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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."
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.
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.
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