iosr-JMCE   Volume-21 ~ Issue-4 ~ Jul. – Aug. 2024

Abstract: This paper aims at combining Newton's method with an approach proposed by S. Weerakoon and T.G.I. Fernando, using the function evaluated at the arithmetic, harmonic, geometric and quadratic means to obtain different iterative formulations, the convergence of one of them is demonstrated, which is the arithmetic mean which is obtained as the order of cubic convergence. The resulting order of convergence is investigated in some examples, and it is found to be less or greater than the cubic convergence, and with some means, convergence is not achieved. Background There are various methods to find the root of a nonlinear equation. Closed methods include bisection, secant.....

Key Word: Simple root; iterative methods; integral; means

[1] S. Weerakoo, , & Fernando, T. G. I. (2000). A Variant Of Newton's Method With Accelerated Third-Order Convergence. Applied Mathematics Letters, 13(1), 97-103.
[2] Saba Akram, Q. Annu. (2015). Newton-Raphson Method. International Journal Of Scientific & Engineering Research, 6(7), 1748-1752.
[3] Ilhan M. Izmirli. (2013). An Elementary Proof Of The Mean Inequalities. Advances In Pure Mathematics, 3(3), 331-334. Doi: 10.4236/Apm.2013.33047 Https://Www.Scirp.Org/Html/4-5300350_31228.Htm
[4] Elena Castiñeira Holgado And Venancio Tomeo Perucha. (2019). Relaciones Entre Las Medias Estadísticas: Demostraciones Relationships Between Statistical Measures: Demonstrations. Universidad Complutense De Madrid. Retrieved From Https://Estudiosestadisticos.Ucm.Es/Data/Cont/Docs/12-2019-11-29-Ct04-2019.Pdf
[5] Stan Sýkora. (2009). Mathematical Means And Averages: Basic Properties. In Stan's Library (Vol. Iii, Pp. 1-22). Castano Primo, Italy: Ed. S. Sykora. Https://Www.Ams.Org/Journals/Bull/1948-54-05/S0002-9904-1948-08994-7/S0002-9904-1948-08994-7.Pdf

Abstract: This study investigated the mechanical properties of African fan palm for its applicability in reinforced concrete works. The African fan palm is characterised as mart wood and its variability to stress and strain (longitudinal, radial and tangential) like other timber species necessitates an understanding of its mechanical properties. Therefore, the objective of this study was to experimentally determine the uniaxial tension, three-point bending, compression and Poisson's ratio of the African fan palm. The Poisson's ratio was obtained through the comparison of the transverse strain against the longitudinal strain when the fan palm bar was tensioned on a 2000kN capacity.....

Keywords: Tensile strength, compression strength, MOR, MOE, deformation, Poisson's ratio

[1] Adedeji R. O. (2020). Determination Of The Utilization Potentials Of Wood Of Borassus Aethiopum Mart Through Its Strength Properties. Journal Of Indian Academy Of Wood Science. Https://Doi.Org/10.1007/S13196-020-00263-Z.
[2] Adewuyi A. P., Otukoya A. A., Olaniyi O. A., Olafusi O. S. (2015). Comparative Studies Of Steel, Bamboo And Rattan As Reinforcing Bars In Concrete: Tensile And Flexural Characteristics. Open Journal Of Civil Engineering.
[3] Adom-Asamoah M., Banahene J. O, Obeng J. B. (2017). Bamboo-Reinforced Self-Compacting Concrete Beams For Sustainable Construction In Rural Areas. Structural Concrete - Doi: 10.1002/Suco.201600205.
[4] Asibe A. A. O., Frimpong-Mensah K. And Darkwa N. A. (2013). Assessment Of The Effect Of Density On Mechanical Properties Variations Of Borassus Aethiopum. Archives Of Applied Science Research, 5 (6); 6-19.
(Http://Scholarsresearchlibrary.Com/Archive.Html).
[5] Astm D143 – 22 Standard Test Methods For Small Clear Specimens Of Timber.

Abstract: A firefighter's job involves detecting and extinguishing fires. In this rapidly developing age of technology, the world is gradually moving towards automated systems. Firefighters, on the other hand, often risk losing their lives. Most of the deaths were due to toxic gasses found in the extinguishing environment. This system was created in order to address the issue with the firefighting robot because of this. This fire fighting robot using Arduino, fire sensors, etc. The robot detects a fire and sends a message to the Arduino. The Arduino then sends a signal to the motor driver and......

