منابع مشابه
Every Sum System Is Divisible
We show that every sum system is divisible. Combined with B. V. R. Bhat and R. Srinivasan’s result, this shows that every product system arising from a sum system (and every generalized CCR flow) is either of type I or type III. A necessarily and sufficient condition for such a product system to be of type I is obtained.
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The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...
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In this note, we show that the set of n such that the arithmetic mean of the first n primes is an integer is of asymptotic density zero. We use the same method to show that the set of n such the sum of the first n primes is a square is also of asymptotic density zero. We also prove that both the arithmetic mean of the first n primes as well as the square root of the sum of the first n primes ar...
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 1995
ISSN: 0894-9840,1572-9230
DOI: 10.1007/bf02213453