Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im portant mathematical works on the arena of supergravity has taken place, starting with Kostant's theory of graded manifolds and continuing with Batchelor's work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe maticians and relativists who bring their experience in differen tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super symmetry is its relationship to the elementary particle spectrum."

The nitrides and carbides of boron and silicon are proving to be an excellent choice when selecting materials for the design of devices that are to be employed under particularly demanding environmental and thermal con- tions. The high degree of cross-linking, due to the preferred coordination numbers of the predominantly covalently bonded constituents equalling or exceeding three, lends these non-oxidic ceramics a high kinetic stability, and is regarded as the microscopic origin of their impressive thermal and mechanical durability. Thus it does not come as a surprise that the chemistry, the physical properties and the engineering of the corresponding binary, ternary, and even quaternary compounds have been the subject of intensive and sustained efforts in research and development. In the five reviews presented in the volumes 101 and 102 of "Structure and Bonding" an attempt has been made to cover both the essential and the most recent advances achieved in this particular field of materials research. The scope of the individual contributions is such as to address both graduate students, specializing in ceramic materials, and all scientists in academia or industry dealing with materials research and development. Each review provides, in its introductory part, the chemical, physical and, to some extent, historical background of the respective material, and then focuses on the most relevant and the most recent achievements.

The nitrides and carbides of boron and silicon are proving to be an excellent choice when selecting materials for the design of devices that are to be employed under particularly demanding environmental and thermal con- tions. The high degree of cross-linking, due to the preferred coordination numbers of the predominantly covalently bonded constituents equalling or exceeding three, lends these non-oxidic ceramics a high kinetic stability, and is regarded as the microscopic origin of their impressive thermal and mechanical durability. Thus it does not come as a surprise that the chemistry, the physical properties and the engineering of the corresponding binary, ternary, and even quaternary compounds have been the subject of intensive and sustained efforts in research and development. In the five reviews presented in the volumes 101 and 102 of "Structure and Bonding" an attempt has been made to cover both the essential and the most recent advances achieved in this particular field of materials research. The scope of the individual contributions is such as to address both graduate students, specializing in ceramic materials, and all scientists in academia or industry dealing with materials research and development. Each review provides, in its introductory part, the chemical, physical and, to some extent, historical background of the respective material, and then focuses on the most relevant and the most recent achievements.

Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im portant mathematical works on the arena of supergravity has taken place, starting with Kostant's theory of graded manifolds and continuing with Batchelor's work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe maticians and relativists who bring their experience in differen tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super symmetry is its relationship to the elementary particle spectrum."

Das Riemannsche Prinzip (Zerlegung der Definitionsmenge B in einfache Mengen B;)liegt fast allen numerischen Berechnungen und physikalischen Messungen von Integralen zugrunde. Das Lebesguesche Prinzip (Zerlegung der Zielmenge IR) fiihrt in allen Fiillen zum Erfolg, in denen das Integral nach 5.1.2.1 existiert. Entgegen dem Eindruck, den man aus einigen Darstellungen der Integrationstheorie gewinnen kann, liegt die Bedeutung des allgemeinen (Uber den Riemannschen weit hinausgehenden) Integralbegriffes nicht in der Moglichkeit, solche stark unstetigen Funktionen wie in 5 (ii) inte- grieren zu konnen (den Physiker interessieren solche Funktionen ohne- hin nicht). Entscheidend ist, daB die Menge der nach Lebesgue integrier- baren Funktionen viel schonere Eigenschaften hat als ihre Teilmenge der Riemartn-integrierbaren Funktionen; iihnlich wie bei dem Obergang von (Q auf IR erhalten wir Vollstiilldigkeitseigenschaftell (siehe Satz 5.1 J. 7 und 7.1.3.4, andererseits Beispiel 5 (iii)). Dadurch, daB im Riemannschen Konzept in 5.1.1.3 und 5.1.0.3 nur endliche Summen zugelassen sind, entrallt zunachst die Moglichkeit, unbeschriinkte Funktionen oder Bereiche zuzulassen. Erst Uber den Umweg der "uneigentlichen Integrale" (5.2.3) sind viele in der Praxis + 00 1 d x2 bedeutsame Integrale wie S e- dx und S;; zu erklaren, obwohl X -x 0 V diese gemaB dem Konzept 5.1.0.3 genauso gute Integrale sind wie 1 2 etwa S x dx. o DaB immer noch in Grundkursen die Riemannsche Methode zur Definitioll des Integrals benutzt wird, ist wohl nur aus historischen GrUnden zu erkliiren.