Journal Vol – 19 No – 10, October 2024

Abstract:

In this paper, the author proved that the product of two negatively directed numbers is a negatively directed number. This article is the outcome of previously published (2021-2024) ten (10) articles of this author. It is true that the negative of a negative number is a positive number. It has been done by applying the inversion process to a negative number. The process of inversion does not satisfy the basic concept of multiplication. Multiplication is defined as the adding of a number concerning another number repeatedly. So, the process of inversion does not comply with the fundamental concept of multiplication. According to the Theory of Dynamics of Numbers there exist three types of numbers: (1) Neutral or discrete numbers (2) Positively directed numbers (3) Negatively directed numbers. In general, we use four types of operators: addition (+), subtraction (-), multiplication (x), and division (÷) in mathematical calculations. Besides these, we use the negative sign (-) as an inversion operator. The positive sign (+) and negative sign (-) also represent the direction of neutral or discrete numbers. In this paper, the author introduced Fermat's Last Theorem: xⁿ + yⁿ = zⁿ for n = 2 in Bhattacharyya's Theorem to prove that the product of two negatively directed numbers is a negatively directed number using the concept of the Theory of Dynamics of Numbers. In this paper, the author framed new laws of multiplication and inversion. Also, the author has given a comparative study between the conventional method of multiplication and the present concept of multiplication citing some practical examples. The author has become successful in finding the root of a quadratic equation in real numbers even if the discriminant, b² – 4ac < 0 without using the concept of the imaginary number and also in determining the radius of a circle even if g² + f² < c, in real number without using the concept of complex numbers. With one example the author proved that this theorem is applicable in ‘Calculus’ also.

Keywords:

Bhattacharyya's Theorem,Concept of limit,Number Theory,Rectangular Bhattacharyya's coordinates,Role of multiplication and inversion,Theory of Dynamics of Numbers,

Refference:

I. Alper Yorulmaz & M. Cihangir Doğan. : ‘An Action Research to Eliminate Mistakes in Multiplication and Division Operations through Realistic Mathematics Education’. Eric. Vol17(3) 2022. 10.29329/epasr.2022.461.12.
II. Arsoetar, N., & Sugiman, S. (2019). Development of student worksheets based on Realistic Mathematics Education (RME) oriented to mathematical reasoning. In Journal of Physics: Conference Series-The 6th International Conference on Research, Implementation, and Education of Mathematics and Science, Yogyakarta, Indonesia, 1397(1), p. 012091, IOP Publishing.
III. Aytekin Uskun, K. (2020). İlkokul dördüncü sınıf öğrencilerinin dört işlem problemlerinde gerçekçi matematik eğitimi yaklaşımının problem çözme ve problem kurma başarılarına etkisinin araştırılması. (Yayınlanmamış yüksek lisans tezi), Kırşehir Ahi Evran Üniversitesi Sosyal Bilimler Enstitüsü, Kırşehir.
IV. Beckmann, S. (2014). Mathematics for elementary teachers with activities. Pearson Education.
V. Boaler, J., Munson, J., & Williams, C. (2018). Mindset mathematics: Visualizing and investigating big ideas, Grade 3. Jossey Bass.
VI. Boaler, J. : ‘Mathematical mindsets: Unleashing students’. potential through creative math, inspiring messages and innovative teaching (2nd ed.) (2022). John Wiley & Sons.
VII. Brahma-Sphuta Siddhanta Vol I – edited by Acharyavara Ramswarup Sharma pg 158.
VIII. Brahma-Sphuta Siddhanta Vol I – edited by Acharyavara Ramswarup Sharma pg 160.
IX. Clements, D. H. , Sarama, J. , Wolfe, C. B. , & Spitler, M. E. : ‘Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies: Persistence of effects in the third year’. American Educational Research Journal. Vol. 50(4), pp. 812–850, 2013.
X. Clements, D. H. , & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach. Routledge.
XI. Colebrooke, I.c., p. 171, fn. 5.
XII. Common Core Standards Writing Team . (2011). Progressions for the Common Core State Standards in Mathematics (draft). K, counting and cardinality; K-5, operations and algebraic thinking. Institute for Mathematics and Education, University of Arizona, Tucson, AZ.
XIII. Common Core Standards Writing Team . (2019). Progressions for the Common Core State Standards in Mathematics (draft, July 25, 2019). Institute for Mathematics and Education. University of Arizona.http://mathematicalmusings.org/wp-content/uploads/2022/05/Progressions-CC-to-RP-07_25_2019.pdf
XIV. Ganita-manjari by Ganesa.
XV. Ganita-Sara-Sangraha – ed. L. C. Jain (1963).
XVI. Gelosia method – David E. Smith, History, II, pg. 115.
XVII. G. H. Hardy and E. M. Wright. : ‘An Introduction to the Theory of Numbers’. Sixth Edition. Page 245 – 247.
XVIII. Hansa, S. (2017). Exploring multiplicative reasoning with grade four learners through structured problem solving. (Unpublished MA thesis), University of the Witwatersrand, Johannesburg.
XIX. History of Hindu Mathematics by Bibhutibhusan Datta and Avadhesh Narayan Singh, 1935, pg 138.
XX. Hulbert, E. , Petit, M. , & Laird, R. (2015). OGAP multiplicative reasoning professional development. Moretown, VT. Unpublished.

XXI. Lobato, J. , & Walters, C. D. (2017). A taxonomy of approaches to learning trajectories and progressions. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 74–101). National Council of Teachers of Mathematics.
XXII. Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2017). Improving mathematics teaching in kindergarten with realistic mathematical education. Early Childhood Education Journal, 45(3), 369-378. https://doi.org/10.1007/s10643-015-0768-4
XXIII. Prabha S. Rastogi, Sandhya Nitin. : ‘HISTORY OF MULTIPLICATION CLASSICAL PERIOD IN INDIAN MATHEMATICS’.
https://instavm.org/wp-content/uploads/2021/05/H16.pdf
XXIV. Prabir Chandra Bhattacharyya : ‘AN INTRODUCTION TO RECTANGULAR BHATTACHARYYA’S CO-ORDINATES: A NEW CONCEPT’. J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, pp 76. November (2021). 10.26782/jmcms.2021.11.00008
XXV. Prabir Chandra Bhattacharyya. : ‘AN INTRODUCTION TO THEORY OF DYNAMICS OF NUMBERS: A NEW CONCET’. J. Mech. Cont. & Math. Sci., Vol.-17, No.-1, pp 37-53, January (2022). 10.26782/jmcms.2022.01.00003
XXVI. Prabir Chandra Bhattacharyya. : A NOVEL CONCEPT IN THEORY OF QUADRATIC EQUATION. J. Mech. Cont. & Math. Sci., Vol.-17, No.-3, March (2022) pp 41-63. l : 10.26782/jmcms.2022.03.00006
XXVII. Prabir Chandra Bhattacharyya. ‘A NOVEL METHOD TO FIND THE EQUATION OF CIRCLES’. J. Mech. Cont. & Math. Sci., Vol.-17, No.-6, June (2022) pp 31-56
XXVIII. Prabir Chandra Bhattacharyya. : ‘AN OPENING OF A NEW HORIZON IN THE THEORY OF QUADRATIC EQUATION: PURE AND PSEUDO QUADRATIC EQUATION – A NEW CONCEPT’. J. Mech. Cont. & Math. Sci., Vol.-17, No.-11, November (2022) pp 1-25.
XXIX. Prabir Chandra Bhattacharyya. : ‘A NOVEL CONCEPT FOR FINDING THE FUNDAMENTAL RELATIONS BETWEEN STREAM FUNCTION AND VELOCITY POTENTIAL IN REAL NUMBERS IN TWO-DIMENSIONAL FLUID MOTIONS’. J. Mech. Cont. & Math. Sci., Vol.-18, No.-02, February (2023) pp 1-19
XXX. Prabir Chandra Bhattacharyya, : ‘A NEW CONCEPT OF THE EXTENDED FORM OF PYTHAGORAS THEOREM’. J. Mech. Cont. & Math. Sci., Vol.- 18, No.-04, April (2023) pp 46-56. 10.26782/jmcms.2023.04.00004
XXXI. Prabir Chandra Bhattacharyya, : ‘A NEW CONCEPT TO PROVE, √(−1) = −1 IN BOTH GEOMETRIC AND ALGEBRAIC METHODS WITHOUT USING THE CONCEPT OF IMAGINARY NUMBERS’. J. Mech. Cont. & Math. Sci., Vol.-18, No.-9, pp 20-43. 10.26782/jmcms.2023.09.00003
XXXII. Prabir Chandra Bhattacharyya, : ‘A NOVEL CONCEPT OF THE THEORY OF DYNAMICS OF NUMBERS AND ITS APPLICATION IN THE QUADRATIC EQUATION’. J. Mech. Cont. & Math. Sci., Vol.-19, No.- 2, pp 93-115, February (2024). 10.26782/jmcms.2024.02.00006
XXXIII. Prabir Chandra Bhattacharyya. : A NOVEL CONCEPT OF THE BHATTACHARYYA’S THEOREM: √−(𝐱 𝟐 + 𝐲 𝟐) = − √ (𝐱𝟐 + 𝐲 𝟐) TO FIND THE SQUARE ROOT OF ANY NEGATIVE NUMBER INTRODUCING FERMAT’S LAST THEOREM IN REAL NUMBERS WITHOUT USING THE CONCEPT OF COMPLEX NUMBERS. J. Mech. Cont.& Math. Sci., Vol.-19, No.-5, May (2024) pp 136-144. 10.26782/jmcms.2024.05.00009
XXXIV. Tanujaya, B., Prahmana, R. C. I., & Mumu, J. (2017). Mathematics instruction, problems, challenges and opportunities: A case study in Manokwari Regency. World Transactions on Engineering and Technology Education, 15(3), 287-291.
XXXV. Theodora, F.R.N., & Hidayat, D. (2018). The use of realistic mathematics education in teaching the concept of equality. Journal of Holistic Mathematics Education, 1(2), 104-113. http://doi.org/10.19166/johme.v1i2.913
XXXVI. Topçu, H. (2021). Gerçekçi matematik eğitimi yaklaşımının 9. Sınıf öğrencilerinin akademik başarıları, kalıcılık ve tutumlarına etkisi. (Yayınlanmamış doktora tezi), Atatürk Üniversitesi Eğitim Bilimleri Enstitüsü, Erzurum.
XXXVII. Trishatika (Pati-Ganit-Sara) by V. Kutumbshastri, 2004, pg 13.
XXXVIII. Uça, S., & Saracaloğlu, A. S. (2017). The use of realistic mathematics education in students’ making sense of decimals: A design research. Elementary Education Online, 16(2), 469-496. 10.17051/ilkonline.2017.304712
XXXIX. Yorulmaz, A. (2018). Gerçekçi matematik eğitiminin ilkokul dördüncü sınıf öğrencilerinin dört işlem becerilerindeki hatalarının giderilmesine etkisi. (Yayımlanmamış doktora tezi), Marmara Üniversitesi Eğitim Bilimleri Enstitüsü, İstanbul.
XL. Yorulmaz, A., Uysal, H. & Sidekli, S. (2021). The use of mind maps related to the four operations in primary school fourth-grade students as an evaluation tool. Journal of Education and Learning, 15(2), 257-266. 10.11591/edulearn.v15i2.19894

