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

Enhancing the performance of conventional solar still using the Nano-doped paint (NDP) coating

Nations are throughout the entire globe continuously confronting the problem of potable water shortage. Recently, it has been thought that using solar energy to desalinate brackish water offers a practical answer to the world\u27s water crises. The output of these stills, is meager, and academics haven\u27t done much to boost it in any way. Solar distillers have been proposed as an efficient method to produce potable water. In recent years, saltwater has produced drinking water by various ways. The efficiency of a solar distiller is significantly influenced by various factors, most important factor of them is the absorber surface. In this research, an effort is made to increase the efficiency of a traditional solar distiller by applying a thin coating of Nano-black paint to increase the thermal conductivity of the absorber surface. The absorber significantly affects how effectively the solar still functions. In the experiment described in this article, a layer of Nano-doped black paint (NDBP) was applied on that which absorbs a standard solar still in an effort to improve the device\u27s performance. The results showed that the nanocoating changed the condensation mechanism of all materials from film-wise to droplet-wise.It was also concluded that drip condensation at larger surface inclination angles leads to increased condensate water production.For example, the formation of condensation on the glass surface was increased by the 23rd nanocoating at a surface tilt angle of 50°. Additionally, an additional collector was used to estimate the droplet volume before and after the coating process. Also, The results indicated that, the productivity of the conventional solar still has been increased with about 25-32% when use the nano thermal coated. While the modification in design produces an average 18% improvement in fresh water productivit

The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

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

Longitudinal transcriptomic and genetic landscape of radiotherapy response in canine melanoma

Canine malignant melanoma (MM) is a highly aggressive tumour with a low survival rate and represents an ideal spontaneous model for the human counterpart. Considerable progress has been recently obtained, but the therapeutic success for canine melanoma is still challenging. Little is known about the mechanisms beyond pathogenesis and melanoma development, and the molecular response to radiotherapy has never been explored before. A faster and deeper understanding of cancer mutational processes and developing mechanisms are now possible through next generation sequencing technologies. In this study, we matched whole exome and transcriptome sequencing in four dogs affected by MM at diagnosis and at disease progression to identify possible genetic mechanisms associated with therapy failure. According to previous studies, a genetic similarity between canine MM and its human counterpart was observed. Several somatic mutations were functionally related to MAPK, PI3K/AKT and p53 signalling pathways, but located in genes other than BRAF, RAS and KIT. At disease progression, several mutations were related to therapy effects. Natural killer cell-mediated cytotoxicity and several immune-system-related pathways resulted activated opening a new scenario on the microenvironment in this tumour. In conclusion, this study suggests a potential role of the immune system associated to radiotherapy in canine melanoma, but a larger sample size associated with functional studies are needed

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