Key Word: Arduino UNO; Flame sensor; Motor driver; Water pump

[1] Saravanan P., Soni Ishawarya, "Android Controlled Integrated Semi-Autonomous Firefighting Robot," International Journal Of Innovative Science Engg. And Technology Vol. 2 Issue 8, Issn 2348 – 7968, August 2015.
[2] Nagesh Ms, Deepika T V, Stafford Michahial, Dr M Shivakumar, "Fire Extinguishing Robot," International Journal Of Advanced Research In Computer And Communication Engineering, Vol. 5, Issue 12, December 2016.
[3] Pushpendra Kumar, Saurabh Verma, Pradeep Kumar, Sandeep, "Automatic Fire Fighting Robot," International Journal Of Creative Research Thoughts (Ijcrt),2018, Volume 6, Issue 2, April 2018.
[4] Lokesh Venkata Ramana Talabhaktula,Veerraju Daliparthi, Tulasi Ravi Kumar, Dulam Chandra Naga Rakesh, "A Novel Fire Fighting Robot With Arduino," International Journal Of Food And Nutritional Sciences (Ijfans), Vol.10, Iss.1, Jan 2021, E-Issn 2320 –7876.
[5] Anam Sheikh, Gopal Purohit, Vaishnavi.C.Raut, Rehan Rashid Abdul, Prof. C. H. Kidile, "Review Paper On Arduino Based Fire Fighting Robot," International Journal For Research In Applied Science & Engineering Technology (Ijraset), Volume 10 Issue V May 2022, Issn: 2321-9653; Ic Value: 45.98..

Abstract: Pressure vessels are widely used in the oil and gas industry to hold and transport liquids and gases at pressures substantially different from atmospheric pressure. Such vessels are usually subjected to internal pressures due to the vapour pressure of the liquid or storage conditions of the gas being held. The design of pressure vessels requires detailed sizing calculations and material selection to ensure that they can withstand the stresses developed due to liquid containment, and thus prevent possible loss of containment.......

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Abstract: The Jean-Baptiste Joseph Fourier and Laplace methods are powerful tools for solving differential equations, but they have their limits. When the boundary conditions of a problem are complex, variational methods such as Ritz's method offer an alternative route. To better understand how Ritz's method works, let's consider a simple problem: the temperature distribution in a rod with an internal heat source. By solving this problem both analytically and in the approximate Ritz method, we can compare the results and evaluate the accuracy of the latter. This comparison will allow us to determine whether Ritz's method is a reliable tool for solving more complex problems.......

Key Word: Walther Heinrich Wilhelm Ritz; Jean-Baptiste Joseph Fourier; Pierre-Simon Laplace; Analytical solution; Approximation.

[1]. Isabel Marrero, Teoría Básica De Espacios De Hilbert(2022), Https://Campusvirtual.Ull.Es/Ocw/Pluginfile.Php/19781/Mod_Resource/Content/2/1-Ehilbert-N-Ocw.Pdf
[2]. O. Christensen, The Hilbert Space L2, (2010), Springer Science, Https://Link.Springer.Com/Content/Pdf/10.1007/978-0-8176-4980-7_6.Pdf
[3]. O. Christensen,( 2010), Functions, Spaces, And Expansions: Mathematical Tools 117 In Physics And Engineering, Applied And Numerical Harmonic Analysis, Doi 10.1007/978-0-8176-4980-7 6, C Springer Science+Business Media
[4]. Sergey Repin.(2027), One Hundred Years Of The Galerkin Method, Doi: 10.1515/Cmam-2017-0013
[5]. A. Gritsans, F. Sadyrbaev, I. Yermachenko,(2016), Dirichlet Boundary Value Problem For The Second Order Asymptotically Linear System, Wiley, Https://Doi.Org/10.1155/2016/5676217

Abstract: Globally, approximately 9–10 kg of waste tyres are discarded per person annually, with minimal landfill usage. The large-scale production and disposal of waste tyres have raised significant environmental concerns. Various recycling and reuse strategies have been explored, including agricultural applications, tyre-derived fuel, sports applications, incorporating waste tyre rubber in new tyre production, and civil engineering uses, such as adding waste tyre rubber powder to bituminous mixes for road construction. The use of waste tyre rubber in bituminous mixes is expected to rise as its benefits gain recognition. Rubber-modified bitumen has been employed globally for the past five.......

Key Word: Waste tyre rubber, bitumen modification, road construction, sustainable infrastructure, environmental impact

[1]. https://auto.economictimes.indiatimes.com/news/tyres/rampant-use-of-end-of-life-tyres-for-pyrolysis-in-india-atra/67941565
[2]. Rahman MM. Characterisation of dry process crumb rubber modified asphalt mixtures, 2004. Thesis submitted to the University of Nottingham for the degree of Doctor of Philosophy. University of Nottingham, School of Civil Engineering;
[3]. https://www.bridgestoneamericas.com/en/corporate-social-responsibility/safety/tyres-101/tyre-construction
[4]. N. Zerin, M. Rasul, M. Jahirul and A. Sayem, "End-of-life tyre conversion to energy: A review on pyrolysis and activated carbon production processes and their challenges".2023. Science of the Total Environment 905 166981
[5]. Alexandra Pehlken, E. Essadiqi; Scrap Tyre Recycling in Canada, 2005, CANMET Materials Technology Laboratory