For any partition of {1, 2, . . . , n} we define its increments Xi, 1 ≤ i ≤ n by Xi = 1 if i is the smallest element in the partition block that contains it, Xi = 0 otherwise. We prove that for partially exchangeable random partitions (where the probability of a partition depends only on its block sizes in order of appearance), the law of the increments uniquely determines the law of the partit...

let a be a unital algebra over a field of characteristic zero. we show that every derivation from( ) n m a into its dual ( ) n m a ∗ is the sum of an inner derivation and a derivation induced by a derivationfrom a into a∗

Canadian and US genetic evaluations for July 1991 were combined for 3304 Holstein bulls evaluated in Canada that had US progeny or a cross-reference code. Canadian evaluations of the bulls and their sires and dams were converted to US PTA. Combined PTA were weighted averages of progeny information from both countries and parent average. Parent average was recomputed from the sire's combined eva...

cal College who has received the title of Kui Bahadur from Government, and we are fully convinced that these gentlemen well deserve the distinctions conferred on them. Nevertheless, it strikes us as somewhat remarkable, that of all the professors attached to the College, only one (Dr. Fayrer) has received any mark of distinction from the Government. This remark applies not only to the medical o...

The aim of this paper is to show that under some mild conditions a functional equation of multiplicative $(alpha,beta)$-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(alpha,beta)$-derivation.

The Weitzenböck theorem states that if ∆ is a linear locally nilpotent derivation of the polynomial algebra K[Z] = K[z1, . . . , zm] over a field K of characteristic 0, then the algebra of constants of ∆ is finitely generated. If m = 2n and the Jordan normal form of ∆ consists of 2 × 2 Jordan cells only, we may assume that K[Z] = K[X,Y ] and ∆(yi) = xi, ∆(xi) = 0, i = 1, . . . , n. Nowicki conj...

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The score of the piano work nr. 7 Klavierstu ck XI by Karlheinz Stockhausen (1957) [4] consists of 19 fragments of music. The performer is instructed to choose at random one of these fragments, and play it; then choose another, different, fragment and play that, and so on. If a fragment is chosen that has already been played twice, the performance ends. It is natural to ask how many different w...