Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if \lambda_n\lambda_{n-1}\ne 0 and \delta_n=0, then the differential equation has a polynomial solution of degree at most n. We show that the classical differential equations of Laguerre, Hermite, Legendre, Jacobi, Chebyshev (first and second kind), Gegenbauer, and the Hypergeometric type, etc, obey this criterion. Further, we find the polynomial solutions for the generalized Hermite, Laguerre, Legendre and Chebyshev differential equations.Comment: 12 page

Photocatalytic degradation efficiency of azo dye in aqueous phase using different photo catalysts

The new azo dye [4-(4-hydroxy-2-methylnaphthyl)diazenyl]benzoic acid was synthesized by the reaction of 2-methyl-1-naphthol with p-amino benzoic acid. The photcatalytic degradation of azo dye has been investigated by using zinc oxide and cadmium sulfide. This degradation was carried out by the irradiation of aqueous suspended solutions containing different concentrations of this dye using 0.11 g/100 mL of metal oxide (semiconductors) ZnO and CdS. A mercury lamp 125 W in a Pyrex photoreaction cell of 100 mL at room temperature was used as an irradiation source. The effect of the catalyst on the photocatalytic degradation of the prepared dye was studied via several experiments at different conditions, where they involve the effect of the catalyst mass and the effect of the dye concentrations. The irradiated solutions were studied using UV-Vis spectrophotometer. It has been the performance of photocatalytic system that using ZnO was observed to be better than cadmium sulfide system for degrade the azo compound from its aqueous solution.                     KEY WORDS: Photocatalytic, Degradation, Semiconductors, Zinc oxide; Cadmium sulphide, Azo dye   Bull. Chem. Soc. Ethiop. 2020, 34(3), 463-469. DOI: https://dx.doi.org/10.4314/bcse.v34i3.

Metabolically Healthy and Unhealthy Obese Phenotypes among Arabs and South Asians:Prevalence and Relationship with Cardiometabolic Indicators

Obesity is a public health crisis in Kuwait. However, not all obese individuals are metabolically unhealthy (MuHO) given the link between obesity and future cardiovascular events. We assessed the prevalence of the metabolically healthy obese (MHO) phenotype and its relationship with high sensitivity C-reactive protein (hs-CRP), serum alanine aminotransferase (ALT), and insulin resistance (HOMA-IR) in Arab and South Asian ethnic groups in Kuwait. The national cross-sectional survey of diabetes and obesity in Kuwait adults aged 18–60 years were analysed. The harmonised definition of metabolic syndrome was used to classify metabolic health. Multinomial logistic regression analysis was used to model the relationship between the MHO and MuHO phenotypes and hs-CRP, ALT and HOMA-IR levels. Overall, the prevalence of MHO for body mass index (BMI)- and waist circumference (WC)-defined obesity was 30.8% and 56.0%, respectively; it was greater in women (60.4% and 61.8%, respectively) than men (39.6% and 38.2%, respectively). Prevalence rates were also lower for South Asians than for Arabs. The MHO phenotype had hs-CRP values above 3 µg/mL for each age group category. Men compared to women, and South Asians compared to Arabs had a lower relative risk for the MHO group relative to the MuHO group. This study shows there is high prevalence of MHO in Kuwait

C-Reactive Protein in the Premature Rupture of the Membranes

Premature rupture of the membranes (PROM) defined as a rupture of membranes before onset of labor, which is one of the most complications of pregnancy that leads to significant maternal and neonatal morbidity and mortality. These complications depend on the gestational age to which it occurred. The aim of this study is to determine diagnostic value of CRP during pregnancy complicated by PROM. Retrospective study performed at Hamad Women's Hospital in Qatar. Data collected from files in the Medical Records over a two period from 27/11/2000 to 27/11/2002. One hundred and fifty cases were chosen and divided into: Group (la) 50 patients with PROM before 37 wks. Group (lb) 50 patients with PROM after 37 wks. Group (2) 50 patients as control. Statistical analysis showed high incidence of Oligohydroamnios and polyhydramnios in the group 1 compared with control Measurement of maternal blood CRP early before 37 weekindicated significant relation between the prevalence of premature rupture of the membranes, associated oligohydramnios with the incidence of positive results of CRP. We recommend that further investigations needed to document our data and to prove the beneficial effect of the test especially before 37 week of gestations.qscienc

Crack Growth Model for Evaluation the Fatigue Life of Aluminum Alloys

The main objective of this study is to experimentally determine the fatigue life of the aluminum alloys AA2014 and AA7075-T651 by measuring the lengths of short and long cracks practically under bending stress with constant amplitude loading and stress ratio (R = -1) at room temperature (RT) 25 C0 by employing Basquin's equation. To determine the fatigue life curve for both alloys at five different levels of constant amplitude stresses, the average failure cycles of three specimens at each stress level were recorded. The surface of specimen was replicated with cellulose paper and liquid acetone. This piece was examined using an optical microscope to record the length of the crack and the number of cycles corresponding to it at a constant stress level. The lengths of the cracks were then measured using the replication approach. A unique mathematical model was created to describe the relationship between crack speed (da/dN) and the length of short and long cracks in order to predict the overall fatigue life of each alloy. When the model's result was contrasted with actual outcomes, the conclusions were reliable and productive

