This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

       The present study was performed to spotlight the potential role of soil bacteria in the Al-Rumaila oil field as a bioindicator of heavy metals pollution. For this purpose, nine soil samples were collected from different sites, with 20cm depth, to assess the pollution status depending on the total and available concentrations of heavy metals.  The result indicates pollution of the studied soils with the following metals: Cd, Cu, Fe, Zn, and Pb. The mean of total concentration for all studied metals was higher than the allowed maximum limit based on the international limit:(3.394, 3.994, 39.993, 8844.979,150.372, and 103.347 µg/g), respectively. While measuring the total Metal concentration is important in determining the de

The study aimed to measure the concentration of some heavy metal elements and represented by (Pb, Cd,Cu) through the use of atomic absorption spectrometer Flame AAS-7000 type SHIMADZU underwent a process modeling to twelve samples from the soil of electricity Dezlat al Jadiriyah station in the Baghdad University compound at a depth of 30-60 cm from the surface and divided the samples into two groups first included six samples from inside the station while the second included six samples from outside the station. For the element of Pb was higher concentration reached by 29.32ppm and less concentration 17.56ppm. were elements Cd and Cu are growing and less and proportions of certain while the highest concentration of copper 9.69 ppm and le

A high sensitivity, low power and low cost sensor has been developed for photoplethysmography (PPG) measurement. The PPG principle was applied to follow the dilatation and contraction of skin blood vessels during the cardiac cycle. A standard light emitting diodes (LEDs) has been used as a light emitter and detector, and in order to reduce the space, cost and power, the classical analogue-to-digital converters (ADCs) replaced by the pulse-based signal conversion techniques. A general purpose microcontroller has been used for the implementation of measurement protocol. The proposed approach leads to better spectral sensitivity, increased resolution, reduction in cost, dimensions and power consumption. The basic sensing configuration prese

The current study was conducted to evaluate the effect a mixture of threespecies of arbuscular mycorrhizal fungi (Glomus etunicatum, G. leptotichum andRhizophagus intraradices) double and triple mixture and organic matter by usingplastic pots in the greenhouse at some mycorrhiza and physiological limitationscharacteristics in tomato plant after four and eight weeks of cultivation. Theresults of the determinants mycorrhiza significant increase the percentage ofmycorrhizal frequency F% dry weight of roots mycorrhiza (g.plant-1) andorganic matter in all mycorrhiza single, double and triple mixture after four andeight weeks cultivation treatments. The highest percentage of mycorrhizalfrequency and increase the dry weight of the root in the trea

One of the Iraqi geotechnical problems is the presence of gypseous soils covering about (27-36) percentage of Iraq soils containing gypsum between (10-70) ratios. The main reason for soil problematic is the gypsum dissolution when these soils are inundated. However, the soluble gypsum can be leached out of the soil particles, so these problems can be led to cracking, tilting, and collapsing the related soil structure and changing the soil properties. The aim of this work is to investigate the performance of under-reamed piles as a new, improved method to reduce the moisture sensitive and the primary triggering mechanism for the volume reduction of collapsible soil, which is considered as a non-elastic deformation; this was done by c

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami

Peer-Reviewed Journal

The goal of this work is to check the presence of PNS (photon number splitting) attack in quantum cryptography system based on BB84 protocol, and to get a maximum secure key length as possible. This was achieved by randomly interleaving decoy states with mean photon numbers of 5.38, 1.588 and 0.48 between the signal states with mean photon numbers of 2.69, 0.794 and 0.24. The average length for a secure key obtained from our system discarding the cases with Eavesdropping was equal to 125 with 20 % decoy states and 82 with 50% decoy states for mean photon number of 0.794 for signal states and 1.588 for decoy states.