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

CO2 laser (10.6 μm) is the most often used laser in the oral surgery due to its high absorption by water of the oral tissues. Several benefits of the use of CO2 laser have been reported for oral surgical procedures. This study aims to evaluate the effect of CO2 laser on soft and hard oral tissues (in vitro study). This study was done on fresh tissues from sheep’s head. CO2Surgical Laser with different operation modes was used; 0.2 mm spot size using different laser parameters on the tongue, and bone making holes, incisions and cutting. The depths and widths of holes and incisions were measured using endodontic file under magnification. The speed of incisions was calculated and the required time for cutting was measured using sport clo

The international humanitarian law found the special rules to protect women meanwhile the armed conflicts whether international or non-international. These rules are adopted for woman because of two reasons : that she is from civilians and on the other hand that her special constitution demands a special protection. The international community's attention of women is increased as a result of the tragic situation that faced women around the world especially in the Middle East and particularly in Iraq during the American-British war and ISIS period, these two periods sort many negative effects that reach women such as captivity, slavery, sexual enslavement and rape women especially Yazidis and Christians....

Abstract:

Robust statistics Known as, resistance to errors caused by deviation from the stability hypotheses of the statistical operations (Reasonable, Approximately Met, Asymptotically Unbiased, Reasonably Small Bias, Efficient ) in the data selected in a wide range of probability distributions whether they follow a normal distribution or a mixture of other distributions deviations different standard .

power spectrum function lead to, President role in the analysis of Stationary random processes, form stable random variables organized according to time, may be discrete random variables or continuous. It can be described by measuring its total capacity as function in frequency.

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Acquisition provisions in Islamic jurisprudence

Eat this research study features Technical Ceramics Islamic and Chinese The study of four chapters , such as the first chapter the general framework for research and containing the problem that put the following question: Mamdy effect features art on porcelain Islamic and Chinese ) , and whether there are dimensions of the aesthetic , intellectual and ideological in porcelain Islamic and Chinese with lies the importance of research in the promise of a qualitative study and add a scientific theme features art in porcelain Islamic and China , and the objectives of this study One was in the detection of features technical Ceramics Islamic and Chinese study examined the length of time the ninth century AD , and the tenth century AD , and in

Diabetes mellitus type 2 (T2DM) formerly called non-insulin dependent diabetes mellitus (NIDDM) or adult-onset diabetes is a common disease. Rheumatoid factor is a well-established test used in the diagnosis and follows the prognosis of rheumatoid arthritis (RA). Rheumatoid factor is sometimes found in serum of patients with other diseases including diabetes mellitus (DM), due to the presence of pro-inflammatory cytokines such as TNF- α which play an important role in chronic inflammatory and autoimmune diseases like rheumatoid arthritis (RA). The aim of the study is to investigate the associations between type 2 diabetes mellitus (T2DM) and rheumatoid arthritis (RA) in scope of rheumatoid factor (RF), hyperglycemia a

Polarization modulation plays an important role in polarization encoding in quantum key distribution. By using polarization modulation, quantum key distribution systems become more compact and more vulnerable as one laser source is used instead of using multiple laser sources that may cause side-channel attacks. Metasurfaces with their exceptional optical properties have led to the development of versatile ultrathin optical devices. They are made up of planar arrays of resonant or nearly resonant subwavelength pieces and provide complete control over reflected and transmitted electromagnetic waves opening several possibilities for the development of innovative optical components. In this work, the Si nanowire metasurface grating polarize