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Abstract:

This paper is concerned with the mathematical modeling of the displacement-traction with elastic bases, under specially selected boundary conditions for place and traction. The approximate approach is based on the theoretical results of the iterative factorization of operators given sufficiently smooth data, and smooth solutions. The problem resulting from the discretization of the original problem using the approximate approach occurs twice at each step of the proposed iterative process. The efficiency of the numerical method of iterative factorization explains that it is suitable for practical implementation in the computer.

Keywords:

Iterative factorization and extension,Mathematical model of displacement-traction,Place and traction boundary conditions,

Refference:

I. Iaccarino, G. L.: Marasco A., Romano, A.: Signorini’s Method for Live Loads and 2nd Order Effects, Int. J. Engrg. Sci 44, issue 5-6, pp. 312-324, 2006. doi:10.1016/j.ijengsci.2005.12.005
II. Marasco, A., Romano, A.: Scientific Computing with Mathematica: Mathematical Problems for Ordinary Differential Equations, Birkhauser, Boston, 2001.
III. Ryazhskikh, A.V. Hydrodynamic initial section during the flow of a highly viscous Newtonian fluid in a round pipe. Bulletin of St. Petersburg University. Series 10. Applied mathematics. Computer science. Management processes. 3, pp. 98–102, 2012. https://www.mathnet.ru/rus/vspui/y2012/i3/p98
IV. Ryazhskikh, V.I., Slyusarev, M.I., Popov, M.I.: Numerical integration of a biharmonic equation in a quadratic domain. Bulletin of St. Petersburg University. Series 10. Applied mathematics. Computer science. Management processes. 1, pp. 52–62, 2013. https://www.mathnet.ru/rus/vspui/y2013/i1/p52
V. Sorokin, S.B.: Exact constants of energy equivalence in the method of recalculating boundary conditions for the biharmonic equation. Bulletin of Novosibirsk State University. Series: Mathematics, Mechanics, Computer Science. 13(3), pp. 113–121, 2013. doi: https://doi.org/10.1134/S1995423913030063
VI. Sorokin, S.B.: Preconditioning in the numerical solution of the Dirichlet problem for a biharmonic equation. Siberian Journal of Computational Mathematics, 14(2), pp. 205–213, 2011. doi: https://doi.org/10.1134/S1995423911020078
VII. Stoppelli, F.: On the existence of solutions of the equations of isothermal electrostatics in the case of stresses with equilibrium axes II, III. Mat. Research 7, pp. 138-152, 1958.
VIII. Stoppelli, F.:An existence and uniqueness theorem relating to the equations of isothermal elastostatics for nite deformations. Mat. Research, 3, pp. 247-267, 1954.
IX. Tahir J. K. : ‘NUMERICAL INVESTIGATION OF THE GROWTH-DIFFUSION MODEL.’ .JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES. Vol. 18(7), pp. 1–6, 2023. https://doi.org/10.26782/jmcms.2023.07.00001

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Abstract:

As fossil fuels run out quickly, researchers studying engines are increasingly interested in alternative fuels. This paper covers the use of plastic paralysis oil as biodiesel in diesel engines. This was done using a four-stroke, multi-cylinder CRDI diesel engine running between 2000 and 2500 rpm. From zero loads to fifty percent load, the performance, combustion, and emission characteristics were computed for a variety of load scenarios. The analysis revealed that the blend D80WPO20 at 2000 rpm reduced hydrocarbon emissions from 0.059 g/kW to 0.045 g/kW, which is lower than that of 25% diesel at 26 kW. At high speed, the blend D80WPO20 at 2000 rpm gave the maximum BTE of 34.53%. The nitric oxide (NOx) emissions from D50WPO50 and diesel at a 26 kW load are 6.48 g/kWh and 5.37 g/kWh, respectively, according to reports. Data envelopment analysis, a multi-response linear programming optimization tool, was used to evaluate the output and emissions of DI diesel engines using waste plastic oil mixtures.

Keywords:

Combustion,Data Envelopment Analysis,Pyrolysis,Waste plastic oil,

Refference:

I. A Pakiya Pradeep& S Gowthaman, “Combustion and Emission A Abdul munaf , A Velmurugan , M Loganathan , M Bakkiyaraj and P Premkumar Studies on CRDI diesel engine performance and emissions using waste plastic oil and fly ash catalyst Engineering Research Express, Vol.6 (1), no. 015518, 2024. 10.1088/2631-8695/ad2cce
II. A Abdul Munaf, P Premkumar, A Velmurugan, Premdasu Nalluri, “Catalytic Degradation of Used Plastics oil as Liquid Fuel for IC Engines”, J. Phys.: Conf. Ser. Vol. 2054, no.012072, 2021. 10.1088/1742-6596/2054/1/012072
III. A Pakiya Pradeep& S Gowthaman, “Combustion and Emission Characteristics of Diesel Engine Fueled with Waste Plastic Oil – A Review”, International Journal of Ambient Energy, Vol. 43(1), pp. 1269-1287, 2019. https://doi.org/10.1080/01430750.2019.1684994
IV. A Velmurugan, M Loganathan, E James Gunasekaran “Experimental investigations on combustion, performance and emission characteristics of thermal cracked cashew nut shell liquid (TC-CNSL)–diesel blends in a diesel engine”, Fuel, Elsevier, Vol.132, pp.236-245, 2014. https://doi.org/10.1016/j.fuel.2014.04.060
V. Ahamed Vessal, “Evaluating the Performance of Universities by using Data Envelopment Analysis”, California Journal of Operation Management, Vol. 5 (1), no. 918856, 2007. https://doi.org/10.1080/23322039.2014.918856
VI. Avinash Kumar Agarwal, Dhananjay Kumar Srivastava, et al., ”Effect of fuel timing and pressure on combustion,emission and performance characteristics of a single cylinder diesel engine”, Fuel, vol.111, pp.374-383, 2013. https://doi.org/10.1016/j.fuel.2013.03.016.
VII. Bridjesh P, Periyasamy P, Krishna Chaitanya AV &Geetha NK, “MEA and DEE as additives on diesel engine using waste plastic oil diesel blends”, Sustainable Environment Research, Vol. 28(3), pp.142-147, 2018. https://doi.org/10.1016/j.serj.2018.01.001
VIII. D. Damodharan, A.P. Sathiyagnanam, D. Rana, et al., “Effective utilization of waste plastic oil in a direct injection diesel engine using high carbon alcohols as oxygenated additives for cleaner emissions”, Energy Conversion and Management, Vol,166, pp.83-97, 2018. https://doi.org/10.1016/j.enconman.2018.04.006
IX. D. Damodharan, B. Sethuramasamyraja, B. Rajesh Kumar, K. Gopal& Melvin Victor De Poures , “Utilization of waste plastic oil in diesel engines: a review”, Rev Environ Sci, Vol. 18, pp. 681–697, 2019. https://doi.org/10.1007/s11157-019-09516-x

