In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

The estimating of ash toxicity collected from Durah power plant (DPP) which is located in Baghdad Governorate was done by exposed cladoceran Simocephalus vetulus to different ash concentrations. Thus, the first of its kind study by assessing the toxic effect of these effluents in the selected laboratory individual's food chain. The acute toxicity test of ash was assessed by LC₅₀ and mortality percentage. LC₅₀ of ash on S. vetulus were 0.14, 0.11 and 0.1 ppt during 24, 48 and 72 hr., respectively. On the other hand, it was shown that increasing the concentrations of ash leads to an increase mortality percentage. It was observed that the maximum mortality percentage  (LC100) when exposed to 0.2

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

In this study used three methods such as Williamson-hall, size-strain Plot, and Halder-Wagner to analysis x-ray diffraction lines to determine the crystallite size and the lattice strain of the nickel oxide nanoparticles and then compare the results of these methods with two other methods. The results were calculated for each of these methods to the crystallite size are (0.42554) nm, (1.04462) nm, and (3.60880) nm, and lattice strain are (0.56603), (1.11978), and (0.64606) respectively were compared with the result of Scherrer method (0.29598) nm,(0.34245),and the Modified Scherrer (0.97497). The difference in calculated results Observed for each of these methods in this study.

Aqueous extract of poppy plant) Papaver nudicaule) with five concentrations (50, 100, 150, 200 and 250) mg/l were used to anesthetize fingerlings of the common carp Cyprinus carpio (Mean total length 8.91 ± 0.31 cm and mean total weight 7.72 ± 1.19 gm) instead of the traditional use of MS-222. Results showed that extracted solution of poppy have partial and overall anesthesia effect on these fishes with inverse relationship between the concentrations used and the time needed to reach partial and overall anesthesia, and also direct relationship between concentrations used and time needed for fish recovery. Best results were obtained by using a concentration of 250 mg/l, where time for partial anesthesia was 8 ± 1.52 m

Al- Masab AL-Aam canal (or the Main Drain) is a vital strategic project in Iraq. It collects the drain water from the agricultural lands and drains to the Arabian Gulf via Shatt Al-Basra. Fifteen water samples were collected from different sites along the course of the Al- Masab Al-Aam canal southern sector extending from Nasiriyah Basra to evaluate the hydrochemical properties. The variation of the sediment’s texture along the southern sector was investigated. The results reflected that the sediment is characterized by the presence of sand, silt, and clay. It is noted that the amount of salt in the water increases during the summer when temperatures are rising, and consequently, the evaporation rate increases. Changes in the saturatio

In this paper, we model the spread of coronavirus (COVID -19) by introducing stochasticity into the deterministic differential equation susceptible  -infected-recovered (SIR model). The stochastic SIR dynamics are expressed using Itô's formula. We then prove that this stochastic SIR has a unique global positive solution I(t).The main aim of this article is to study the spread of coronavirus COVID-19 in Iraq from 13/8/2020 to 13/9/2020. Our results provide a new insight into this issue, showing that the introduction of stochastic noise into the  deterministic model for the spread of COVID-19 can cause the disease to die out, in scenarios where deterministic models predict disease persistence. These results were also clearly ill

In most recent studies, long-term retention after orthodontic treatment has been hypothesized that may be necessary to maintain the stability of the dentition and avoid post-treatment changes. The bonded fixed retainer is characterized by its clinical effectiveness, patient acceptance, and lack of patient complaints as compared with a removable retainer. An electronic database (such as PubMed, PubMed Central, Web of Science, Science Direct, Cochrane Library, Scopus, and ResearchGate) has been collected using specific keywords. Of the 152 articles, only randomized clinical trials that investigated different types of fixed retainers or compared fixed with removable retainers were illustrated in tables and included in this review. The

The proton-neutron interacting boson model (IBM-2) has been used to make a schematic study of the Ruthenium ( ) isotopes of mass region around with and . For each isotope of the values of the IBM-2 Hamiltonian parameters, which yield an acceptable results for excitation energies in comparison with those of experimental data, have been determined. Fixed values of the effective charges ( ) and of the proton and neutron g factors ( and ) have been chosen for all isotopes under study. The calculated electric quadrupole moments of state, transitions, the magnetic dipole moments transitions and mixing ratios are in reasonable agreement with the experimental data.

The construction project is a very complicated work by its nature and requires specialized knowledge to lead it to success. The construction project is complicated socially, technically and economically in its planning, management and implementation aspects due to the fact that it has many variables and multiple stakeholders in addition to being affected by the surrounding environment. Successful projects depend on three fundamental points which are cost-time, performance and specifications. The project stakeholder's objective to achieve best specifications and the cost-time frame stipulated in the contract.

The question is, was the optimum implementation accomplished? The provision for the success of the project