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DENSE INFINITE Bh SEQUENCES

For h = 3 and h = 4 we prove the existence of infinite Bh sequences B with counting function B(x) = x √ (h−1)2+1−(h−1)+o(1). This result extends a construction of I. Ruzsa for B2 sequences.

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Bh Sequences in Higher Dimensions

In this article we look at the well-studied upper bounds for |A|, where A ⊂ N is a Bh sequence, and generalise these to the case where A ⊂ N d. In particular we give d-dimensional analogues to results of Chen, Jia, Graham and Green.

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First Bh Cochrane Symposium Held

The first BH Cochrane Symposium was held on 12 October 2015 in Sarajevo, Bosnia and Herzegovina (BH), organized by the Agency for Quality and Accreditation in Healthcare in Federation of BH (AKAZ) and Medical Faculty University of Sarajevo. A group of ten national and international experts presented the Cochrane organization and systematic reviews, as well as the IMPACT Observatory, development...

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The Small Scatter in BH-Host Correlations & The Case for Self-Regulated BH Growth

Supermassive black holes (BHs) obey tight scaling relations between their mass and their host galaxy properties such as total stellar mass, velocity dispersion, and potential well depth. This has led to the development of self-regulated models for BH growth, in which feedback from the central BH halts its own growth upon reaching a critical threshold. However, models have also been proposed in ...

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NEW UPPER BOUNDS FOR FINITE Bh SEQUENCES

Let Fh(N) be the maximum number of elements that can be selected from the set {1, . . . , N} such that all the sums a1 + · · · + ah, a1 ≤ · · · ≤ ah are different. We introduce new combinatorial and analytic ideas to prove new upper bounds for Fh(N). In particular we prove F3(N) ≤   4 1 + 16 (π+2)4 N   1/3 + o(N), F4(N) ≤   8 1 + 16 (π+2)4 N   1/4 + o(N). Besides, our techniques have an...

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For any positive integers h ≥ 2 and g ≥ 1, we present a greedy algorithm that provides an infinite Bh[g] sequence with an ≤ 2gnh+(h−1)/g.

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