Alternating quaternary algebra structures on irreducible representations of sl(2,C)

We determine the multiplicity of the irreducible representation V(n) of the simple Lie algebra sl(2,C) as a direct summand of its fourth exterior power $\Lambda^4 V(n)$. The multiplicity is 1 (resp. 2) if and only if n = 4, 6 (resp. n = 8, 10). For these n we determine the multilinear polynomial identities of degree $\le 7$ satisfied by the sl(2,C)-invariant alternating quaternary algebra structures obtained from the projections $\Lambda^4 V(n) \to V(n)$. We represent the polynomial identities as the nullspace of a large integer matrix and use computational linear algebra to find the canonical basis of the nullspace.Comment: 26 pages, 13 table

Kinetic simulation of the sheath dynamics in the intermediate radio-frequency regime

The dynamics of temporally modulated plasma boundary sheaths is studied in the intermediate radio frequency regime where the applied radio frequency and the ion plasma frequency are comparable. Two kinetic simulation codes are employed and their results are compared. The first code is a realization of the well-known scheme, Particle-In-Cell with Monte Carlo collisions (PIC/MCC) and simulates the entire discharge, a planar radio frequency capacitively coupled plasma (RF-CCP) with an additional heating source. The second code is based on the recently published scheme Ensemble-in-Spacetime (EST); it resolves only the sheath and requires the time resolved voltage across and the ion flux into the sheath as input. Ion inertia causes a temporal asymmetry (hysteresis) of the sheath charge-voltage relation; also other ion transit time effects are found. The two codes are in good agreement, both with respect to the spatial and temporal dynamics of the sheath and with respect to the ion energy distributions at the electrodes. It is concluded that the EST scheme may serve as an efficient post-processor for fluid or global simulations and for measurements: It can rapidly and accurately calculate ion distribution functions even when no genuine kinetic information is available

Early Invasive Strategy and In‐Hospital Survival Among Diabetics With Non‐ST‐Elevation Acute Coronary Syndromes: A Contemporary National Insight

Background: There are limited data on the merits of an early invasive strategy in diabetics with non‐ST‐elevation acute coronary syndrome, with unclear influence of this strategy on survival. The aim of this study was to evaluate the in‐hospital survival of diabetics with non‐ST‐elevation acute coronary syndrome treated with an early invasive strategy compared with an initial conservative strategy. Methods and Results: The National Inpatient Sample database, years 2012–2013, was queried for diabetics with a primary diagnosis of non‐ST‐elevation acute coronary syndrome defined as either non‐ST‐elevation myocardial infarction or unstable angina (unstable angina). An early invasive strategy was defined as coronary angiography±revascularization within 48 hours of admission. Propensity scores were used to assemble a cohort managed with either an early invasive or initial conservative strategy balanced on \u3e50 baseline characteristics and hospital presentations. Incidence of in‐hospital mortality was compared in both groups. In a cohort of 363 500 diabetics with non‐ST‐elevation acute coronary syndrome, 164 740 (45.3%) were treated with an early invasive strategy. Propensity scoring matched 21 681 diabetics in both arms. Incidence of in‐hospital mortality was lower with an early invasive strategy in both the unadjusted (2.0% vs 4.8%; odds ratio [OR], 0.41; 95% CI, 0.39–0.42; P\u3c0.0001) and propensity‐matched models (2.2% vs 3.8%; OR, 0.57; 95% CI, 0.50–0.63; P\u3c0.0001). The benefit was observed across various subgroups, except for patients with unstable angina (Pinteraction=0.02). Conclusions: An early invasive strategy may be associated with a lower incidence of in‐hospital mortality in patients with diabetes. The benefit of this strategy appears to be superior in patients presenting with non‐ST‐elevation myocardial infarction compared with unstable angina

Outcomes with plug‐based versus suture‐based vascular closure device after transfemoral transcatheter aortic valve replacement: A systematic review and meta‐analysis

Background Studies comparing plug-based (i.e., MANTA) with suture-based (i.e., ProStar XL and ProGlide) vascular closure devices (VCDs) for large-bore access closure after transcatheter aortic valve replacement (TAVR) have yielded mixed results. Aims To examine the comparative safety and efficacy of both types of VCDs among TAVR recipients. Methods An electronic database search was performed through March 2022 for studies comparing access-site related vascular complications with plug-based versus suture-based VCDs for large-bore access site closure after transfemoral (TF) TAVR. Results Ten studies (2 randomized controlled trials [RCTs] and 8 observational studies) with 3113 patients (MANTA = 1358, ProGlide/ProStar XL = 1755) were included. There was no difference between plug-based and suture-based VCD in the incidence of access-site major vascular complications (3.1% vs. 3.3%, odds ratio [OR]: 0.89; 95% confidence interval [CI]: 0.52−1.53). The incidence of VCD failure was lower in plug-based VCD (5.2% vs. 7.1%, OR: 0.64; 95% CI: 0.44−0.91). There was a trend toward a higher incidence of unplanned vascular intervention in plug-based VCD (8.2% vs. 5.9%, OR: 1.35; 95% CI: 0.97−1.89). Length of stay was shorter with MANTA. Subgroup analyses suggested significant interaction based on study designs such that there was higher incidence of access-site vascular complications and bleeding events with plug-based versus suture-based VCD among RCTs. Conclusion In patients undergoing TF-TAVR, large-bore access site closure with plug-based VCD was associated with a similar safety profile as suture-based VCD. However, subgroup analysis showed that plug-based VCD was associated with higher incidence of vascular and bleeding complications in RCTs