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We investigate conditions that are sufficient to make the Extalgebra of an object in a (triangulated) category into a Frobenius algebra, and compute the corresponding Nakayama automorphism. As an application, we prove the conjecture that hdet(μA) = 1 for any noetherian Artin-Schelter regular (hence skew Calabi-Yau) algebra A.

Let S denote the 3-dimensional Sklyanin algebra over an algebraically closed field k and assume that S is not a finite module over its centre. (This algebra corresponds to a generic noncommutative ℙ2.) Let A=⊕i≥0 Ai be any connected graded k-algebra that is contained in and has the same quotient ring as a Veronese ring S(3n). Then we give a reasonably complete description of the structure of A. This is most satisfactory when A is a maximal order, in which case we prove, subject to a minor technical condition, that A is a noncommutative blowup of S(3n) at a (possibly noneffective) divisor on the associated elliptic curve E. It follows that A has surprisingly pleasant properties; for example, it is automatically noetherian, indeed strongly noetherian, and has a dualising complex.

We show that the twisted homogeneous coordinate rings of elliptic curves by infinite order automorphisms have the curious property that every subalgebra is both finitely generated and noetherian. As a consequence, we show that a localisation of a generic Skylanin algebra has the same property.

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]

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.)