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Dr. Erwin Brommer 《Mathematical Methods of Operations Research》1956,1(1):18-21
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Renate Jaritz 《Journal of Geometry》1993,47(1-2):39-52
An elementary content I is a real valued, non-negative, invariant and monotonous homomorphism on a decomposition structure of elementary figures. The semigroup (H,+,) of abstract classes is introduced (§3) by using the relation of equidecomposability and it's natural generalizations. Each elementary content divides into I= where and are canonical homomorphisms with respect to the relations studied before and : H + is a monotonous homomorphism called content (cf. Satz 3, §3). In §4 (Satz 4) the Existence-Theorem on contents is stated and it is proved in §5. The last section §6 gives the application on Archimedean decomposition structures including the case of volume measurement on polyhedrons. 相似文献
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Artur Bergmann 《Archiv der Mathematik》1959,10(1):243-256
Ohne ZusammenfassungDer Deutschen Forschungsgemeinschaft danke ich für die Unterstützung bei der Durchführung der vorliegenden Untersuchungen. 相似文献
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Ohne ZusammenfassungHerrnE. Kamke zum 70. Geburtstag am 18. August 1960 gewidmet 相似文献
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Summary Conditions on a linear algebraic eigenvalue problem are given, under which there are exactlyk–1 changes of sign in the sequence of components of thek-th eigenvector. This is analogous to the oscillation theorems of differential equations. A class of difference equations which satisfies these conditions is defined. Finally a modification of a method ofCollatz is given, by means of which upper and lower bounds for thek-th eigenvalue may be derived from a trial vector havingk–1 sign changes in the sequence of its components. This paper is merely a summary of results; no proofs are given. 相似文献
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Ragmar Rudolph 《Monatshefte für Mathematik》1982,94(2):149-153
The aim of this paper is to prove that certain 2-generator modular groups are infinite if and only if they contain a Tarski-Monster as a subgroup. This restricts considerably the structure of these groups and allows to give a structure theorem for this kind of groups. 相似文献
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We shall prove the following partition theorems:
- For every setS and for each cardinal ? ≥ ω, |S| ≥ ? there exists a partitionT: [S]? → 2? such that for every pairwise disjoint familie and everyα < 2? there exists a set
- Suppose ? ≥ ω, 2 andS an arbitrary set, 2|S| ≤ (2?)+ω Then there exists a partitionT: P(S) → 2? such that for every pairwise disjoint family and everyα < 2? there exists a set Both theorems will give partial answers to an Erd?s problem.
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