Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates

First we prove a new inequality comparing uniformly the relative volume of a Borel subset with respect to any given complex euclidean ball \B \sub \C^n with its relative logarithmic capacity in \C^n with respect to the same ball \B. An analoguous comparison inequality for Borel subsets of euclidean balls of any generic real subspace of \C^n is also proved. Then we give several interesting applications of these inequalities. First we obtain sharp uniform estimates on the relative size of \psh lemniscates associated to the Lelong class of \psh functions of logarithmic singularities at infinity on \C^n as well as the Cegrell class of \psh functions of bounded Monge-Amp\`ere mass on a hyperconvex domain \W \Sub \C^n. Then we also deduce new results on the global behaviour of both the Lelong class and the Cegrell class of \psh functions.Comment: 25 page

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Impact of an interatrial shunt device on survival and heart failure hospitalization in patients with preserved ejection fraction

Aims: Impaired left ventricular diastolic function leading to elevated left atrial pressures, particularly during exertion, is a key driver of symptoms and outcomes in heart failure with preserved ejection fraction (HFpEF). Insertion of an interatrial shunt device (IASD) to reduce left atrial pressure in HFpEF has been shown to be associated with short‐term haemodynamic and symptomatic benefit. We aimed to investigate the potential effects of IASD placement on HFpEF survival and heart failure hospitalization (HFH). Methods and results: Heart failure with preserved ejection fraction patients participating in the Reduce Elevated Left Atrial Pressure in Patients with Heart Failure study (Corvia Medical) of an IASD were followed for a median duration of 739 days. The theoretical impact of IASD implantation on HFpEF mortality was investigated by comparing the observed survival of the study cohort with the survival predicted from baseline data using the Meta‐analysis Global Group in Chronic Heart Failure heart failure risk survival score. Baseline and post‐IASD implant parameters associated with HFH were also investigated. Based upon the individual baseline demographic and cardiovascular profile of the study cohort, the Meta‐analysis Global Group in Chronic Heart Failure score‐predicted mortality was 10.2/100 pt years. The observed mortality rate of the IASD‐treated cohort was 3.4/100 pt years, representing a 33% lower rate (P = 0.02). By Kaplan–Meier analysis, the observed survival in IASD patients was greater than predicted (P = 0.014). Baseline parameters were not predictive of future HFH events; however, poorer exercise tolerance and a higher workload‐corrected exercise pulmonary capillary wedge pressure at the 6 months post‐IASD study were associated with HFH. Conclusions: The current study suggests IASD implantation may be associated with a reduction in mortality in HFpEF. Large‐scale ongoing randomized studies are required to confirm the potential benefit of this therapy

Color flows for the process gg --> Bc + c + b-bar

The contributions of different color flows into the gluonic Bc-meson production cross section has been calculated. This study is essential to simulate Bc-meson production with the help of Pythia program. The essence of matter is that in the frame work of the Lund model used by Pythia the hadronization way of the final partons and hadronic remnants depends on the color flow type. The modified method for calculation of the color flow contributions has been proposed.Comment: 16 pages, 5 figures, RevTeX

Antibacterial, Anti-HIV-1 Protease and Cytotoxic Activities of Aqueous Ethanolic Extracts from Combretum Adenogonium Steud. Ex A. Rich (Combretaceae).

\ud \ud Records have shown that Combretum adenogonium Steud. Ex A. Rich (Combretaceae) is used in traditional medicine systems of several tribes in Tanzania. This study focused on the investigation of antibacterial activity, anti-HIV-1 protease activity, toxicity properties and classes of phytochemicals in extracts from C. adenogonium Steud. Ex A. Rich (Combretaceae) to evaluate potential of these extracts for development as herbal remedies. Dried plant material were ground to fine powder and extracted using 80% aqueous ethanol to afford root, leaf and stem bark extracts. The extracts were assayed for anti-HIV-1 protease activities, antibacterial activities using microdilution methods and cytotoxicity using brine shrimps lethality assay. Screening for major phytochemical classes was carried out using standard chemical tests. All extracts exhibited antibacterial activity to at least one of the test bacteria with MIC-values ranging from 0.31-5.0 mg/ml. Two extracts, namely, root and stem bark exhibited anti-HIV-1 PR activity with IC50 values of 24.7 and 26.5 μg/ml, respectively. Stem bark and leaf extracts showed mild toxicity with LC50 values of 65.768 μg/ml and 76.965 μg/ml, respectively, whereas roots were relatively non-toxic (LC50 = 110.042 μg/ml). Phytochemical screening of the extracts indicated presence of flavonoids, terpenoids, alkaloids, tannins, glycosides and saponins. These results provide promising baseline information for the potential development of C. adenogonium extracts in treatment of bacterial and HIV/AIDS-related opportunistic infections