In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.
SUMMARY. – Absorption, flourescence, quantum yield and lifetime of rhodamine B in chloroform, methanol and dimethyl sulfoxide were measured. A comparison was done of these quantities with those for solid solutions, which are obtained by mixing constant volume proportions of dye at a concentration of 1×10–4M/l with different volume proportions from the concentrated solution of polymer in chloroform and dimethyl sulfoxide. The results showed that the addition of polymer to liquid concentrated solutions (1×10–4M/l) of rhodamine B dye from expecting, which leads to development of active medium for laser dye at high concentration, increase the spectra shift toward high energies, and the luminescence quantum yield but decreasing radiative
... Show MoreThe Wheat husk is one of the common wastes abundantly available in the Middle East countries especially in Iraq. The present study aimed to evaluate the Wheat husk as low cost material, eco-friendly adsorbents for the removal of the carcinogenic dye (Congo red dye) from wastewater by investigate the effect of, at different conditions such as, pH(3-10), amount of adsorbents (1-2.3gm/L),and particle size (125-1000) μm, initial Congo red dye concentration(10, 25 , 50 and 75mg/l) by batch experiments. The results showed that the removal percentage of dye increased with increasing adsorbent dosage, and decreasing particle size. The maximum removal and uptake reached (91%) , 21.5mg/g, respectively for 25 initial concent
... Show MoreAbsorption, fluorescence, quantum yield and lifetime of rhodamine 6G in chloroform, methanol and dimethyl sulfoxide were measured. From a comparison of these quantities, with those for solid solutions (solid solutions are obtained by mixing constant volume proportions of dye at a concentration of 1*10-4M/l with different volume proportions from the concentrated solution of polymer in chloroform and dimethyl sulfoxide). The results showed that the addition of polymer to liquid concentrated solutions (1*10-4M/l )of rhodamine 6G dye from expecting [which leading to development active medium for laser dye at high concentration] increase the spectra shift toward high energies, and the luminescence quantum yield but decreasing radiative lifetim
... Show MoreAims to find out the (Extent of mathematics teachers' appreciation of the mathematical problem `multiple solutions) Research sample consisted of (100) mathematics teachers distributed on the General Directorates of Education in Baghdad (Rusafa 1/2/3) and (Karkh 1/2/ 3) There was two research approach which are: The first - two different answers of students to the same issue where teachers must assess each answer and explain which one the teacher will accept and why? The second - Different solutions of students' to the same issue, including wrong answers , Teachers should correct the answers and give them final grades (0-10). Descriptive and analytical Approch was used in this research methodology And zero hypotheses, which are as f
... Show MoreThis study proposes a mathematical approach and numerical experiment for a simple solution of cardiac blood flow to the heart's blood vessels. A mathematical model of human blood flow through arterial branches was studied and calculated using the Navier-Stokes partial differential equation with finite element analysis (FEA) approach. Furthermore, FEA is applied to the steady flow of two-dimensional viscous liquids through different geometries. The validity of the computational method is determined by comparing numerical experiments with the results of the analysis of different functions. Numerical analysis showed that the highest blood flow velocity of 1.22 cm/s occurred in the center of the vessel which tends to be laminar and is influe
... Show MoreThis investigation integrates experimental and numerical approaches to study a novel solar air heater aimed at achieving an efficient design for a solar collector suitable for drying applications under the meteorological conditions of Iraq. The importance of this investigation stems from the lack of optimal exploitation of solar energy reaching the solar collector, primarily attributable to elevated thermal losses despite numerous designs employed in such solar systems. Consequently, enhancing the thermal performance of solar collectors, particularly those employed in crop drying applications, stands as a crucial focal point for researchers within this domain. Two identical double-pass solar air heaters were designed and constructed for
... Show MoreAs tight gas reservoirs (TGRs) become more significant to the future of the gas industry, investigation into the best methods for the evaluation of field performance is critical. While hydraulic fractured well in TRGs are proven to be most viable options for economic recovery of gas, the interpretation of pressure transient or well test data from hydraulic fractured well in TGRs for the accurate estimation of important reservoirs and fracture properties (e.g. fracture length, fracture conductivity, skin and reservoir permeability) is rather very complex and difficult because of the existence of multiple flow profiles/regimes. The flow regimes are complex in TGRs due to the large hydraulic fractures n
The paper aims to propose Teaching Learning based Optimization (TLBO) algorithm to solve 3-D packing problem in containers. The objective which can be presented in a mathematical model is optimizing the space usage in a container. Besides the interaction effect between students and teacher, this algorithm also observes the learning process between students in the classroom which does not need any control parameters. Thus, TLBO provides the teachers phase and students phase as its main updating process to find the best solution. More precisely, to validate the algorithm effectiveness, it was implemented in three sample cases. There was small data which had 5 size-types of items with 12 units, medium data which had 10 size-types of items w
... Show MoreAn oil spill is a leakage of pipelines, vessels, oil rigs, or tankers that leads to the release of petroleum products into the marine environment or on land that happened naturally or due to human action, which resulted in severe damages and financial loss. Satellite imagery is one of the powerful tools currently utilized for capturing and getting vital information from the Earth's surface. But the complexity and the vast amount of data make it challenging and time-consuming for humans to process. However, with the advancement of deep learning techniques, the processes are now computerized for finding vital information using real-time satellite images. This paper applied three deep-learning algorithms for satellite image classification
... Show MoreThe problem of water scarcity is becoming common in many parts of the world, to overcome part of this problem proper management of water and an efficient irrigation system are needed. Irrigation with a buried vertical ceramic pipe is known as a very effective in the management of irrigation water. The two- dimensional transient flow of water from a buried vertical ceramic pipe through homogenous porous media is simulated numerically using the HYDRUS/2D software. Different values of pipe lengths and hydraulic conductivity were selected. In addition, different values of initial volumetric soil water content were assumed in this simulation as initial conditions. Different value
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