X. Das, A.K., Padhi, M.R., Hansdah, D. et al. “Optimization of Engine Parameters and Ethanol Fuel Additive of a Diesel Engine Fuelled with Waste Plastic Oil Blended Diesel”, Process Integration and Optimization for Sustainability Vol. 4, pp.465–479, 2020. https://doi.org/10.1007/s41660-020-00134-7
XI. Gerhard Reichmann, “Measuring University Library efficiency using Data Envelopment Analysis”, Libri, Vol. 54 (2), pp. 136-146, 2004. https://doi.org/10.1515/LIBR.2004.136
XII. Kundan Kumar Jha, T.T.M. Kannan, N. Senthilvelan, “Optimization of catalytic pyrolysis process for change of plastic waste into fuel” Materials Today: Proceedings, Vol. 39 (1), pp. 708-711, 2021. https://doi.org/10.1016/j.matpr.2020.09.263
XIII. Lin T, Lo Y.F and CheinF.C,”Using Data Envelopment Analysis to measure the relative, 2007.efficiency of the service center and improve operation efficiency through reorganization”, IEEE Transaction on Power Systems, Vol. 18 (1), pp. 366-373, 2003. https://doi.org/10.1109/TPWRS.2002.807081
XIV. M. Abbott, C.Doucouliagos, “The Efficiency of Australian University: A Data Envelopment Analysis”, Economics of education review, Vol. 22 (1), pp. 89-97, 2003. https://doi.org/10.1016/S0272-7757(01)00068-1
XV. Muhamad Sharul Nizam Awang, Nurin Wahidah Mohd Zulkifl, et al., “Effect of Addition of Palm Oil Biodiesel in Waste Plastic Oil on Diesel Engine Performance, Emission and Lubricity”, ACS Omega, Vol. 6 (33), pp.21655-21675, 2021. https://doi.org/10.1021/acsomega.1c03073
XVI. MuruganMariappan, Mebin Samuel Panithasan, GnanamoorthiVenkadesan, “Pyrolysis plastic oil production and optimisation followed by maximum possible replacement of diesel with bio-oil/methanol blends in a CRDI engine”, Journal of Cleaner Production, Vol.312, no. 127687, 2021. https://doi.org/10.1016/j.jclepro.2021.127687
XVII. P. Premkumar, PremdasuNalluri, and A. Abdul Munaf, “Effect of waste plastic oil diesel blend on variant injection pressure of a diesel engine”, AIP Conf. Proc.. Vol. 2316 (1), no. 030020, 2021. https://doi.org/10.1063/5.0037160
XVIII. Sunaryo, PriyoAdi Sesotyo, et al., “Performance and Fuel Consumption of Diesel Engine Fueled by Diesel Fuel and Waste Plastic Oil Blends: An Experimental Investigation”, Automotive Experiences, Vol. 4(1), pp. 20-26, 2021. https://doi.org/10.31603/ae.3692
XIX. Yu M, Wang R, ”Evaluating the efficiency of Hospitals Department using Data Envelopment Analysis”, IEEE Transaction, pp. 1167-1170, 2006. https://doi.org/10.1109/SOLI.2006.328916.

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Abstract:

The paper presents an efficient energy management system designed for a small-scale hybrid microgrid incorporating wind, solar, and battery-based energy generation systems using the droop control technique. The heart of the proposed system is the energy management system, which is responsible for maintaining power balance within the microgrid. The EMS continuously monitors variations in renewable energy generation and load demand and adjusts the operation of the energy conversion systems and battery storage to ensure optimal performance and reliability. The primary objective of the energy management system is to maintain power balance within the microgrid, even in the face of fluctuations in renewable energy generation and load demand. This involves dynamically adjusting the operation of the renewable energy sources and battery storage system to match the instantaneous power requirements of the microgrid. Overall, the paper presents a comprehensive approach to designing and implementing an efficient energy management system for a small-scale hybrid wind-solar-battery-based microgrid to extract maximum profit from electricity generation. By integrating renewable energy sources with energy storage and advanced control algorithms, the proposed system aims to enhance the reliability, stability, and sustainability of the microgrid's power supply.

Keywords:

Battery Storage,Droop Control,Energy Management System,Microgrids,Optimization,Photovoltaic (PV),Uncertainties,Wind Energy,

Refference:

I. AlKassem, A., Draou, A., Alamri, A., & Alharbi, H. (2022). Design Analysis of an Optimal Microgrid System for the Integration of Renewable Energy Sources at a University Campus. Sustainability, 14(7), 4175. https://doi.org/10.3390/su14074175.
II. Almada, J., Leão, R., Sampaio, R., & Barroso, G. (2016). A centralized and heuristic approach for energy management of an AC microgrid. Renewable and Sustainable Energy Reviews, 60, 1396–1404.
III. Alvarez, G., Moradi, H., Smith, M., & Zilouchian, A. (2017). Modeling a Grid-Connected PV/Battery Microgrid System with MPPT Controller. 2017 IEEE 44th Photovoltaic Specialist Conference (PVSC), 2941–2946.
IV. Arcos-Aviles, D., Pascual, J., Guinjoan, F., Marroyo, L., Sanchis, P., & Marietta, M.P. (2017). Low complexity energy management strategy for grid profile smoothing of a residential grid-connected microgrid using generation and demand forecasting. Applied Energy, 205, 69–84.
V. Cabrera-Tobar, A., Massi Pavan, A., Petrone, G., & Spagnuolo, G. (2022). A Review of the Optimization and Control Techniques in the Presence of Uncertainties for the Energy Management of Microgrids. Energies, 15(23), 9114. https://doi.org/10.3390/en15239114.
VI. Cecati, C., Dell’Aquila, A., Liserre, M., & Monopoli, V.G. (2003). A passivity-based multilevel active rectifier with adaptive compensation for traction applications. IEEE Transactions on Industry Applications, 39(5), 1404–1413.
VII. Franquelo, L.G., Rodriguez, J., Leon, J.I., Kouko, S., & Portillo, R. (2008). The age of multilevel converters arrives. IEEE Industrial Electronics Magazine, 2(2), 28–39.
VIII. Genikomsakis, K.N., Lopez, S., Dallas, P.I., & Ioakimidis, C.S. (2017). Simulation of Wind-Battery Microgrid Based on Short-Term Wind Power Forecasting. Applied Sciences, 7(11), 1142. https://doi.org/10.3390/app7111142.
IX. Gonzalez, R., Gubia, E., Lopez, J., & Marroyo, L. (2008). Transformerless single-phase multilevel-based photovoltaic inverter. IEEE Transactions on Industrial Electronics, 55(7), 2694–2702.
X. Ganthia, B. P., & Upadhyaya, M. (2021). Bridgeless AC/DC Converter & DC-DC Based Power Factor Correction with Reduced Total Harmonic Distortion. Design Engineering, 2012-2018.
XI. Ganthia, B. P., Pradhan, R., Das, S., & Ganthia, S. (2017). Analytical study of MPPT based PV system using fuzzy logic controller. 2017 International Conference on Energy, Communication, Data Analytics and Soft Computing (ICECDS), 3266-3269. IEEE.
XII. Ganthia, B. P., Sahu, P. K., & Mohanty, A. Minimization Of Total Harmonic Distortion Using Pulse Width Modulation Technique. IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-ISSN, 2278-1676.
XIII. Ganthia, B.P., & Praveen, B.M. (2023). Review on Scenario of Wind Power Generations in India. Electrical Engineering, 13(2), 1-27p.
XIV. Ganthia, B.P., Barik, S., & Nayak, B. (2020). Application of hybrid facts devices in DFIG based wind energy system for LVRT capability enhancements. J. Mech. Cont. Math. Sci., 15(6), 245-256.
XV. Ganthia, B.P., Barik, S.K., & Nayak, B. (2020). Transient analysis of grid integrated stator voltage oriented controlled type-III DFIG driven wind turbine energy system. Journal of Mechanics of Continua and Mathematical Sciences, 15(6), 139-157.
XVI. Ganthia, B.P., Monalisa Mohanty, Sushree Shataroopa Mohapatra, Rosalin Pradhan, Subhasmita Satapathy, Shilpa Patra, & Sunita Pahadasingh. (2023). Artificial Neural Network Optimized Load Forecasting of Smartgrid using MATLAB. Control Systems and Optimization Letters, 1(1), 46-51.
XVII. Ganthia, B.P., Mannam, P., & Manchireddy, S. (2021). Grid Tied PV with Reduced THD Using NN and PWM Techniques. Design Engineering, 2019-2027.
XVIII. Hasan, M., Mekhilef, S., & Metselaar, I.H. (2013). Photovoltaic System Modeling with Fuzzy Logic Based Maximum Power Point Tracking Algorithm. International Journal of Photoenergy, Article ID 762946, 10 pages. https://doi.org/10.1155/2013/762946.
XIX. Jigar S. Sarda, K., Lee, K., Patel, H., Patel, N., & Patel, D. (2022). Energy Management System of Microgrid using Optimization Approach. IFAC-Papers On Line, 55(9), 280-284. https://doi.org/10.1016/j.ifacol.2022.07.049.
XX. Jena, S., Mishra, S., Ganthia, B. P., & Samal, S. K. (2022). Load Frequency Control of a Four-Area Interconnected Power System Using JAYA Tuned PID Controller and Derivative Filter. In Sustainable Energy and Technological Advancements: Proceedings of ISSETA 2021 (pp. 497-511). Singapore: Springer Singapore.