Investigation of enhanced double weight code in point to point access networks

© 2020 Published under licence by IOP Publishing Ltd. In this paper, an investigation and evaluation to enhanced double weight (EDW) code is performed, a new technique for code structuring and building using modified arithmetical model has been given for the code in place of employing previous technique based on Trial Inspections. Innovative design has been employed for the code into P2P networks using diverse weighted EDW code to be fitting into optical CDMA relevance applications. A new developed relation for EDW code is presented, the relation is based on studying and experimenting the effect of input transmission power with code weight, and the relation developed using numerical analysis method. This relation makes the estimation for the system input power needed more efficient. The results of the code has been explained by eye diagram and parametric illustrations from the simulated results. The result shows a magnificent performance of the code during high number of users and weight. On the other hand, the relation developed for power measurement helps to prevent power loss and consumption

Investigation the nonlinear optical properties of silver nanoparticles using femtosecond laser

© 2020 Published under licence by IOP Publishing Ltd. In this research, the fabrication of silver nanoparticles and experimental nonlinear response (NLO). The fabrication of the silver nanoparticles has been done using E-Beam evaporation on a glass substrate (Ag-NPs) and investigation of their nonlinear optical response (NLO). The silver nanoparticles was evaluated by optical spectrum (UV-Vis) that shows localized surface Plasmon band at 375 nm. The experiment shows the nonlinear absorption and nonlinear refraction effect of silver nanoparticles, the silver nanoparticles is analysed by Z-Scan technique using a femtoseconds laser with 800 nm wavelength. The result shows the nonlinear absorption (NLA) is at 4.8710-4cmW-1, while (NLR) is at 7.9410-9cmW-1

Prognostic Impacts of Angiopoietins in NSCLC Tumor Cells and Stroma: VEGF-A Impact Is Strongly Associated with Ang-2

INTRODUCTION: Angiopoietins and their receptor Tie-2 are, in concert with VEGF-A, key mediators in angiogenesis. This study evaluates the prognostic impact of all known human angiopoietins (Ang-1, Ang-2 and Ang-4) and their receptor Tie-2, as well as their relation to the prognostic expression of VEGF-A. METHODS: 335 unselected stage I-IIIA NSCLC-patients were included and tissue samples of respective tumor cells and stroma were collected in tissue microarrays (TMAs). Immunohistochemistry (IHC) was used to semiquantitatively evaluate the expression of markers in duplicate tumor and stroma cores. PRINCIPAL FINDINGS: In univariate analyses, low tumor cell expression of Ang-4 (P = 0.046) and low stromal expressions of Ang-4 (P = 0.009) and Ang-2 (P = 0.017) were individually associated with a poor survival. In the multivariate analysis, low stromal Ang-2 (HR 1.88; CI 95% 1.15-3.08) and Ang-4 (HR 1.47, CI 95% 1.02-2.11, P = 0.04) expressions were independently associated with a poor prognosis. In patients with high tumor cell expression of Ang-2, a concomitantly high tumor VEGF-A expression mediated a dramatic survival reduction (P<0.001). In the multivariate analysis of patients with high Ang-2 expression, high tumor VEGF-A expression appeared an independent poor prognosticator (HR 6.43; CI 95% 2.46-16.8; P<0.001). CONCLUSIONS: In tumor cells, only Ang-4 expression has prognostic impact in NSCLC. In tumor stroma, Ang-4 and Ang-2 are independently associated with survival. The prognostic impact of tumor cell VEGF-A in NSCLC appears strongly associated with a concomitantly high tumor cell expression of Ang-2

The Klein-Gordon equation with the Kratzer potential in d dimensions

We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r)=V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.Comment: 13 page

Exploring the views of young women and their healthcare professionals on dietary habits and supplementation practices in adolescent pregnancy: a qualitative study

Background: Nutrition is a modifiable factor affecting foetal growth and pregnancy outcomes. Inadequate nutrition is of particular concern in adolescent pregnancies with poor quality diet and competing demands for nutrients. The aim of this study was to explore knowledge and understanding of nutrition advice during adolescent pregnancy,and identify barriers and facilitators to dietary change and supplementation use in this vulnerable population. Methods: Semi-structured interviews were conducted with young women and key antenatal healthcare providers: midwives, family nurses and obstetricians. Doncaster, Manchester and London were chosen as sites offering different models of midwifery care alongside referral to the Family Nurse Partnership programme. Results: A total of 34 young women (adolescents aged 16–19 years) and 20 health professionals were interviewed. Young women made small changes to their dietary intake despite limited knowledge and social constraints. Supplementation use varied; the tablet format was identified by few participants as a barrier but forgetting to take them was the main reason for poor adherence. Health professionals provided nutrition information but often lack the time and resources to tailor this appropriately. Young women’s prime motivator was a desire to have a healthy baby; they wanted to understand the benefits of supplementation and dietary change in those terms. Conclusion: Pregnancy is a window of opportunity for improving nutrition but often constrained by social circumstances. Health professionals should be supported in their role to access education, training and resources which build their self-efficacy to facilitate change in this vulnerable population group beyond the routine care they provide