In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

Abstract:  The aim of the current research is to find out the extent to which systems thinking skills are included in the mathematics textbook scheduled for the third intermediate grade for the academic year (2020-2021) by answering the main research question: What are the systems thinking skills included in the mathematics textbook for middle third grade?   The analytical descriptive approach was used, and to achieve the goal of the research, a list of the main systemic thinking skills and sub-skills was prepared, and after analyzing the content of the mathematics textbook, the reliability of the analysis was verified through the analysis over time and through others, and it obtained a reliability rate of 98% us

The logistic regression model is one of the oldest and most common of the regression models, and it is known as one of the statistical methods used to describe and estimate the relationship between a dependent random variable and explanatory random variables. Several methods are used to estimate this model, including the bootstrap method, which is one of the estimation methods that depend on the principle of sampling with return, and is represented by a sample reshaping that includes (n) of the elements drawn by randomly returning from (N) from the original data, It is a computational method used to determine the measure of accuracy to estimate the statistics, and for this reason, this method was used to find more accurate estimates. The ma

Distribution of light intensity in the flat photobioreactor for microalgae cultivation as a step design for production of bio-renewable energy was addressed in the current study. Five sizes of bioreactors with specific distances from the main light source were adopted as independent variables in experiential design model. The results showed that the bioreactor’s location according to the light source, determines the nature of light intensity distribution in the reactor body. However, the cross-section area plays an important role in determining the suitable location of reactor to achieve required light homogeneity. This area could change even the expected response of the light passing through the reactor if Beer-Lambert's law is adopted.

Dairy wastewater generally contains fats, lactose, whey proteins, and nutrients. Casein precipitation causes the effluent to decompose into a dark, strong-smelling sludge. Fluid waste contains soluble organic matter, suspended solids, and gaseous organic matter, which cause undesirable taste and smell, grant tone and turbidity, and advance eutrophication, which plays an essential role in increasing biological oxygen demand (BOD) in water. It also contains detergents and disinfecting agents from the rinses and washing processes, which increase the need for chemical oxygen (COD). One of the characteristics of dairy effluents is their relatively high temperature, high organic contents, and wide pH range, so the discharge of wastewater into

Entropy define as uncertainty measure has been transfared by using the cumulative distribution function and reliability function for the Burr type – xii. In the case of data which suffer from volatility to build a model the probability distribution on every failure of a sample after achieving limitations function, probabilistic distribution. Has been derived formula probability distribution of the new transfer application entropy on the probability distribution of continuous Burr Type-XII and tested a new function and found that it achieved the conditions function probability, been derived mean and function probabilistic aggregate in order to be approved in the generation of data for the purpose of implementation of simulation

The paper comprise comparative palynological study of (11) species belong to the genus Echinops L. in Iraq i.e( E.armatus Boiss. & Hausskn ، E.bicolor Nabelek. ، E.cephalotes DC., E.haussknetchii Boiss. ، E.mosulensis ، Rech. ،
E.nitens Bornm. ، E.orientalis Trautv., E.parviflorous BOISS & BUHSE ،
E.spinossisms Turra . ، E.tenuisectus Rech. ، E.viscosus DC.، Pollen grain were found to be Tricolporate and with spherical shaped ,in polar view the grain found to be Interangular , while in equatorial view the grain found to be ellipsoid .

المستخلص

يهدف البحث إلى وضع إطار معرفي ومفاهيمي شامل لموضوع البحث, واغناء القارئ والمستفيد بالمعلومات الوافية عنه وتقليص الفجوات المعرفية للمهتمين به وقياس مدى ما هو متوفر وغير متوفر من المتطلبات الأساسية والضرورية لإنشاء صناديق التحوط في البيئة العراقية, وتمثلت صناديق التحوط بالمتغير الرئيس للبحث اما المتغيرات الفرعية فشملت (المتطلبات المالية, المتطلبات البشرية, البيئة التشريعية, الب

 My research deals with the positions that the Prophet (PBUH) distressed. And condolences to those who lost her father and other problems and calamities that impede the life of women, has been given to the Lord of men, and good qualities, to strike the nation's finest proverbs in ensuring lost and lost of women and children, to be shown to us humanity in its finest form, and the best analyzed, and I hope God help And guidance and Rashad