XXI. Kabat, S.R., Panigrahi, C.K., & Ganthia, B.P. (2022). Comparative analysis of fuzzy logic and synchronous reference frame controlled LVRT capability enhancement in wind energy system using DVR and STATCOM. In Sustainable Energy and Technological Advancements: Proceedings of ISSETA 2021 (pp. 423-433). Singapore: Springer Singapore.
XXII. Khan, R. A., Farooqui, S. A., Sarwar, M. I., Ahmad, S., Tariq, M., Sarwar, A., Zaid, M., Ahmad, S., & Shah, N. M. A. (2022). Archimedes Optimization Algorithm Based Selective Harmonic Elimination in a Cascaded H-Bridge Multilevel Inverter. Sustainability, 14(1), 310. https://doi.org/10.3390/su14010310.
XXIII. Krithiga, G., & Mohan, V. (2022). Elimination of Harmonics in Multilevel Inverter Using Multi-Group Marine Predator Algorithm-Based Enhanced RNN. International Transactions on Electrical Energy Systems, Article ID 8004425, 13 pages. https://doi.org/10.1155/2022/8004425.
XXIV. Lai, J-S., & Peng, F. Z. (1996). Multilevel converters—A new breed of power converters. IEEE Transactions on Industry Applications, 32(3), 509–517.
XXV. Mannam, P., Manchireddy, S., & Ganthia, B. P. (2021). Grid Tied PV with Reduced THD Using NN and PWM Techniques. Design Engineering, 2019-2027.
XXVI. Mohanty, R., Chatterjee, D., Mohanty, S., Dhanamjayulu, C., & Khan, B. (2023). THD Reduction of Improved Single Source MLI Using Upgraded Black Widow Optimization Algorithm. International Transactions on Electrical Energy Systems, Article ID 6724716, 16 pages. https://doi.org/10.1155/2023/6724716.
XXVII. Refaai, M. R. A., Dhanesh, L., Ganthia, B. P., Mohanty, M., Subbiah, R., & Anbese, E. M. (2022). Design and Implementation of a Floating PV Model to Analyse the Power Generation. International Journal of Photoenergy, Article ID 8004425.

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Abstract:

This study introduces a six-compartmental mathematical model (S, , , E, I, R) to examine the impact of administering a double dose vaccine on the dynamic spread of diarrhea within a community. The mathematical analysis shows the existence of equilibrium points for both disease-free and endemic states in the model. The basic reproduction number  was determined using the Next Generation Matrix. Analysis has shown that the basic reproduction number  which indicates the disease-free equilibrium point is locally asymptotically stable. Also, using a suitable Lyapunov functional for the model system expressed in state variables and parameters defining the dynamic characteristics of spread and control strategies of the rotavirus diarrhea to obtain the global stability of disease-free equilibrium point over time. A numerical simulation was carried out by Wolfram Mathematica to show the effect of a second-dose vaccine. The inclusion of a double-dose vaccine has been found to have a significant effect on completely eliminating the outbreak of diarrhea. This is evidenced by the local and global stability results, which indicate that effective measures have been taken to prevent the reintroduction or transmission of the disease, and if there may be a risk of outbreaks or reemergence of the disease, very little continuous monitoring and intervention strategies are required to maintain control as this should be taken seriously by medical practitioners or policy health makers.

Keywords:

Stability,Basic Reproduction Number,Vaccination,Diarrhea Model,Lyapunov function,

Refference:

I. Adewale S. O., Olapade L. A., Ajao S. O., Adeniran G. A., : ’Analysis of diarrhea in the presence of vaccine’. Int. J. Sci. Eng. Res. Vol. 6, pp. 396–400, 2015.
II. Akinola E. I., Awoyemi B. E., Olopade I. A., Falomo O. D., Akinwumi T. O., : ’Mathematical analysis of a diarrhea model in the presence of vaccination and treatment waves with sensitivity analysis.’ J. Appl. Sci. Environ. Manage. Vol. 25, pp. 1107-1114, 2021. 10.4314/jasem.v25i7.2
III. Ardkaew J., Tongkumchum P., : ’Statistical modeling of childhood diarrhea in northeastern Thailand Southeast Asian’, J. Trop. Med. Pub. Health. Vol. 40, pp. 807–811, 2009.
IV. Berhe H. W., Makinde O. D., Theuri D. M.., : ’Parameter estimation and sensitivity analysis of dysentery diarrhea epidemic model’ J. Appl. Math. Article ID 8465747, 13 pages, 2019. 10.1155/2019/8465747
V. Bonyah E., Twagirumukiza G., Gambrah P., : ’Analysis of Diarrhea model with saturated incidence rate’. Open J. Math. Sci. Vol. 3, pp. 29–39, 2019. 10.30538/oms2019.0046
VI. Borisov M., Dimitrova N., Simeonov I., : ’Mathematical modeling and stability analysis of a two-phase biosystem’. Processes. Vol. 8, pp. 791, 2020. 10.3390/pr8070791
VII. Cherry B. R., Reeves M. J., Smith G., : ’Evaluation of bovine viral diarrhea virus control using mathematical model of infection dynamics’. Prev. Vet. Med. Vol. 33, pp. 91–108, 1998. 10.1016/S0167-5877(97)00050-0
VIII. Egbetade S. A., Salawu I. A., Fasanmade P. A., : ’Local stability of equilibrium points of sir mathematical model of infections diseases’. World J. Res. Rev. Vol. 6, pp. 79–81, 2018.
IX. Forde J. E., : ’Delay differential equation models in mathematical biology’ Doctoral Thesis, University of Michigan, United States of America. 2005. api.semanticscholar.org/CorpusID:125373845, hdl.handle.net/2027.42/125360
X. Lungu E., Chaturvedi O., Jeffrey M., Masupe S., : ’Rotavirus diarrhea and analysis through epidemic modeling’. J. Biomed. Eng. Inform. Vol. 4, pp. 21–37, 2018. 10.5430/jbei.v4n2p21
XI. Olutimo A. L., Adams D. O., : ’On the stability and boundedness of solutions of certain non-autonomous delay differential equation of third order’. Appl. Math. Vol. 7, pp. 457–467, 2016. 10.4236/am.2016.76041
XII. Olutimo A. L., Adams D. O., Abdurasid A. A., : ’Stability and boundedness analysis of a prey-predator system with predator cannibalism’ J. Nig. Math. Soc. Vol. 41, pp. 275–286, 2022. ojs.ictp.it/jnms
XIII. Olutimo A. L., Akinmoladun O. M., Omoko I. D., : ’Stability and boundedness analysis of Lotka-Volterra prey-predator model with prey refuge and predator cannibalism’. J. Comp. Model. Vol. 12, pp. 5–18, 2022. 10.47260/jcomod/1212
XIV. Olutimo A. L., Williams F. A., Adeyemi M. O., Akewushola J. R., : ’Mathematical modeling of diarrhea with vaccination and treatment factor’. J. Adv. Math. Comput. Sci. Vol. 39, pp. 59–72, 2024. 10.9734/jamcs/2024/v39i51891

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Abstract:

An analytical technique employing the variable separable method has been used in an attempt to precisely grasp and assess the impact of the property non-local elasticity upon the wave transmission response of an anisotropic fiber-reinforced material embedded over a semi-infinite, inhomogeneous medium that changes linearly. As depth increases, the stiffness and density of a semi-infinite substrate are believed to alter linearly. Availing the Whittaker function, a relation about dispersion has been acquired to analyze the response of SH waves. The visual representation depicts a significant influence of non-local elasticity on the propagation of SH-wave modes. Special cases have been found assessing the concurrency of the model with the original form equation of Love wave. The effects of non-locality, fiber-reinforcement parameters, and inhomogeneity parameters carry implications in designing and gradation of material characteristics some important parameters on the wave characteristics of the studied model.

Keywords:

Fiber-reinforced,Inhomogeneous,Love wave,Non-local elasticity,

Refference:

I. Abd-Alla AM. and Ahmed SM. : ‘Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium.’ Applied Mathematics and Computation. Vol. 106(2), pp. 265–275, 1999. 10.1016/S0096-3003(98)10128-5
II. Abd-Alla AM., Hammad HAH. and Abo-Dahab SM. : ‘Rayleigh waves in a magnetoelastic half-space of orthotropic material under influence of initial stress and gravity field.’ Applied Mathematics and Computation. Vol. 154, pp. 583–597, 2004. 10.1016/S0096-3003(03)00767-7
III. Abd-Alla AM., Nofal TA., Abo-Dahab SM., Al-Mullise A. : ‘Surface waves propagation in fiber-reinforced anisotropic elastic media subjected to gravity field.’ Int J Phys Sci. Vol. 2013;8(14), pp. 574–84. 2004. 10.5897/IJPS2013.3812
IV. A. C. Eringen and D. Edelen. : ‘On nonlocal elasticity.’ Int. J. Eng. Sci. Vol. 10(3), pp. 233–248, 1972.
V. A. C. Eringen. : ‘Screw dislocation in non-local elasticity.’ J. Phys. D Appl. Phys. 10(5), pp. 671, 1977.
VI. A. C. Eringen : ‘Theory of nonlocal elasticity and some applications.’ Princeton University, Department of Civil Engineering, Princeton, NJ. 1984.
VII. A. C. Eringen and J. L. Wegner. : ‘Nonlocal continuum field theories’ Appl. Mech. Rev. 56(2), pp. B20–B22, 2003.
VIII. Ahmed SM. and Abo-Dahab SM. : ‘Propagation of Love waves in an orthotropic granular layer under initial stress overlying a semi-infinite granular medium.’ Journal of Vibration and Control. 16(12): pp. 1845–1858, 2010. 10.1177/1077546309341154
IX. Andrianova ZS. : ‘Seismic love waves.’ Springer Science & Business Media. 2012.
X. Biot M. A. : ‘Mechanics of Incremental Deformations.’ Wiley, New York. 1965.
XI. Chattopadhyay A (1975) On the dispersion equation for Love wave due to irregularity in the thickness of non-homogeneous crustal layer. Acta Geophysica Polonica 23: 307–317.
XII. Chakraborty SK and Dey S (1982) The propagation of Love waves in water saturated soil underlain by heterogeneous elastic medium. Acta Mechanica 44: 169–176. 10.1007/BF01303335
XIII. Chattaraj R, Samal SK. Love waves in the fiber-reinforced layer over a gravitating porous half-space. Acta Geophys 2013;61(5):1170–83. 10.2478/s11600-012-0100-2
XIV. D. G. B. Edelen, A. E. Green, and N. Laws, Nonlocal continuum mechanics, Arch. Ration. Mech. Anal. 43 (1971), no. 1, 36–44.
XV. Dey S, Gupta S and Gupta AK (1996) Propagation of Love waves in heterogeneous crust over a heterogeneous mantle. Journal of Acta Geophysica Polonica XLIX (2): 125–137.
XVI. Dey S, Gupta S and Gupta AK (2004) Propagation of Love waves in an elastic layer with void pores. Sadhana 29: 355–363. 10.1007/BF02703687
XVII. D. Karlicic, T. Murmu, S. Adhikari, and M McCarthy, Non-local structural mechanics, John Wiley & Sons, New York, USA, 2015.
XVIII. Eskandari M, Shodja HM. Love waves propagation in functionally graded piezoelectric materials with quadratic variation. J Sound Vib 2008;313(1-2): 195–204. 10.1016/j.jsv.2007.11.037
XIX. Gubbins D. Seismology and plate tectonics. Cambridge University Press; 1990.
XX. Gupta S, Ahmed M. On propagation of Love waves in dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space. Earthq Struct 2017;12(6):619–28. 10.12989/eas.2017.12.6.619
XXI. Gupta S, Vishwakarma SK, Majhi DK, Kundu S. Possibility of Love wave propagation in a porous layer under the effect of linearly varying directional rigidities. Appl Math Model 2013; 37(10-11) : 6652–60. 10.1016/j.apm.2013.01.008
XXII. Kalyani VK, Sinha A, Pallavika, et al. (2008) Finite difference modeling of seismic wave propagation in monoclinic media. Acta Geophysica 56(4): 1074–1089. 10.2478/s11600-008-0049-3
XIII. Kundu S, Kumari A, Gupta S, Pandit DK. Effect of periodic corrugation, reinforcement, heterogeneity and initial stress on Love wave propagation. Waves Random Complex Media 2016;26(4):485–515. 10.1080/17455030.2016.1168951
XIV. Kundu S, Gupta S, Manna S, Dolai P. Propagation of Love wave in fiber-reinforced medium over a nonhomogeneous half-space. Int J Appl Mech 2014;6(5):1450050. 10.1142/S1758825114500501
XV. Kuznetsov SV. Love waves in layered anisotropic media. J Appl Math Mech 2006; 70(1):116–27. 10.1016/j.jappmathmech.2006.03.004
XVI. Love AEH. Some problems of geodynamics. London: Cambridge University Press; 1911.
XVII. Liu JX, Fang DN, Wei WY, Zhao XF. Love waves in layered piezoelectric/ piezomagnetic structures. J Sound Vib 2008;315(1-2):146–56. 10.1016/j.jsv.2008.01.055
XVIII. Markham MF. Measurement of the elastic constants of fiber composites by ultrasonics. Composites 1970;1(3):145–9.
XIX. M. N. L. Narasimhan and B. M. McCay, Dispersion of surface waves in nonlocal dielectric fluids, Arch. Mech. 33 (1981), no. 3, 385–400.
XXX. Manna S, Kundu S, Gupta S. Effect of reinforcement and inhomogeneity on the propagation of Love waves. Int J GeoMech 2016;16(2):04015045. 10.1061/(ASCE)GM.1943-5622.0000517
XXXI. Manna S, Kundu S, Gupta S. Propagation of love waves in piezoelectric layered system over an isotropic half-space under initial stress. In: Conference GSI; 2016. p. 74–9. 10.17491/cgsi/2016/95898
XXXII. Manna, S. and Bhat, M., 2022. Love wave fields in a non-local elastic model with reinforced and inhomogeneous media. Soil Dynamics and Earthquake Engineering, 161, p.107388. 10.1016/j.soildyn.2022.107388
XXXIII. Manna, S., Kundu, S. and Gupta, S., 2015. Love wave propagation in a piezoelectric layer overlying in an inhomogeneous elastic half-space. Journal of Vibration and Control, 21(13), pp.2553-2568. 10.1177/1077546313513626
XXXIV. Pradhan A, Samal SK, Mahanti NC. Influence of anisotropy on the love waves in a self-reinforced medium. J Appl Sci Eng 2003;6(3):173–8. 10.6180/jase.2003.6.3.06
XXXV. Son MS, Kang YJ. Propagation of shear waves in a poroelastic layer constrained between two elastic layers. Appl Math Model 2012;36(8):3685–95. 10.1016/j.apm.2011.11.008
XXXVI. S.B. Altan, Uniqueness in the linear theory of nonlocal elasticity, Bull. Tech. Univ. Istanb 37 (1984), 373–385.
XXXVII. S. B. Altan, Existence in nonlocal elasticity, Archiwum Mechaniki Stosowanej 41 (1989), no. 1, 25–36.
XXXVIII. Wang Q, Quek ST, Varadan VK. Love waves in piezoelectric coupled solid media. Smart Mater Struct 2001;10(2):380. 10.1088/0964-1726/10/2/325

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Abstract:

In this paper, we examine the dominating metric dimension of various graph types. A resolving set is a subset of vertices that uniquely identifies each vertex in the graph based on its distances to others, and the metric dimension is the minimum size of such a set. A dominating set ensures each vertex is adjacent to at least one vertex in the set. When a set is both resolving and dominating, it forms a dominating resolving set, and the smallest such set defines the dominating metric dimension, denoted as . We calculate the dominating metric dimension for the splitting graph of  book graph, globe graph, tortoise graph, and  graph.

Keywords:

Distance,Dominant Metric Dimension,Dominant Resolving Set,Metric Dimension,Resolving Set,

Refference:

I. A. H. Karbasi, R. E. Atani: ‘Application of dominating sets in wireless sensor networks’, International Journal of Security and Its Applications. Vol. 7, pp. 185-202, 2013.‏

II. A. Sebő, E. Tannier: ‘On metric generators of graphs’. Mathematics of Operations Research. Vol. 29, pp. 383-393, 2004. 10.1287/moor.1030.0070

III. B. Deng, M. F. Nadeem, M. Azeem: ‘On the edge metric dimension of different families of möbius networks’. Mathematical Problems in Engineering. Vol. 2021, p. 623208, 2021. 10.1155/2021/6623208

IV. B. Mohamed, L. Mohaisen, M. Amin: ‘Binary Archimedes optimization algorithm for computing dominant metric dimension problem’. Intelligent Automation & Soft Computing. Vol. 38, pp. 19-34, 2023. 10.32604/iasc.2023.031947

V. B. Mohamed, L. Mohaisen, M. Amin: ‘Binary equilibrium optimization algorithm for computing connected domination metric dimension problem’. Scientific Programming. Vol. 2022, p. 6076369, 2022. 10.1155/2022/6076369

VI. B. Mohamed, L. Mohaisen, M. Amin: ‘Computing connected resolvability of graphs using binary enhanced Harris Hawks optimization’. Intelligent Automation and Soft Computing. Vol. 36, pp. 2349-2361, 2023. 10.32604/iasc.2023.032930

VII. B. Mohamed, M. Amin: ‘Domination number and secure resolving sets in cyclic networks’. Applied and Computational Mathematics. Vol. 12, pp. 42-45, 2023. 10.11648/j.acm.20231202.12

VIII. B. Mohamed, M. Amin: ‘Some new results on domination and independent dominating set of some graphs’. Applied and Computational Mathematics. Vol. 13, pp. 53-57, 2024. 10.11648/j.acm.20241303.11

IX. B. Mohamed, M. Amin: ‘The metric dimension of subdivisions of Lilly graph, tadpole graph and special trees’. Applied and Computational Mathematics. Vol. 12, pp. 9-14, 2023. 10.11648/j.acm.20231201.12

X. B. Mohamed: ‘Metric dimension of graphs and its application to robotic navigation’. International Journal of Computer Applications. Vol. 184, pp. 1-3, 2022. 10.5120/ijca2022922090

