Action of overalgebra in Plancherel decomposition and shift operators in imaginary direction

Consider the Plancherel decomposition of the tensor product of a highest weight and a lowest weight unitary representations of $SL_2$. We construct explicitly the action of the Lie algebra $sl_2 + sl_2$ in the direct integral of Hilbert spaces. It turns out that a Lie algebra operator is a second order differential operator in one variable and second order difference operator with respect to another variable. The difference operators are defined in terms of the shift in the imaginary direction $f(s)\mapsto f(s+i)$, $i^2=-1$ (the Plancherel measure is supported by real $s$).Comment: 12 page

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Supersonic flow of non-ideal fluids in nozzles: An application of similitude theory and lessons for ORC turbine design and flexible use considering system performance

A significant improvement in the economy-of-scale of small-scale organic Rankine cycle (ORC) systems can arise from the appropriate design of components that can be manufactured in large volumes and implemented flexibly into a wide range of systems and potential applications. This, in turn, requires accurate predictions of component performance that can capture variations in the cycle conditions, parameters or changes to the working fluid. In this paper previous work investigating a modified similitude theory used to predict the performance of subsonic ORC turbines is extended to analyse the supersonic flow of organic fluids within 2D converging-diverging nozzles. Two nozzles are developed using a minimum length method of characteristics design model coupled to REFPROP. These are designed for R245fa and Toluene as working fluids with nozzle exit Mach numbers of 1.4 and 1.7 respectively. First, the nozzle performance is confirmed using CFD simulations, and then further CFD simulations are performed to evaluate the performance of the same nozzles over a range of different inlet conditions and with different working fluids. The CFD simulations are compared to predictions made using the original and modified similitude theories, and also to predictions made by conserving the Prandtl-Meyer function for the different operating conditions. The results indicate that whilst the modified similitude model does not accurately predict nozzle performance, conserving the Prandtl-Meyer function allows to predict the nozzle outlet Mach number to within 2% providing there is not a significant change in the polytropic index. Finally, the effect of working fluid replacement on the ORC system is discussed, and preliminary results demonstrate the possibility of matching a particular turbine to a heat source through optimal working fluid selection

Surveillance for pancreatic cancer in high-risk individuals

Background Surveillance of individuals at high risk of pancreatic ductal adenocarcinoma (PDAC) and its precursors might lead to better outcomes. The aim of this study was to determine the prevalence and outcomes of PDAC and high-risk neoplastic precursor lesions among such patients participating in surveillance programmes. Methods A multicentre study was conducted through the International CAncer of the Pancreas Screening (CAPS) Consortium Registry to identify high-risk individuals who had undergone pancreatic resection or progressed to advanced PDAC while under surveillance. High-risk neoplastic precursor lesions were defined as: pancreatic intraepithelial neoplasia (PanIN) 3, intraductal papillary mucinous neoplasia (IPMN) with high-grade dysplasia, and pancreatic neuroendocrine tumours at least 2 cm in diameter. Results Of 76 high-risk individuals identified in 11 surveillance programmes, 71 had undergone surgery and five had been diagnosed with inoperable PDAC. Of the 71 patients who underwent resection, 32 (45 per cent) had PDAC or a high-risk precursor (19 PDAC, 4 main-duct IPMN, 4 branch-duct IPMN, 5 PanIN-3); the other 39 patients had lesions thought to be associated with a lower risk of neoplastic progression. Age at least 65 years, female sex, carriage of a gene mutation and location of a lesion in the head/uncinate region were associated with high-risk precursor lesions or PDAC. The survival of high-risk individuals with low-risk neoplastic lesions did not differ from that in those with high-risk precursor lesions. Survival was worse among patients with PDAC. There was no surgery-related mortality. Conclusion A high proportion of high-risk individuals who had surgical resection for screening- or surveillance-detected pancreatic lesions had a high-risk neoplastic precursor lesion or PDAC at the time of surgery. Survival was better in high-risk individuals who had either low- or high-risk neoplastic precursor lesions compared with that in patients who developed PDAC

Role of bone and kidney in tumor-induced hypercalcemia and its treatment with bisphosphonate and sodium chloride.

The efficacy of intravenous aminohydroxypropylidene bisphosphonate as treatment for the hypercalcemia of malignancy was examined in a phase II multicenter study in 132 patients with a large variety of primary tumors. This provided an opportunity for an analysis of the separate influences of bone resorption and renal calcium handling on the genesis and maintenance of hypercalcemia. The results demonstrated that increased bone resorption is the major contributory factor and that inhibition with bisphosphonate normalizes the serum calcium concentration within five days in more than 90 percent of patients. Hypercalcemia is sustained by an inability of the kidney to deal efficiently with a chronically increased calcium load. This is influenced by the requirements of volume regulation in the presence of a sodium diuretic effect of hypercalcemia and is very sensitive to induced variations of sodium load. In addition, in a minority of patients, direct renal actions of tumor-derived humoral factors adversely reduce the ability to excrete calcium. For optimal treatment of tumor-induced hypercalcemia, bisphosphonate treatment should be combined with intravenous administration of saline solution.Clinical TrialJournal ArticleResearch Support, Non-U.S. Gov'tinfo:eu-repo/semantics/publishe