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A comparative study on the water quality of the interstitial water of two creeks in Rivers State was conducted. Temperature, pH, Conductivity, Dissolved oxygen, biochemical oxygen demand, Salinity, and Total dissolved solid were checked with an in-situ hand-held multi-meter (The EZODO Multi-meter). Dissolved oxygen (DO) was measured with a Milwaukee Dissolved oxygen meter while Biochemical Oxygen Demand (BOD) was determined by the 5-day BOD test (APHA, 2005). The temperature ranged between 28.3 to 29.3℃ in the Opro-ama creek and 26.0 -26.8℃ in Buguma creek. The pH value ranged from 6.2 to 6.8 in Opro-ama creek while that of Sa-ama creek was between 6.8 and 6.99. Salinity ranges from 9.1 to 9.5 (ppt) in the Opro-ama creek while Sa-ama creek recorded a range between 11.2 to 12.0 (ppt). The dissolved oxygen was between 1.5 and 2.3 (µS/cm) in Okpoka creek meanwhile Sa-ama creek varied between 4.6 and 4.10 (µS/cm). The biochemical oxygen demand values were between 1.4 to 2.3 (µS/cm) in Opro-ama creek while that of Sa-ama was between 1.9 to 2.4 (µS/cm). The conductivity values for the Opro-ama creek were between 10.3 and 10.6 while Sa-ama creek recorded a value of 12.5 to12.6 (µS/cm). there were significant variations (P

In this paper, a set of functions were constructed that transforms Black-Scholes partial differential equation into weak formulations. The analytical solutions: existence, uniqueness and other estimates were also obtained in weak form with the use of boundary conditions to establish the effects of its financial implications in Sobolev spaces. The regularity conditions of the problem were considered which the coefficients, the boundary of the domain are all smooth functions. To this end, the definitions, assumptions which paved way to useful assertions are illustrated in this paper

In recent work, Hollands, Kovács and Reall have built on previous work of Wall to provide a definition of dynamical black hole entropy for gravitational effective field theories (EFTs). This entropy satisfies a second law of black hole mechanics to quadratic order in perturbations around a stationary black hole. We determine the explicit form of this entropy for the EFT of 4d vacuum gravity including terms in the action with up to 6 derivatives. An open question concerns the gauge invariance of this definition of black hole entropy. We show that gauge invariance holds for the EFT of vacuum gravity with up to 6 derivatives but demonstrate that it can fail when 8 derivative terms are included. We determine an entropy for Einstein-Gauss-Bonnet theory by treating it as an EFT with vanishing 6 derivative terms.

Background: Risk benefit strategies in managing inflammatory bowel diseases (IBD) are dependent upon understanding the risks of uncontrolled inflammation vs those of treatments. Malignancy and mortality in IBD have been associated with disease-related inflammation and immune suppression, but data are limited due to their rare occurrence. Aim: To identify and describe the most common causes of mortality, types of cancer and previous or current therapy among children and young adults with paediatric-onset IBD. Methods: Information on paediatric-onset IBD patients diagnosed with malignancy or mortality was prospectively collected via a survey in 25 countries over a 42-month period. Patients were included if death or malignancy occurred after IBD diagnosis but before the age of 26years. Results: In total, 60 patients were identified including 43 malignancies and 26 fatal cases (9 due to cancer). Main causes of fatality were malignancies (n=9), IBD or IBD-therapy related nonmalignant causes (n=10; including 5 infections), and suicides (n=3). Three cases, all fatal, of hepatosplenic T-cell lymphoma were identified, all were biologic-naive but thiopurine-exposed. No other haematological malignancies were fatal. The 6 other fatal cancer cases included 3 colorectal adenocarcinomas and 3 cholangiocarcinomas (CCAs). Primary sclerosing cholangitis (PSC) was present in 5 (56%) fatal cancers (1 colorectal carcinoma, 3 CCAs and 1 hepatosplenic T-cell lymphoma). Conclusions: We report the largest number of paediatric-onset IBD patients with cancer and/or fatal outcomes to date. Malignancies followed by infections were the major causes of mortality. We identified PSC as a significant risk factor for cancer-associated mortality. Disease-related adenocarcinomas were a commoner cause of death than lymphomas.