XI. F. Harary, R. A. Melter: ‘On the metric dimension of a graph’. Combinatoria. Vol. 2, pp. 191-195, 1976.

XII. G. Chartrand, L. Eroh, M. A. Johnson, O. R. Ollermann: ‘Resolvability in graphs and the metric dimension of a graph’. Discrete Applied Mathematics. Vol. 105, pp. 99-113, 2000. 10.1016/S0166-218X(00)00198-0

XIII. H. Al-Zoubi, H. Alzaareer, A. Zraiqat, T. Hamadneh, W. Al-Mashaleh: ‘On ruled surfaces of coordinate finite type’. WSEAS Transactions on Mathematics. Vol. 21, pp. 765–769, 2022. 10.37394/23206.2022.21.87

XIV. H. M. A. Siddiqui, M. Imran: ‘Computing the metric dimension of wheel related graphs’. Applied Mathematics and Computation. Vol. 242, pp. 624-632, 2014. 10.1016/j.amc.2014.06.006

XV. I. M. Batiha, B. Mohamed: ‘Binary rat swarm optimizer algorithm for computing independent domination metric dimension problem’. Mathematical Models in Engineering. Vol. 10, pp. 6-13, 2024. 10.21595/mme.2024.24037‏

XVI. I. M. Batiha, B. Mohamed, I. H. Jebril: ‘Secure metric dimension of new classes of graphs’. Mathematical Models in Engineering. Vol. 10, pp. 1-6, 2024. 10.21595/mme.2024.24168

XVII. I. M. Batiha, J. Oudetallah, A. Ouannas, A. A. Al-Nana, I. H. Jebril: ‘Tuning the fractional-order PID-Controller for blood glucose level of diabetic patients’. International Journal of Advances in Soft Computing and its Applications. Vol. 13, pp. 1–10, 2021. https://www.i-csrs.org/Volumes/ijasca/2021.2.1.pdf

XVIII. I. M. Batiha, M. Amin, B. Mohamed, H. I. Jebril: ‘Connected metric dimension of the class of ladder graphs’. Mathematical Models in Engineering. Vol. 10, pp. 65–74, 2024. 10.21595/mme.2024.23934

XIX. I. M. Batiha, N. Anakira, A. Hashim, B. Mohamed: ‘A special graph for the connected metric dimension of graphs’. Mathematical Models in Engineering. Vol. 10, pp. 1-8, 2024. 10.21595/mme.2024.24176

XX. I. M. Batiha, N. Anakira, B. Mohamed: ‘Algorithm for finding domination resolving number of a graph’. Journal of Mechanics of Continua and Mathematical Sciences. Vol. 19, pp. 18-23, 2024. 10.26782/jmcms.2024.09.00003

XXI. I. M. Batiha, S. A. Njadat, R. M. Batyha, A. Zraiqat, A. Dababneh, S. Momani: ‘Design fractional-order PID controllers for single-joint robot ARM model’. International Journal of Advances in Soft Computing and its Applications. Vol. 14, pp. 97–114, 2022. 10.15849/IJASCA.220720.07

XXII. J. L. Hurink, T. Nieberg: ‘Approximating minimum independent dominating sets in wireless networks’. Information Processing Letters. Vol. 109, pp. 155-160, 2008.‏ 10.1016/j.ipl.2008.09.021

XXIII. K. Wijaya, E. Baskoro, H. Assiyatun, D. Suprijant: ‘Subdivision of graphs in R(mK_2,P_4)’. Heliyon. Vol. 6, p e03843, 2020. 10.1016/j.heliyon.2020.e03843

XXIV. L. Susilowati, I. Sa’adah, R. Z. Fauziyyah, A. Erfanian: ‘The dominant metric dimension of graphs’. Heliyon. Vol. 6, e03633, 2020. 10.1016/j.heliyon.2020.e03633

XXV. M. R. Garey, D. S. Johnson: ‘Computers and Intractability: A Guide to the Theory of NP-Completeness’. Freeman, 1979.

XXVI. P. Singh, S. Sharma, S. K. Sharma, V. K. Bhat: ‘Metric dimension and edge metric dimension of windmill graphs’. AIMS Mathematics. Vol. 6, pp. 9138-9153, 2021. 10.3934/math.2021531

XXVII. P. J. Slater: ‘Leaves of trees’. Congressus Numerantium. Vol. 14, pp. 549–559, 1975.

XXVIII. R. A. Melter, I. Tomescu: ‘Metric bases in digital geometry’. Computer Vision, Graphics, and Image Processing. Vol. 25, pp. 113-121, 1984. 10.1016/0734-189X(84)90051-3

XXIX. R. Manjusha, A. S. Kuriakose: ‘Metric dimension and uncertainty of traversing robots in a network’. International Journal on Applications of Graph Theory in Wireless Ad Hoc Networks and Sensor Networks. Vol.7, pp. 1-9, 2015. 10.5121/jgraphoc.2015.7301

XXX. R. P. Adirasari, H. Suprajitno, L. Susilowati: ‘The dominant metric dimension of corona product graphs’. Baghdad Science Journal. Vol. 18, p. 0349, 2021. 10.21123/bsj.2021.18.2.0349

XXXI. S. Nazeer, M. Hussain, F. A. Alrawajeh, S. Almotairi: ‘Metric dimension on path-related graphs’. Mathematical Problems in Engineering. Vol. 2021, p. 2085778, 2021. 10.1155/2021/2085778

XXXII. T. W. Haynes, S. T. Hedetneimi, P. J. Slater: ‘Domination in Graphs: Advanced Topics’. Marcel Dekker Inc, New York, 1998.

XXXIII. V. Chvátal: ‘Mastermind’. Combinatorica. Vol. 3, pp. 325-329, 1983. 10.1007/BF02579188

XXXIV. Z. Beerliova, F. Eberhard, T. Erlebach, A. Hall, M. Hoffmann, M. Mihal’ak, L. S. Ram: ‘Network discovery and verification’. IEEE Journal on Selected Areas in Communications. Vol. 24, pp. 2168-2181, 2006. 10.1109/JSAC.2006.884015

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Abstract:

Road surfaces have long been made with bituminous mix because of its low cost and versatile applications. However, environmental variables, traffic loads, and ageing frequently affect its endurance. Many additives have been introduced to overcome these problems, and epoxy resin has shown great promise. This study evaluates bituminous binder and bituminous mixes with different percentages of epoxy modification.  Epoxy asphalt binder's (EAB) rheological properties were described. Following that, an evaluation was conducted on the engineering properties of an epoxy asphalt mixture (EAM).  The results demonstrated that the rheological properties of EAB outperform those of neat binders. Furthermore, the outcomes demonstrated that EAM had better moisture damage performance in terms of static immersion test and retained Marshall stability test than the conventional hot dense graded bituminous mixes. According to the results, the ideal content for both VG 30 and VG 40 binders is 2% epoxy modification. Out of all the mix permutations, bituminous mixes with 2% epoxy modification yielded the best results. Comparing blends with control mixes or unmodified bituminous mixes, on the other hand, revealed a lower resistance to moisture damage than mixes with 3% epoxy modification with both binders. The study concludes that epoxy resin can significantly improve the performance and longevity of asphalt concrete roadways, offering benefits to the road construction industry.

Keywords:

Sustainable pavement,Bituminous Mix,Epoxy Modified Asphalt,Rheology,Marshall Stability,

Refference:

I. Bahmani, Hossein, Hamed Khani Sanij, and Farideddin Peiravian. “Estimating moisture resistance of asphalt mixture containing epoxy resin using surface free energy method and modified Lottman test.” International Journal of Pavement Engineering 23.10 (2022): 3492-3504.
https://doi.org/10.1080/10298436.2021.1904236

II. Bocci, Edoardo, Andrea Graziani, and Francesco Canestrari. “Mechanical 3D characterization of epoxy asphalt concrete for pavement layers of orthotropic steel decks.” Construction and Building Materials 79 (2015): 145-152, https://doi.org/10.1016/j.conbuildmat.2014.12.120

III. Cong, Peiliang, Shanfa Chen, and Jianying Yu. “Investigation of the properties of epoxy resin‐modified asphalt mixtures for application to orthotropic bridge decks.” Journal of Applied Polymer Science 121.4 (2011): 2310-2316, https://doi.org/10.1002/app.33948

IV. Çubuk, Meltem, Metin Gürü, and M. Kürşat Çubuk. “Improvement of bitumen performance with epoxy resin.” Fuel 88.7 (2009): 1324-1328, https://doi.org/10.1016/j.fuel.2008.12.024

V. Huang, Ming, and Weidong Huang. “Analyses of viscosity variation in solidifying procedure of epoxy asphalt.” ICTE 2011. 2011. 1439-1444. https://doi.org/10.1061/41184(419)238

VI. Isacsson, U., and X. Lu. “Testing and appraisal of polymer modified road bitumens—state of the art.” Materials and structures 28 (1995): 139-159. https://link.springer.com/article/10.1007/BF02473221

VII. Asphalt Institute. (1993). Mix design methods for asphalt concrete and other hot-mix types (Manual Series No. 2 (MS-2)) (6th ed.). Lexington, KY.

