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    Tower sets and other configurations with the Cohen-Macaulay property

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    Some well-known arithmetically Cohen-Macaulay configurations of linear varieties in Pr as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z+c called tower set. We prove that the tower schemes are arithmetically Cohen-Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen-Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes (in codimension 2). Our main result consists in showing that the support of these configurations (the generalized tower set) gives a combinatorial characterization of the primary decomposition of the arithmetically Cohen-Macaulay squarefree monomial ideals

    Linear quotients of Artinian Weak Lefschetz algebras

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    We study the Hilbert function and the graded Betti numbers for "generic" linear quotients of Artinian standard graded algebras, especially in the case of Weak Lefschetz algebras. Moreover, we investigate a particular property of Weak Lefschetz algebras, the Betti Weak Lefschetz Property, which makes possible to completely determine the graded Betti numbers of a generic linear quotient of such algebras

    Recombinant human bone morphogenetic protein-7 for treatment of long bone non-union: An observational, retrospective, non-randomized study of 105 patients

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    Autogenous bone-grafting is frequently used in the treatment of fracture non-union. The donor-site morbidity and potentially limited supply of suitable autogenous bone are commonly recognized drawbacks. Recent studies advocated the benefit and safety of recombinant human bone morphogenetic protein-7 (rhBMP-7) in several anatomical sites. An observational, retrospective, non-randomized study on the use of BMP-7 in treating non-union in various sites has been carried out by the BMP-7 Italian Observational Study (BIOS) Group. The clinical series included 105 patients. Additional grafts were used based on the surgeon's decision. Radiographic and clinical assessments were carried out at progressive time intervals on two groups: BMP-7+autograft (A) or BMP-7 (B). The mean follow-up was 29.2 months. The last assessment showed an 88.8% success rate with an average healing time of 7.9 months. At >/=9 months there was overlapping between the unions recorded in the two groups (PA-PB=1.5%; CI 95%: -0.149; 0.119). This is an observational study that illustrates the efficacy of BMP-7 with and without bone grafting for the treatment of long bone non-unions
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