Big q-Laguerre and q-Meixner polynomials and representations of the algebra U_q(su(1,1))

Diagonalization of a certain operator in irreducible representations of the positive discrete series of the quantum algebra U_q(su(1,1)) is studied. Spectrum and eigenfunctions of this operator are found in an explicit form. These eigenfunctions, when normalized, constitute an orthonormal basis in the representation space. The initial U_q(su(1,1))-basis and the basis of eigenfunctions are interrelated by a matrix with entries, expressed in terms of big q-Laguerre polynomials. The unitarity of this connection matrix leads to an orthogonal system of functions, which are dual with respect to big q-Laguerre polynomials. This system of functions consists of two separate sets of functions, which can be expressed in terms of q-Meixner polynomials M_n(x;b,c;q) either with positive or negative values of the parameter b. The orthogonality property of these two sets of functions follows directly from the unitarity of the connection matrix. As a consequence, one obtains an orthogonality relation for q-Meixner polynomials M_n(x;b,c;q) with b<0. A biorthogonal system of functions (with respect to the scalar product in the representation space) is also derived.Comment: 15 pages, LaTe

A record-linkage study of the development of hepatocellular carcinoma in persons with hepatitis C infection in Scotland

We investigated trends in first time hospital admissions and deaths attributable to hepatocellular carcinoma (HCC) in a large population based cohort of 22 073 individuals diagnosed with hepatitis C viral (HCV) infection through laboratory testing in Scotland in 1991 2006. We identified new cases of HCC through record linkage to the national inpatient hospital discharge database and deaths registry. A total of 172 persons diagnosed with HCV were admitted to hospital or died with first time mention of HCC. Hepatocellular carcinoma incidence increased between 1996 and 2006 (average annual change of 6.1, 95% confidence interval (CI):0.9 11.6%, P¼0.021). The adjusted relative risk of HCC was greater for males (hazard ratio¼2.7, 95% CI: 1.7 4.2), for those aged 60 years or older (hazard ratio ¼2.7, 95% CI: 1.9 4.1) compared with 50 59 years, and for those with a previous alcohol related hospital admission (hazard ratio¼2.5, 95% CI: 1.7 3.7). The risk of individuals diagnosed with HCV developing HCC was greatlyincreased compared with the general Scottish population (standardised incidence ratio¼127, 95% CI: 102 156). Owing to the advancing age of the Scottish HCV diagnosed population, the annual number of HCC cases is projected to increase, with a consequent increasing burden on the public healthcare system

Projections of the current and future disease burden of hepatitis C virus infection in Malaysia

The prevalence of hepatitis C virus (HCV) infection in Malaysia has been estimated at 2.5% of the adult population. Our objective, satisfying one of the directives of the WHO Framework for Global Action on Viral Hepatitis, was to forecast the HCV disease burden in Malaysia using modelling methods.An age-structured multi-state Markov model was developed to simulate the natural history of HCV infection. We tested three historical incidence scenarios that would give rise to the estimated prevalence in 2009, and calculated the incidence of cirrhosis, end-stage liver disease, and death, and disability-adjusted life-years (DALYs) under each scenario, to the year 2039. In the baseline scenario, current antiviral treatment levels were extended from 2014 to the end of the simulation period. To estimate the disease burden averted under current sustained virological response rates and treatment levels, the baseline scenario was compared to a counterfactual scenario in which no past or future treatment is assumed.In the baseline scenario, the projected disease burden for the year 2039 is 94,900 DALYs/year (95% credible interval (CrI): 77,100 to 124,500), with 2,002 (95% CrI: 1340 to 3040) and 540 (95% CrI: 251 to 1,030) individuals predicted to develop decompensated cirrhosis and hepatocellular carcinoma, respectively, in that year. Although current treatment practice is estimated to avert a cumulative total of 2,200 deaths from DC or HCC, a cumulative total of 63,900 HCV-related deaths is projected by 2039.The HCV-related disease burden is already high and is forecast to rise steeply over the coming decades under current levels of antiviral treatment. Increased governmental resources to improve HCV screening and treatment rates and to reduce transmission are essential to address the high projected HCV disease burden in Malaysia

Recombinant human activated protein C improves endotoxemia-induced endothelial dysfunction: a blood-free model in isolated mouse arteries

Recombinant human activated protein C (rhAPC) is one of the treatment panels for improving vascular dysfunction in septic patients. In a previous study, we reported that rhAPC treatment in rat endotoxemia improved vascular reactivity, although the mechanisms involved are still under debate. In the present study, we hypothesized that rhAPC may improve arterial dysfunction through its nonanticoagulant properties. Ten hours after injection of LPS in mice (50 mg/kg ip), aortic rings and mesenteric arteries were isolated and incubated with or without rhAPC for 12 h. Aortic rings were mounted in a myograph, after which arterial contractility and endothelium-dependent relaxation were measured in the presence or absence of nitric oxide synthase or cyclooxygenase inhibitors. Flow (shear stress)-mediated dilation with or without the above inhibitors was also measured in mesenteric resistance arteries. Protein expression was assessed by Western blotting. Lipopolysaccharide (LPS) reduced aortic contractility to KCl and phenylephrine as well as dilation to acetylcholine. LPS also reduced flow-mediated dilation in mesenteric arteries. In rhAPC-treated aorta and mesenteric arteries, contractility and endothelial responsiveness to vasodilator drug and shear stress were improved. rhAPC treatment also improved LPS-induced endothelial dysfunction; this effect was associated with an increase in the phosphorylated form of endothelial nitric oxide synthase and protein kinase B as well as cyclooxygenase vasodilatory pathways, thus suggesting that these pathways, together with the decrease in nuclear factor-κB activation and inducible nitric oxide synthase expression in the vascular wall, are implicated in the endothelial effect of rhAPC. In conclusion, ex vivo application of rhAPC improves arterial contractility and endothelial dysfunction resulting from endotoxemia in mice. This finding provides important insights into the mechanism underlying rhAPC-induced improvements on arterial dysfunction during septic shock

slq(2)sl_q(2) Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for q-canonical transformation is deduced. q-Schr\"{o}dinger equation for a Kepler like potential is obtained from the q-oscillator Schr\"{o}dinger equation. Energy spectrum and the ground state wave function are calculated.Comment: 12 pages, Latex twice, (Comparison with the other approaches and some refs. added. The version which will appear in J. Phys. A