VIII. Modarres, Amir, and Hamidreza Hamedi. “Effect of waste plastic bottles on the stiffness and fatigue properties of modified asphalt mixes.” Materials & Design 61 (2014): 8-15., https://doi.org/10.1016/j.matdes.2014.04.046

IX. Pattanaik, Madhu Lisha, Rajan Choudhary, and Bimlesh Kumar. “Moisture susceptibility of open-graded friction course mixes with EAF steel slag and modified binders.” Advances in Civil Engineering Materials 8.1 (2019): 248-266, https://doi.org/10.1520/ACEM20180158

X. Roberts, Freddy L., et al. “Hot mix asphalt materials, mixture design and construction.” (1996), NAPA Research Education and Foundation, Lanham.
XI. Roque, Reynaldo, et al. Guidelines for use of modified binders. No. UF Project No. 4910-4504-964-12. 2005, https://fdotwww.blob.core.windows.net/sitefinity/docs/default source/research/reports/fdot-bc354-77-rpt.pdf

XII. Specification for road and bridge works. Ministry of Road Transport and Highway (MoRTH). 5th Revision, Indian Roads Congress, New Delhi, 2013.

XIII. Specifications for Dense Graded Bituminous Mixes. IRC Special Publication. No. 111, Indian Roads Congress, 2009.

XIV. Yu, Jianying, Peiliang Cong, and Shaopeng Wu. “Laboratory investigation of the properties of asphalt modified with epoxy resin.” Journal of Applied Polymer Science 113.6 (2009): 3557-3563, https://doi.org/10.1002/app.30324
XV. Zhou, Wei, et al. “Effects of compound curing agent on the thermo-mechanical properties and structure of epoxy asphalt.” International Journal of Pavement Engineering 18.10 (2017): 928-936, https://doi.org/10.1080/10298436.2016.1138109

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Abstract:

The Internet of Things (IoTs) are emerging and become a vital need in our daily routine. The privacy protection and insecurity of these IoT-based devices face many challenges. Distributed denial of service (DDoS) attacks in IoT networks become a significant growing challenge that is addressed in this research. The resilience and strategy for IoT devices due to distributed denial of service (DDoS) attacks assess current security measures by proposing modern procedures to upgrade the strength of IoT frameworks. This article proposes a mechanism that mitigiates the effects of DDoS attacks in IoTs, that cause significant destruction to existing systems. Utilizing secondary data from Kaggle, the machine is trained and tested. Our proposed approach incorporates descriptive statistics, correlations, t-tests, chi-square tests, and regression analyses to supply a systematic understanding of IoT security by critically analyzing the existing variants of numerous DDoS attacks, Security issues in IoTs, and creation of them in Botnets or zombies. Our findings show that the proposed security techniques are viable and detection rates correlate with security viability. The proposed model asses various network threat and cybersecurity arrangements for mitigating DDoS attacks in IoT’s and outperforms the previously implemented Web Application Firewall (WAF), Bot Mitigation, Resource Prioritisation, and Content Delivery Networks (CDNs)based DDoS mitigation techniques by 80.5%, 88%, 86% in terms of effectiveness, T-test, chi test, and correlation.

Keywords:

DDoS attacks,Data analysis,IoT security,Security measures,

Refference:

I. Aldawood, H., & Skinner, G.. Educating and raising awareness on cyber security social engineering: A literature review. In 2018 IEEE International Conference on Teaching, assessment, and Learning for Engineering (TALE), vol 10, no. 5, pp. 62-68). IEEE. 2018, December
II. Al-Hadhrami, Y., & Hussain, F. K. DDoS attacks in IoT networks: a comprehensive systematic literature review. World Wide Web, Vol 24, no 3, pp 971-1001. 2021.
III. Ali, I., Sabir, S., & Ullah, Z. Internet of things security, device authentication and access control: a review. arXiv preprint arXiv: Vol 14, no 2, pp 1901-1920, 2019.
IV. Hassan, H. Khan, I. Uddin, A. Sajid, “Optimal Emerging trends of Deep Learning Technique for Detection based on Convolutional Neural Network”, Bulletin of Business and Economics (BBE), Vol.12, No.4, pp. 264-273, 2023
V. H. Khan, A. Ali, S. Alshmrany, “Energy-Efficient Scheduling Based on Task Migration Policy Using DPM for Homogeneous MPSoCs”, Computers, Materials & Continua, Vol.74, No.1, pp. 965-981, 2023
VI. H. Sarwar, H. Khan, I. Uddin, R. Waleed, S. Tariq, “An Efficient E-Commerce Web Platform Based on Deep Integration of MEAN Stack Technologies”, Bulletin of Business and Economics (BBE), Vol. 12, No.4, pp. 447-453, 2023
VII. Hammad. A , E. Zhao, “Mitigating link insecurities in smart grids via QoS multi-constraint routing“, In 2016 IEEE International Conference on Communications Workshops (ICC)”, pp. 380-386. 2016
VIII. H. Khan, I. Uddin, A. Ali, M. Husain, “An Optimal DPM Based Energy-Aware Task Scheduling for Performance Enhancement in Embedded MPSoC” Computers, Materials & Continua, Vol.74, No.1, pp. 2097-2113, 2023
IX. Hammad, A. A., Ahmed, “Deep Reinforcement Learning for Adaptive Cyber Defense in Network Security”, In Proceedings of the Cognitive Models and Artificial Intelligence Conference, pp. 292-297, 2016
X. H. Khan, M. U. Hashmi, Z. Khan, R. Ahmad, “Offline Earliest Deadline first Scheduling based Technique for Optimization of Energy using STORM in Homogeneous Multi-core Systems,” IJCSNS Int. J. Comput. Sci. Netw. Secur, Vol.18, No.12, pp 125-130, 2018
XI. Hossein Shirazi, Bruhadeshwar. B,”Kn0w Thy Doma1n Name”: Unbiased Phishing Detection Using Domain Name Based Features. In Proceedings Of The 23nd Acm On Symposium On Access Control Models And Technologies (Sacmat ’18). Association For Computing Machinery, New York, Ny, Usa, pp. 69-75, 2018
XII. Hussain, S., Rajput, U. A., Kazi, Q. A., & Mastoi, S, “Numerical investigation of thermohydraulic performance of triple concentric-tube heat exchanger with longitudinal fins”, J. Mech. Cont. & Math. Sci, Vol. 16, No. 8, pp 61-73, 2021.
XIII. H. Khan, S. Ahmad, N. Saleem, M. U. Hashmi, Q. Bashir, “Scheduling Based Dynamic Power Management Technique for offline Optimization of Energy in Multi Core Processors” Int. J. Sci. Eng. Res, Vol.9, No.12, pp 6-10, 2018
XIV. H. Khan, K. Janjua, A. Sikandar, M. W. Qazi, Z. Hameed, “An Efficient Scheduling based cloud computing technique using virtual Machine Resource Allocation for efficient resource utilization of Servers” In 2020 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-7, 2020
XV. Hammad, M., Jillani, R. M., Ullah, S., Namoun, A., Tufail, A., Kim, K. H., & Shah, H, “Security framework for network-based manufacturing systems with personalized customization”, An industry 4.0 approach, Sensors, vol. 23. No. 17-55, 2022
XVI. H. Khan, Q. Bashir, M. U. Hashmi, “Scheduling based energy optimization technique in multiprocessor embedded systems” In 2018 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-8, 2018
XVII. H. Khan, A. Yasmeen, S. Jan, U. Hashmi, “Enhanced Resource Leveling Indynamic Power Management Techniqueof Improvement In Performance For Multi-Core Processors”, Journal Of Mechanics Of Continua And Mathematical Sciences, Vol.6, No.14, pp. 956-972, 2019
XVIII. H. Khan, K. Janjua, A. Sikandar, M. W. Qazi, Z. Hameed, “An Efficient Scheduling based cloud computing technique using virtual Machine Resource Allocation for efficient resource utilization of Servers” In 2020 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-7, 2020
XIX. H. Huang, J. Tan And L. Liu, “Countermeasure Techniques For Deceptive Phishing Attack”, International Conference On New Trends In Information And Service Science, Beijing, pp. 636-641, 2009
XX. H. Khan, M. U. Hashmi, Z. Khan, R. Ahmad, “Offline Earliest Deadline first Scheduling based Technique for Optimization of Energy using STORM in Homogeneous Multi-core Systems” IJCSNS Int. J. Comput. Sci. Netw. Secur, Vol.18, No.12, pp 125-130, 2018

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Abstract:

To solve differential equations, we utilize an extended Laplace-ARA transform result that we offer in this work to verify the existence of other pertinent theorems.

Keywords:

ARA transform,Laplace transform,Triple Laplace-ARA transform,Volterra Integral equation,Volterra-integrodifferential equation,integro-partial differential equation,

Refference:

I. AL-Qmari S. K. Q. (2020), Estimation of a modified integral associated with a special function kernel of fox’s h-function type, Commun. Korean Math. Soc. , No. 1, pp. 125–136.

II. BhatterSanjay(2022), On Certain New Results of Fractional Calculus Involving Product of Generalized Special Functions, Int. J. Appl. Comput. Math. 10.1007/s40819-022-01253-0.

III. Choi J. H.(2013), Applications of multivalent functions associated with generalized fractional integral operator, Scientific Research, Advances in Pure Mathematics, 3, 1 – 5.

