In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

Recently, there has been a major trend towards environmental issues and concern for the green product because traditional products cause serious environmental impacts such as reduced resources, global warming, energy consumption, emissions and other environmental damage. Under these developments, economic units are looking for cost-effective technologies that reduce the cost of a green product that has four main dimensions: reducing energy, reducing resource consumption, preventing pollution, and using renewable energy while not compromising quality and satisfying customers in order to enhance competitive advantage.

This research will address one of the most important cost-effective green technologies, Gr

In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

Ticks (Acari: Ixodidae) are ectoparasites that infest livestock in every geographic region of the world and are vectors of several viral, bacterial, and protozoan pathogens to both animals and humans. There is little information is available is about tick presence in Buffalo Bubalus bubalis (Linnaeus, 1758) (Artiodactyla, Bovidae) in Iraq. The current study determined the species of ticks parasitizing Buffalo in some central and southern regions included: Baghdad (Al Fathelia), Karbala (Al-Hussainia), Wasit (Kut and Al-Suwairah), Al-Qadisia (Al- Diwaniyah, Al- Saniya, Al-Mihnawea, and Afak), Thi Qar (Al-Nasiriyah and Al-chibayish), Missan (Amara and Qalaat Salih) and Basrah (Al-Haretha, Al-Madena and Al-Deer). A total of 150 Buffal

           The support qualitative information regards as an additional step in the process of decision-making where the method following by companies to provide information help in the creation of value because it is very important to deliver information to investors about their stratigies and what happen truly inside the companies i.e.  every case relating with the expectations of stockhotslder and the prices of markets depending on those expectation ,and if the matter isn’t that there will be lack of confidence thate couldn’t be backed again. The decisions of the investors effected by security ,economic ,political, psychological, emotional ,and financial factors .

Lung cancer is the most common dangerous disease that, if treated late, can lead to death. It is more likely to be treated if successfully discovered at an early stage before it worsens. Distinguishing the size, shape, and location of lymphatic nodes can identify the spread of the disease around these nodes. Thus, identifying lung cancer at the early stage is remarkably helpful for doctors. Lung cancer can be diagnosed successfully by expert doctors; however, their limited experience may lead to misdiagnosis and cause medical issues in patients. In the line of computer-assisted systems, many methods and strategies can be used to predict the cancer malignancy level that plays a significant role to provide precise abnormality detectio