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Let A be a commutative integral domain that is a finitely generated algebra over a field k of characteristic 0 and let ø be a k-algebra automorphism of A of finite order m. In this note we study the ring D(A;ø of differential operators introduced by A.D. Bell. We prove that if A is a free module over the fixed sub-ring Aø, with a basis containing 1, then D(A;ø) is isomorphic to the matrix ring Mm(D(Aø). It follows from Grothendieck's Generic Flatness Theorem that for an arbitrary A there is an element cεAsuch that D(A[c-1];ø)≅Mm(D(A[c-1]ø)). As an application, we consider the structure of D(A;ø)when A is a polynomial or Laurent polynomial ring over k and ø is a diagonalizable linear automorphism.

Introduction: The risk of developing deep vein thrombosis (DVT) is high even after the period of bed rest following major general surgery including total joint arthroplasty (TJA). Mobile intermittent pneumatic compression (IPC) devices allow the application of IPC during postoperative exercise. Although ambulation included ankle movement, no reports have been made regarding the effects of IPC during exercise, including active ankle exercise (AAE), on venous flow. This study was performed to examine whether using a mobile IPC device can effectively augment the AAE-induced increase in peak velocity (PV).Methods: PV was measured by Doppler ultrasonography in the superficial femoral vein at rest, during AAE alone, during IPC alone, and during AAE with IPC in 20 healthy subjects in the sitting position. PV in AAE with IPC was measured with a mobile IPC device during AAE in the strong compression phase. AAE was interrupted from the end of the strong compression phase to minimize lower limb fatigue.Results: AAE with IPC (76.2 cm/s [95%CI, 69.0–83.4]) resulted in a significant increase in PV compared to either AAE or IPC alone (47.1 cm/s [95%CI, 38.7–55.6], p< 0.001 and 48.1 cm/s [95%CI, 43.7–52.4], p< 0.001, respectively).Discussion: Reduced calf muscle pump activity due to the decline in ambulation ability reduced venous flow. Therefore, use of a mobile IPC device during postoperative rehabilitation in hospital and activity including self-training in an inpatient ward may promote venous flow compared to postoperative exercise without IPC.Conclusion: Use of a mobile IPC device significantly increased the PV during AAE, and simultaneous AAE with IPC could be useful evidence for the prevention of DVT in clinical settings, including after TJA.

Purpose: There is a pressing need for safe venous thromboembolism (VTE) prophylaxis in orthopedic patients with the highest risks of both venous thrombosis and bleeding. Portable intermittent pneumatic compression device (IPCD) has proven to be effective and safe in patients with a high risk of venous thrombosis and low bleeding risk. Therefore, this study examined the effectiveness, safety, and wearing compliance of portable IPCD for postoperative VTE prophylaxis in patients with the highest risks of both venous thrombosis and bleeding.Methods: The cases consisted of 38 patients who had used a portable IPCD and had the highest risks of both venous thrombosis and bleeding. We examined the incidence of VTE to assess the effectiveness of the portable IPCD, the presence of hemorrhagic adverse events to assess safety, and the wearing rate to assess wearing compliance.Results: The incidences of asymptomatic and symptomatic deep vein thrombosis were 5.3% and 2.6%, respectively. The incidence of hemorrhagic adverse events was 21.1% in patients who received anticoagulants and wore an IPCD simultaneously and 0% in patients who wore an IPCD but did not receive anticoagulants. The wearing rate (i.e. ≥18 h/day) was 100%.Conclusion: Portable IPCD has the potential for safe VTE prophylaxis in patients at high risks for both venous thrombosis and bleeding. Therefore, we suggest that such patients use a portable IPCD for VTE prophylaxis.