Multiple Factorizations of Bivariate Linear Partial Differential Operators

We study the case when a bivariate Linear Partial Differential Operator (LPDO) of orders three or four has several different factorizations. We prove that a third-order bivariate LPDO has a first-order left and right factors such that their symbols are co-prime if and only if the operator has a factorization into three factors, the left one of which is exactly the initial left factor and the right one is exactly the initial right factor. We show that the condition that the symbols of the initial left and right factors are co-prime is essential, and that the analogous statement "as it is" is not true for LPDOs of order four. Then we consider completely reducible LPDOs, which are defined as an intersection of principal ideals. Such operators may also be required to have several different factorizations. Considering all possible cases, we ruled out some of them from the consideration due to the first result of the paper. The explicit formulae for the sufficient conditions for the complete reducibility of an LPDO were found also

Concomitant Hepatorenal Dysfunction and Malnutrition in Valvular Heart Surgery:Long-Term Prognostic Implications for Death and Heart Failure

BACKGROUND: Strategies to improve long-term prediction of heart failure and death in valvular surgery are urgently needed because of an increasing number of procedures globally. This study sought to report the prevalence, changes, and prognostic implications of concomitant hepatorenal dysfunction and malnutrition in valvular surgery. METHODS AND RESULTS: In 909 patients undergoing valvular surgery, 3 groups were defined based on hepatorenal function (the modified model for end-stage liver disease excluding international normalized ratio score) and nutritional status (Controlling Nutritional Status score): normal hepatorenal function and nutrition (normal), hepatorenal dysfunction or malnutrition alone (mild), and concomitant hepatorenal dysfunction and malnutrition (severe). Overall, 32%, 46%, and 19% of patients were classified into normal, mild, and severe groups, respectively. Over a 4.1-year median follow-up, mild and severe groups in-curred a higher risk of mortality (hazard ratio [HR], 3.17 [95% CI, 1.40–7.17] and HR, 9.30 [95% CI, 4.09– 21.16], respectively), cardiovascular death (subdistribution HR, 3.29 [95% CI, 1.14– 9.52] and subdistribution HR, 9.29 [95% CI, 3.09– 27.99]), heart failure hospitalization (subdistribution HR, 2.11 [95% CI, 1.25– 3.55] and subdistribution HR, 3.55 [95% CI, 2.04– 6.16]), and adverse outcomes (HR, 2.11 [95% CI, 1.25– 3.55] and HR, 3.55 [95% CI, 2.04– 6.16]). Modified model for end-stage liver disease excluding international normalized ratio and controlling nutritional status scores improved the predictive ability of European System for Cardiac Operative Risk Evaluation (area under the curve: 0.80 versus 0.73, P<0.001) and Society of Thoracic Surgeons score (area under the curve: 0.79 versus 0.72, P=0.004) for all-cause mortality. One year following surgery (n=707), patients with persistent concomitant hepatorenal dysfunction and malnutrition (severe) experienced worse outcomes than those without.  CONCLUSIONS: Concomitant hepatorenal dysfunction and malnutrition was frequent and strongly linked to heart failure and mortality in valvular surgery

Multi-trait genome-wide association study identifies new loci associated with optic disc parameters

A new avenue of mining published genome-wide association studies includes the joint analysis of related traits. The power of this approach depends on the genetic correlation of traits, which reflects the number of pleiotropic loci, i.e. genetic loci influencing multiple traits. Here, we applied new meta-analyses of optic nerve head (ONH) related traits implicated in primary open-angle glaucoma (POAG); intraocular pressure and central corneal thickness using Haplotype reference consortium imputations. We performed a multi-trait analysis of ONH parameters cup area, disc area and vertical cup-disc ratio. We uncover new variants; rs11158547 in PPP1R36-PLEKHG3 and rs1028727 near SERPINE3 at genome-wide significance that replicate in independent Asian cohorts imputed to 1000 Genomes. At this point, validation of these variants in POAG cohorts is hampered by the high degree of heterogeneity. Our results show that multi-trait analysis is a valid approach to identify novel pleiotropic variants for ONH

A simplified approach to the drying of solids in a batch fluidised bed

A simplified model for drying solids in the constant rate period in a batch fluidised bed was developed.It assumes the bed to be divided into dense and bubble phases with heat and mass transfer between the phases.The model predicts the constant-rate drying period, provided the fluid bed shape and material characteristics are known.The model is compared with experimental data reported in the literature covering a wide range of materials, gas flow rates, column diameters, material hold-ups, air temperatures and humidities.Model predictions compare satisfactorily with the experimental data