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Van den Bergh has defined the blowup of a noncommutative surface at a point lying on a commutative divisor [VdB]. We study one aspect of the construction, with an eventual aim of defining more general kinds of noncommutative blowups. Our basic object of study is a quasi-scheme X (a Grothendieck category). Given a closed subcategory Z, in order to define a blowup of X along Z one first needs to have a functor FZ which is an analog of tensoring with the defining ideal of Z. Following Van den Bergh, a closed subcategory Z which has such a functor is called well-closed. We show that well-closedness can be characterized by the existence of certain projective effacements for each object of X, and that the needed functor FZ has an explicit description in terms of such effacements. As an application, we prove that closed points are well-closed in quite general quasi-schemes. [ABSTRACT FROM AUTHOR]

The Weyl algebra over a field k of characteristic 0 is a simple ring of Gelfand-Kirillov dimension 2, which has a grading by the group of integers. We classify all Z-graded simple rings of GK-dimension 2 and show that they are graded Morita equivalent to generalized Weyl algebras as defined by Bavula. More generally, we study Z-graded simple rings A of any dimension which have a graded quotient ring of the form K[t, t-1; σ] for a field K. Under some further hypotheses, we classify all such A in terms of a new construction of simple rings which we introduce in this paper. In the important special case that GKdimA = tr. deg(K/k) + 1, we show that K and σ must be of a very special form. The new simple rings we define should warrant further study from the perspective of noncommutative geometry. [ABSTRACT FROM AUTHOR]

We construct an interesting family of connected graded domains of Gel’fand–Kirillov dimension 4, and show that the general member of this family is noetherian. The algebras we construct are Koszul and have global dimension 4. They fail to be Artin–Schelter Gorenstein, however, showing that a theorem of Zhang and Stephenson for dimension 3 algebras does not extend to dimension 4. The Auslander–Buchsbaum formula also fails to hold for these algebras. The algebras we construct are birational to ℙ2, and their existence disproves a conjecture of the first author and Stafford. The algebras can be obtained as global sections of a certain quasicoherent graded sheaf on ℙ1×ℙ1, and our key technique is to work with this sheaf. In contrast to all previously known examples of birationally commutative graded domains, the graded pieces of the sheaf fail to be ample in the sense of Van den Bergh. Our results thus require significantly new techniques. [ABSTRACT FROM AUTHOR]

Abstract: We describe some interesting graded rings which are generated by degree-3 elements inside the Sklyanin algebra S, and prove that they have many good properties. Geometrically, these rings R correspond to blowups of the Sklyanin at 7 or fewer points. We show that the rings R are exactly those degree-3-generated subrings of S which are maximal orders in the quotient ring of the 3-Veronese of S. [Copyright &y& Elsevier]

Abstract: An infinite-dimensional -graded k-algebra A is called projectively simple if for every nonzero two-sided ideal . We show that if a projectively simple ring A is strongly noetherian, is generated in degree 1, and has a point module, then A is equal in large degree to a twisted homogeneous coordinate ring . Here X is a smooth projective variety, is an automorphism of X with no proper -invariant subvariety (we call such automorphisms wild), and is a -ample line bundle. We conjecture that if X admits a wild automorphism then every irreducible component of X is an abelian variety. We prove several results in support of this conjecture; in particular, we show that the conjecture is true if . In the case where X is an abelian variety, we describe all wild automorphisms of X . Finally, we show that if A is projectively simple and admits a balanced dualizing complex, then is Cohen–Macaulay and Gorenstein. [Copyright &y& Elsevier]

Pharmacists have traditionally supported the prescribing process, arguably in reactive or corrective roles. The advent of pharmacist prescribing in 2004 represented a major shift in practice, leading to greater responsibility for making clinical decisions with and for patients. Prescribing rights require pharmacists to take a more prescriptive role that will allow them to contribute to long-standing prescribing challenges such as poor medication adherence, overprescribing, and the need for shared decision-making and person-centered care. Central to these endeavors are the development and possession of effective consultation skills. University schools of pharmacists in the UK now routinely include consultation skills training, which is also provided by national education bodies. These challenges remain difficult to overcome, even though it is understood, for example, that increasing the effectiveness of adherence interventions may have a far greater impact on the health of the population than any improvement in specific medical treatments. More recently, a concerted effort has been made to tackle overprescribing and the harm that may occur through the inappropriate use of medication. In routine pharmacy work, these priorities may linger at the bottom of the list due to the busy and complex nature of the work. Solutions to these problems of adherence, optimizing benefits of medication, and overprescribing have typically been pragmatic and structured. However, an arguably reductionist approach to implementation fails to address the complex patient interactions around prescribing and taking medication, and the heterogeneity of the patient's experience, leaving the answers elusive. We suggest that it is essential to explore how person-centered care is perceived and to emphasize the relational aspects of clinical consultations. The development of routine pharmacist prescribing demands building on the core values of person-centered care and shared decision making by introducing the concepts of "relational prescribing" and "open dialogue" to cultivate an essential pharmacotherapeutic alliance to deliver concrete positive patient outcomes. We provide a vignette of how a clinical case can be approached using principles of relational prescribing and open dialogue. We believe these are solutions that are not additional tasks but must be embedded into pharmacy practice. This will improve professional satisfaction and resilience, and encourage curiosity and creativity, particularly with the advent of all pharmacists in Great Britain becoming prescribers at graduation from 2026.

Background and Hypothesis: The acquired von Willebrand syndrome (AvWS), which predisposes to bleeding events, is often related to valvular heart diseases. We investigated possible implications of AvWS and factor VIII levels in patients with moderate to severe mitral regurgitation (MR) undergoing transcatheter mitral valve repair (TMVR)., Methods and Results: 123 patients with moderate to severe MR were prospectively enrolled. Complete measurements of von Willebrand Factor activity (vWFAct), von Willebrand Factor antigen (vWFAg), and factor VIII expression before and 4 weeks after TMVR were available in 85 patients. At baseline, seven patients had a history of gastrointestinal bleeding, two patients suffered bleeding events during their hospital stay, and one patient had a bleeding 4 weeks after TMVR. Even though vWFAct, vWFAct/vWFAg ratio and vWFAg values did not change after TMVR, we observed a significantly lower vWFAct/vWFAg ratio in patients with primary MR as compared to patients with secondary MR both at baseline (p = 0.022) and 4 weeks following the TMVR procedure (p = 0.003). Additionally, patients with a mean mitral valve gradient ≥4 mmHg after TMVR had significantly lower vWFAct/vWFAg ratios as compared to patients with a mean mitral valve gradient <4 mmHg (p = 0.001)., Conclusions: MR of primary etiology was associated with lower vWFAct/vWFAg ratio, hinting toward HMWM loss due to shear stress caused by eccentric regurgitation jets. In addition, morphological changes leading to postprocedural transmitral gradients ≥4 mmHg were related to lower vWFAct/vWFAg ratio 4 weeks after the procedure. Alterations of the vWFAct/vWFAg ratio in turn did not translate into a greater risk for bleeding events., (© 2020 The Authors. Clinical Cardiology published by Wiley Periodicals LLC.)