning of the book the author defines a hierarchical classification of the world of living organisms, which is made up of levels of organization of varying complexity. A consideration of how these individual levels fit together provides explanations for many apparently unconnected results. This approach from the viewpoint of systems and functions is becoming increasingly important in modern biology. It is a concept to which E. M. Kosower frequently refers back in this book, thereby making many of the relationships easier to understand. It is only very recently that detailed knowledge has been gained about the mechanism of vision, the olfactory system, the sense of taste, and the transduction of signals. From this a number of common principles and levels of function have been recognized; the receptors, which belong to the lowest level, appear to have similar structures (containing seven W-6940 Weinheim. 1992 0570-0833/92/0S05-0659$3.50+ .Dl0 659 transmembrane helices) in different organisms. This is found not only for bacterial receptors, such as the archaebacterial photoreceptors, but also for eukaryontic receptors such as rhodopsin. At the next level the signal is amplified and converted into a cellular response. A system in which this has been studied especially thoroughly is the G-protein cascade in the mechanism of vision. The transmission, processing and storage of signals is made possible by the communication between neurons. As illustrative examples the author has chosen the nicotinic acetylcholine receptor and the sodium ion channels. The book ends with a discussion of the problems of learning and memory. A wealth of information is presented in this book, not least through the comprehensive bibliography, which contains 1394 references and provides detailed coverage of results reported up to about 1989. For this reason it could be thoroughly recommended as an introduction to this field, were it not for the author’s somewhat individual presentation and interpretation of the results. He gives prominence to his own molecular models of rhodopsin, of the acetylcholine nicotine receptor, and of the sodium ion channel. These ideas regarding their molecular structures are intellectually appealing and are enjoyable to read, and they also allow one to specify some predictions that any theory should satisfy. Nevertheless, one should always bear in mind that these models have not yet been experimentally verified, and that (at least in the case of rhodopsin) some of the details appear to be contradicted by the most recent results. The data given are often unnecessarily detailed, which is annoying as they are only of interest as examples. Thus, it is not particularly useful to give the structures of so many odor substances and to list the amino acid sequences in such detail as here. Also it is questionable whether secondary structural features such as the a-helix or P-folding need to be described yet again in a book about the molecular mechanisms of sensory perception. Moreover, the quality of the diagrams in these descriptions is very disappointing compared with, for example, those found in textbooks of biochemistry. To summarize, there are difficulties in the way of recommending this book for a wide readership. However, for those who are interested in an unorthodox treatment of the subject, and who already have at least some relevant knowledge, the book is well worth reading. Martin Engelhard Max-Planck-Institut fur Ernahrungsphysiologie, Dortmund (FRG) Electron Deficient Boron and Carbon Clusters. Edited by G. A . Olah, K. Wade and R . E. Williams. Wiley, Chichester, 1991. xii, 379 pp., hardcover. E 47.50.-1SBN 0-471-52795-5 For some decades now, we chemists have had access to the theoretical tools needed for the correct quantitative description of bonding in molecules, and nowadays, thanks to developements in computers and programs, they are available for everyone to use. Nevertheless, it still remains true that for the majority of molecules one can, to a good approximation, describe the bonding by assuming the limiting case of localized two-center two-electron bonds. An adequately good approximation often provides qualitative insights that might be obscured by using other, quantitatively more accurate, theoretical methods. In this respect the majority of classical molecules can be contrasted to those types of molecules that are still regarded as “exotic” and cannot be described even to a 660 0 VCH Verlagrgr.~eNschaJt mhH, W-6940 Weinhrim, 1992 crude approximation in terms of two-center localized bonding; these are the nonclassical molecules, to which the Lewis description cannot be applied because they are electron-deficient. Although elements belonging to any part of the Periodic Table can be involved in the formation of nonclassical molecules, it is boron compounds that continue to provide the most striking examples. The monograph reviewed here, which is dedicated to W N. Lipscomb on the occasion of his 70th birthday, consists of fourteen articles, eleven of which are on boron cluster compounds. A contribution by T. C. Flood describes some remarkable studies of the oxidative addition of C-H bonds to soluble osmium and iridium complexes, but does not cover electron-deficient boron and carbon compounds. There is only one contribution dealing with carbon clusters, namely that by G. A. Olah on the hypercoordinated nonclassical carbonium ions of which CHY is the prototype; this article, a sequel to a recently published monograph on the subject,’*’ clearly brings out the relationships between carbon and boron clusters and is well worth reading. These relationships are also emphasized in the editors’short introduction to the book. In their other contributions the editors go beyond their own research in order to explore more general relationships. Olah’s article has already been mentioned. R. E. Williams returns to the simple “styx” rules developed by Lipscomb. These state that the bonding skeleton of the boron hydrides and their heteroatom derivatives can be described qualitatively in terms of two-electron bonding between two or three centers, namely between two or three boron atoms or between one hydrogen atom and one (endo B-H) or two (B-H-B bridging) boron atoms, provided that where several canonical distributions of these four bond types are possible, resonance is assumed. Williams defines formal charges and derives the structure and the dynamic behavior of the nido cluster compounds from the distribution of these charges over the molecule. Boron hydride specialists will benefit from the wealth of knowledge presented here by this doyen of cluster systematics. In a shorter and more general contribution, K. Wade also starts from charge distributions in localized bonding structures according to the styx model to continue with an MO approach to such charge distributions involving more than three centers. A completely different theoretical approach is described by M. Buhl and P. von R. Schleyer, who report laborious ab initio calculations of the geometries of some boron hydrides and hydroborates. The essential conclusion is that the calculated geometries are better than those determined experimentally, taking as a criterion the ‘‘B NMR signals calculated by the IGLO method; it is well known that these match the observed NMR signals strictly, depending on the correctness of the assumed molecular geometry. A contribution by D. M. P. Mingos and D. J. Wales is concerned with the mechanism of the “diamond-square-diamond” process, in which a polyhedral lattice opens up along one edge of its triangular network to form a square, then closes up again in a direction perpendicular to the original one. (A striking example of this is the Berry pseudorotation.) The remaining seven articles deal with synthetic, structural, or mechanistic aspects. L G. Sneddon and S. D. Kang describe some new hypho clusters and point out that there are regions in these open cluster structures which contain classical bonds. The rest of the contributions are concerned with recent developments, some of the most impressive ones coming from the Fehlner and Greenwood/Kennedy groups in the [*] G. A. Olah, G. K. S. Prakash, R. E. Williams, L. D. Field, K. Wade, Hypercarbon Chemistry, Wiley, New York, 1987. 0570-0833J92j0505-0660 $3.50+ ,2510 Angew. Chem. Int. Ed. EngI. 31 (1992) No. 5

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