By Antje Düsterhöft, Meike Klettke, Klaus-Dieter Schewe
This Festschrift, released in honor of Bernhard Thalheim at the get together of his sixtieth birthday offers 20 articles by way of colleagues from around the globe with whom Bernhard Thalheim had cooperation in quite a few respects; additionally integrated is a systematic biography contributed through the quantity editors. The 20 contributions replicate the breadth and the intensity of the paintings of Bernhard Thalheim in conceptual modeling and database idea in the course of his clinical profession spanning greater than 35 years of lively study. specifically, ten articles are targeting subject matters like database dependency concept, object-oriented databases, triggers, summary kingdom machines, database and knowledge structures layout, internet semantics, and enterprise processes.
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Extra resources for Conceptual Modelling and Its Theoretical Foundations: Essays Dedicated to Bernhard Thalheim on the Occasion of His 60th Birthday
6, Durrett, 1991) gives that 1/2 D (1,0) → N (0, ζ1,0 ) as n → ∞, Zn,1 + . . + Zn,n1 = n1 Hn,r Statistical Inference for R´enyi Entropy Functionals 1/2 49 (0,1) D and similarly n2 Hn,r get that → N (0, ζ0,1 ) as n → ∞. Hence, by independence we (1,0) (0,1) + r2 Hn,r ) n1/2 (r1 Hn,r r1 1/2 (1,0) r2 1/2 (0,1) D = 1/2 n1 Hn,r + n Hn,r → N (0, κr ) as n → ∞. 1/2 2 (1 − p ) n pn So, (10) and the Slutsky theorem imply ˜ n,r − q˜r, ) n1/2 (Q D (1,0) (0,1) = n1/2 (r1 Hn,r + r2 Hn,r ) + n1/2 Rn → N (0, κr ) as n → ∞.
Inf. Process. Lett. H. hu Dedicated to Professor Bernhard Thalheim for his 60th birthday Abstract. A model of random databases is given, with arbitrary correlations among the data of one individual. This is given by a joint distribution function. The individuals are chosen independently, their number m is considered to be (approximately) known. The probability of the event that a given functional dependency A → b holds (A is a set of attributes, b is an attribute) is determined in a limiting sense.
Then maxk qk →0 k qk (12) implies 2 k qk k qk ) ( 2 → 0. (13) Proof. Use (11) of Lemma 2 with c(n) = maxk qk and s = 2 k qk ( k qk ) 2 ≤ k qk c(n) + 1 c2 (n) 2 k qk ) ( = c(n) + k qk k qk : c(n) k qk 2 shows that (12) really implies (13). Return to the proof of Theorem 2. Lemma 3 will be applied for the values p2κ (A) in place of qi . Condition (12) becomes exactly (8), therefore (13) gives ( 4 κ pκ (A) 2 2 κ pκ (A)) → 0. H. Katona Let us now give a lower estimate on p(α, ξb , I) using (ii) (that is (9)) p(α, ξb , I) = p2κ (A) − κ p2κ, (A, b) ≥ (1 − u) κ, κ p2κ (A).
Conceptual Modelling and Its Theoretical Foundations: Essays Dedicated to Bernhard Thalheim on the Occasion of His 60th Birthday by Antje Düsterhöft, Meike Klettke, Klaus-Dieter Schewe