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 effective tool for reducing both the dependency problem and the wrapping effect. By construction, Taylor model methods appear particularly suitable for integrating nonlinear ODEs. In this paper, we analyze Taylor model based integration of ODEs and compare Taylor model with traditional enclosure methods for IVPs for ODEs. More advanced Taylor model integration methods are discussed in the algorithm (1). For clarity, we summarize the major steps of the naive Taylor model method as algorithm 1.
The challenge to incorporate usability evaluation values and practices into agile development process is not only persisting but also systemic. Notable contributions of researchers have attempted to isolate and close the gaps between both fields, with the aim of developing usable software. Due to the current absence of a reference model that specifies where and how usability activities need to be considered in the agile development process. This paper proposes a model for identifying appropriate usability evaluation methods alongside the agile development process. By using this model, the development team can apply usability evaluations at the right time at the right place to get the necessary feedback from the end-user. Verificatio
... Show MorePost-structural critical studies highlighted the importance of studying the texts surrounding the text as an important part in the process of receiving and understanding texts, and although this topic was dealt with by the ancient Arabs and Europeans, interest in it appeared clearly after the appearance of Gerard Genet's book (SEUILS), which separated it Text Thresholds. Or what he called paratexte, and dealt with them with interest as he reads them on books. With the development of semiotic studies, interest in paratexte studies began in a broader way and in various literary and non-literary texts, including journalistic texts. And since specialized magazines are one of the press releases that enjoy their privacy in terms of topics and
... Show MoreCircular data (circular sightings) are periodic data and are measured on the unit's circle by radian or grades. They are fundamentally different from those linear data compatible with the mathematical representation of the usual linear regression model due to their cyclical nature. Circular data originate in a wide variety of fields of scientific, medical, economic and social life. One of the most important statistical methods that represents this data, and there are several methods of estimating angular regression, including teachers and non-educationalists, so the letter included the use of three models of angular regression, two of which are teaching models and one of which is a model of educators. ) (DM) (MLE) and circular shrinkage mod
... Show MoreSome experiments need to know the extent of their usefulness to continue providing them or not. This is done through the fuzzy regression discontinuous model, where the Epanechnikov Kernel and Triangular Kernel were used to estimate the model by generating data from the Monte Carlo experiment and comparing the results obtained. It was found that the. Epanechnikov Kernel has a least mean squared error.
Every so often, a confluence of novel technologies emerges that radically transforms every aspect of the industry, the global economy, and finally, the way we live. These sharp leaps of human ingenuity are known as industrial revolutions, and we are currently in the midst of the fourth such revolution, coined Industry 4.0 by the World Economic Forum. Building on their guideline set of technologies that encompass Industry 4.0, we present a full set of pillar technologies on which Industry 4.0 project portfolio management rests as well as the foundation technologies that support these pillars. A complete model of an Industry 4.0 factory which relies on these pillar technologies is presented. The full set of pillars encompasses cyberph
... Show MoreIn this study, oxidative desulfurization of dibenzothiophene (DBT) with H2O2 as an oxidant was studied, whereas the catalyst used was zirconium oxide supported on Activated carbon (AC). Zirconium oxide (ZrO2) was impregnated over prepared activated carbon (AC) and characterized by various techniques such as XRD, FTIR, BET, SEM, and EDX. This composite was used as a heterogeneous catalyst for oxidation desulfurization of simulated oil. The results of this study showed that ZrO2/AC composite exhibited significant catalytic activity and stability, effectively lowering sulfur content under mild conditions. Factors such as reaction temperature (30, 40, 50, 60°C), time (5, 10, 15,20,30,60, 80 100 min), catalyst dose (0.3, 0.5,
... Show MoreWe investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio
... Show MoreThis research aims to present a proposed model for disclosure and documentation when performing the audit according to the joint audit method by using the questions and principles of the collective intelligence system, which leads to improving and enhancing the efficiency of the joint audit, and thus enhancing the confidence of the parties concerned in the outputs of the audit process. As the research problem can be formulated through the following question: “Does the proposed model for disclosure of the role of the collective intelligence system contribute to improving joint auditing?”
The proposed model is designed for the disclosure of joint auditing and the role
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