In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

يعد الالف الأول قبل الميلاد هو عهد ازدهار عظيم للعصر الأشوري الحديث إذ يمتد هذا التاريخ  من  بداية  حكم آدد  نراري الثاني عام 911 قبل الميلاد وحتى نهاية حكم الاشوريين السياسي عام 612 قبل الميلاد عندما  سقطت  نينوى على ايدي  المقاتلين الميديين والكلدانيين الذين تحالفوا ضد الاشوريين،و وصل الأشوريون في هذا العهد قمة مجدهم في جميع النواحي العسكرية  والسياسية حتى  أن سلطتهم وصلت الى معظم انحاء

This study investigates the influence of fear, refuge, and migration in a predator–prey model, where the interactions between the species follow an asymmetric function response. In contrast to some other findings, we propose that prey develop an anti-predator response in response to a concentration of predators, which in turn increases the fear factor of the predators. The conditions under which all ecologically meaningful equilibrium points exist are discussed in detail. The local and global dynamics of the model are determined at all equilibrium points. The model admits several interesting results by changing the rate of fear of predators and predator aggregate sensitivity. Numerical simulations have been performed to verify our theoret

It aim current researchs֬ to identify the impact of a proposed strategy in accordance with the objectives of science in the achievement and some science processes, where the experimental method was adopted, and define the research community was students second grade averag in Education Bagdad / Rusafa third, research sample intentionally chosen as school Radwan, and (30) students experimental group and (29) of control group, research tools were achievement test and the test of science operations and use the appropriate statistical tools to process information and data, showing results, the experimental group surpassed the control group in the collection and operations science, and light it, the researcher recommended several recommendat

The modern teaching methods, and their importance in achieving the desired learning goals for the individual and the society, have been addressed, as it is necessary to develop the methods, ways and strategies used in the process of teaching the intermediate stages in the various fields in general and the field of physical education in particular, the importance of research is the effect of using the strategy of similarities in teaching some basic skills of basketball for students of the second intermediate. As for the problem of research, the researcher mentioned the lack of use of teachers’ strategy method similarities in the educational units because of its importance, and after study and analysis the researcher found it necessary to i

The objective of the research is to identify the effect of the five-finger strategy on the holistic thinking of chemistry students in the second intermediate grade, where the sample consisted of 60 female students in a second classfrom one of the intermediate schools in Baghdad city, divided into two groups: control and experimental. The experimental design was based on the partial control; the scientific course was defined in the third and fourth chapters of the science book of the second intermediate grade.The two research tools were prepared: the attainment test with the scientific course and the holistic thinking scale paragraph (36) of multiple-choice pre- and posttest. The results showed a statistically significant difference between

Abstract

            Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t

The objective of this research is to identify the effect of Using Fryer strategy on achievement and systemic thinking in the subject of chemistry of second class intermediate school students. The sample of research consisted of 59 students in one intermediate school in Baghdad/Iraq, split into two groups; experimental and control. The scientific material of the study is related to Chapters II and III of the Science Book for the second Intermediate School for the Year (2019-2020). The scientific test is composed of 25 test items whilst the second instrument for research related to systematic thinking test consisted of 12 items. The results of the research showed that the use of Fryer's chemistry-teaching strategy has increased achievement an

The objective of this research is to identify the effect of Using Fryer strategy on achievement and systemic thinking in the subject of chemistry of second class intermediate school students. The sample of research consisted of 59 students in one intermediate school in Baghdad/Iraq, split into two groups; experimental and control. The scientific material of the study is related to Chapters II and III of the Science Book for the second Intermediate School for the Year (2019-2020). The scientific test is composed of 25 test items whilst the second instrument for research related to systematic thinking test consisted of 12 items. The results of the research showed that the use of Fryer's chemistry-teaching strategy has increased achieve

Climate change is one of the global issues that is receiving wide attention due to its clear impact on all living organisms. This is essential for Iraq since it was classified as the fifth most vulnerable country to climate change. One of the manifestations of these changes in Iraq is the increasing frequency and severity of dust storms. In this study, the Normalized Difference Dust Index (NDDI) spectral index for Moderate Resolution Imaging Spectroradiometer (MODIS) sensor bands was used to measure and track the dust storm that occurred on May 16, 2022, as well as to test the validity of one of the daily products of this sensor, MOD11A1, to measure surface temperature and emissivity before and after the storm. It was found that the MOD0