Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an ef

This paper is specifically a detailed review of the Spatial Quantile Autoregressive (SARQR) model that refers to the incorporation of quantile regression models into spatial autoregressive models to facilitate an improved analysis of the characteristics of spatially dependent data. The relevance of SARQR is emphasized in most applications, including but not limited to the fields that might need the study of spatial variation and dependencies. In particular, it looks at literature dated from 1971 and 2024 and shows the extent to which SARQR had already been applied previously in other disciplines such as economics, real estate, environmental science, and epidemiology. Accordingly, evidence indicates SARQR has numerous benefits compar

Almost all thermal systems utilize some type of heat exchanger. In a lot of cases, evaporators are important for systems like organic Rankine cycle systems. Evaporators give a share in a large portion of the capital cost, and their cost is significantly attached to their size or transfer area. Open-cell metal foams with high porosity are taken into consideration to enhance thermal performance without increase the size of heat exchangers. Numerous researchers have tried to find a representation of the temperature distribution closer to reality due to the different properties between the liquid and solid phases. Evaporation heat transfer in an annular pipe of double pipe heat exchanger (DPHEX) filled with cooper foam is investigated numerical

The body has the ability to effect the audience in the the theatrical show , since he or she is transmitter , sender , seen and viewer of the humanitarian discourse as well the the images and connotations of the theatrical show, it is a tool of communication that substitutes for millions of spoken words, the modern schools of direction focused on the body language of the actor and gave it prominence in depicting facts by different connotations. The researcher studies the physical performance of the actor throughout focusing on the connotational dimensions of the body within the theatrical show , as well as the positioning of performative body within the modern schools of direction depending on the theatrical show (Rebuke ) of the Iraqi d

The study highlighted the transformation of value systems and educational patterns between past and present, especially with the introduction of modern variables and means, such as mobile phones, the internet, social media, and others. These factors have contributed both positively and negatively to the study. The study highlights the integral role of the school in collaboration with the family in guiding and educating children. It also emphasizes the active role of the school in developing students' abilities and skills, either attracting them to school or vice versa. This includes an examination of the essential skills required in education and their role in achieving a state of psychological well-being and systematically developing child

The Sunnah of the Prophet has a great impact in building human behavior, and the formation of Islamic thought, has worked to spread science in all of Egypt, as it carried to the people of the eternal prophecy of the love of science, it was a source of knowledge and civilization. It is a generous source, a rich source of the Islamic nation, always tender, and renewed benefit, which is not only a source of legislation and language but is a source of guidance for thought and guidance of behavior, and the Hadith The importance is obvious In the integration of Islam, and show aspects of human integration in the personality of Mustafa , and the Muslims are interested in talking - collected and codification -, and made the effort of the cent