IV. Debnath, L., Bhatta, D.: Integral Transforms and Their Applications, 3rd edn. Chapman Haubold H. J.(2009), Mittag-Leffler Functions and their applications, Journal of Applied Mathematics, arXiv:0909.0230v2 .

V. Gupta K.(2011), A Study of modified H-transform and generalized fractional integral operator of weyl type, International Journal of Pure and Applied Sciences and Technology, 7(1) (2011), pp. 59-67, ISSN 2229-6107.

VI. Gupta K. and Vandana Agrawal (2010). A Theorem Connecting the H-Transform and Fractional Integral Operators Involving the Multivariable H-Function*, Tamsui Oxford Journal of Mathematical Sciences, Aletheia University, 26(4) , 383-395.

VII. Gupta K. C. and Gupta T. (2005), On unified Eulerian type integrals having general arguments, Soochow Journal of Mathematics, Volume – 31, No. 4, pp. 543-548.

VIII. Haubold H. J.(2009). Mittag-Leffler Functions and their applications, Journal of Applied Mathematics, arXiv:0909.0230v2 .

IX. Jangid K.(2020),Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions , Advances in Difference Equations , 2020:606 https://doi.org/10.1186/s13662-020-03067-0

X. Koul C. L(1971), On fractional integral operators of functions of two variables, Proc. Nat. Acad. Sci.India,41A,233-240.

XI. Kumar D (2013), Generalized Fractional Differentiation of the–Function Involving General Class of Polynomials, Int. J. Pure Appl. Sci. Technol., 16(2) , pp. 42-53, 2229 – 6107.

XII. Kumar D.(2013), New Fractional-Calculus Results Involving General Class of Multivariable Polynomials and Multivariable H-function, International Journal of Modern Mathematical Sciences. 7(1): 55-64,2166-286X.

XIII. Kiryakoya V.(2010),The special functions of fractional calculus as generalized fractional calculus operators of some basic functions, Comp& mathematics with applications, 59(3) ,1128-1141. 10.1016/j.camwa.2009.05.014.

XIV. Oparnica L (2001), Generalized fractional calculus with applications in mechanics, MATEMATИЧKИ BECHИK, 53, 151 – 158.

XV. Singh S.K. (2018), Integral Transform and the Solution of Fractional Kinetic Equation Involving Some Special Functions, International Journal of Mathematics Trends and Technology (/IJMTT) –V (55), pp. 5- 16.

XVI. Satyanarayana B. and Kumar Pragathi(2011). Some finite integrals involving multivariable polynomials, H-function of one variable and H-function of ‘r’ variables, African Journal of Mathematics and Computer Science Research Vol. 4(8), pp. 281-285.

XVII. Sharma B. L(1961), On a generalized function of two variables, I. Ann. Soc. Sci., Bruxellers Ser. I 79(1965), 26-40.Fox C. The G and H-functions as symmetrical Fourier kernel, Amer. Math. Soc. Transl., 98 , pp.395-429

XVIII. Srivastava H. M. (1983). The Weyl fractional integral of a general class of polynomials, Boll. Un. Mat. Italy 602-B , pp.219-228.

XIX. Srivastava H. M.(1976), Some bilateral generating functions for a class of generalized hypergeometric polynomials, J. Reine Angew. Math., 283/284, 265-274.

XX. Thakur A.K, S.K. Sahani and J.K. Kushwaha (2020), Some applications of Quadraple Hypergeometric functions in functions Spaces, Vol 17(12) 894 -903| 10.5281/zenodo.7451049.

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Abstract:

This paper introduces and studies four concepts of  supra fuzzy bitopological spaces. We have exhibited that all these four concepts are ‘good extensions’ of the corresponding concepts  bitopological spaces and building relationships among them. It has been justified that all the definitions are hereditary, productive, and projective. Furthermore, additional properties of these concepts are studied.

Keywords:

Fuzzy set,Fuzzy bitopological space,Good extension,Supra fuzzy bitopological space,

Refference:

I. Abd EL-Monsef, M. E., Ramadan, A. E. 1987. On fuzzy supra topological spaces. Indian J. Pure and Appl. Math. 18(4), (1987), 322-329.

II. Abu Sufiya, A.S., Fora, A. A. and Warner, M. W. 1994. Fuzzy separation axioms and fuzzy continuity in fuzzy bitopological spaces. Fuzzy Sets and Systems 62: 367-373.

III. Ali, D. M., A note on T₀ and R₀ fuzzy topological spaces, Proc. Math. Soc. B. H. U. Vol. 3, (1987), 165-167.

IV. Azad, K.K., On fuzzy semi-continuity, fuzzy almost continuity, and fuzzy weakly continuity. J. Math. Anal. Appl. 82(1), (1981), 14-32.

V. Chang, C. L., 1968. Fuzzy topological spaces. J. Math. Anal. Appl. 24, (1968), 182-192.

VI. Hannan Miah and Ruhul Amin, Some features of pairwise α-T₀ spaces in supra fuzzy bitopology, Journal of Mechanics of Continua and Mathematical Sciences, 15(11), (2020), 1-11.

VII. Hossain, M. S., Ali, D. M., On R₀ and R₁ fuzzy topological spaces; R U Studies Part-B J Sc. 33, (2005), 51-63.

VIII. Kandil, A., El-Shafee, M., Separation axioms for fuzzy bitopological spaces. J. Ins. Math. Comput. Sci. 4(3), (1991), 373-383.

IX. Kandil, A., Nouh, A.A. and El-Sheikh, S. A., Strong and ultra-separation axioms on fuzzy bitopological spaces. Fuzzy Sets and Systems. 105, (1999), 459-467.

X. Lowen, R., Fuzzy topological spaces and fuzzy compactness. J. Math. Anal. Appl. 56, (1976), 621-633.

XI. Mashour, A. S., Allam, A. A., Mahmoud, F. S., Khedr, F.H., On supra topological spaces. Indian J. Pure and Appl. Math. 14(4), (1983), 502-510.

XII. Pao-Ming, P., Ying-Ming, L., Fuzzy topology. II. Product and quotient spaces, J. Math. Anal. App. 77, (1980), 20-37.

XIII. Mukherjee, A., Completely induced bifuzzy topological spaces, Indian J. Pure Appl. Math. 33, (2002), 911-916.

XIV. Nouh, A. A., On separation axioms in fuzzy bitopological spaces, Fuzzy Sets and Systems, 80, (1996), 225-236.

XV. Srivastava, A.K., Ali, D.M., A comparison of some FT₂ concepts, Fuzzy Sets and Systems 23, (1987), 289-294.

XVI. Wong, C. K., Fuzzy points and local properties of fuzzy topology; J. Math. Anal. Appl. 46, (1974), 316-328.

XVII. Wong, C. K., Fuzzy topology: product and quotient theorems. J. Math. Anal. Appl. 45(2), (1974), 512-521.

XVIII. Zadeh, L. A., Fuzzy sets. Information and Control 8, (1965), 338-353.

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Abstract:

This study focuses on integrating mathematical and statistical modeling, where a statistical model estimates the parameters of a mathematical model, or a mathematical model generates data to train a statistical model. This integration benefits both approaches: mathematical models improve the accuracy of statistical models, while statistical models help reduce bias in mathematical ones. The findings demonstrate that this combination is a valuable tool for understanding and predicting dynamic systems, offering more accurate and flexible models. Research consistently shows that integrating these models is an ideal approach for solving complex problems and understanding various systems.

Keywords:

Complex problem,Mathematical Modeling,Statistical Modeling Sustainability,Ultimately Indicated,

Refference:

I. A. Dababneh, N. Djenina, A. Ouannas, G. Grassi, I. M. Batiha, I. H. Jebril. : ‘A new incommensurate fractional-order discrete COVID-19 model with vaccinated individuals compartment’. Fractal and Fractional. Vol. 6, p. 456, 2022. 10.3390/fractalfract6080456
II. C. D. Himmel, G. S. May. : ‘Advantages of plasma etch modeling using neural networks over statistical techniques’. IEEE Transactions on Semiconductor Manufacturing. Vol. 6, pp. 103-111, 1993. 10.1109/66.216928
III. D. R. Cavagnaro, J. L. Myung, M. A. Pitt, J. Myung. : ‘The Oxford Handbook of Quantitative Methods’. Oxford University Press, Oxford, 2013.
IV. H. E. Tinsley, S. D. Brown. : ‘Hand-book of Applied Multivariate Statistics and Mathematical Modeling’. Academic Press, Cambridge, 2000.
V. I. M. Batiha, A. A. Abubaker, I. H. Jebril, S. B. Al-Shaikh, K. Matarneh, M. Almuzini. : ‘A mathematical study on a fractional-order SEIR Mpox model: analysis and vaccination influence’. Algorithms. Vol. 16, p. 418, 2023. 10.3390/a16090418
VI. I. M. Batiha, A. A. Al-Nana, R. B. Albadarneh, A. Ouannas, A. Al-Khasawneh, S. Momani. : ‘Fractional-order coronavirus models with vaccination strategies impacted on Saudi Arabia’s infections’. AIMS Mathematics. Vol. 7, pp. 12842–12858, 2022. 10.3934/math.2022711
VII. I. M. Batiha, A. Obeidat, S. Alshorm, A. Alotaibi, H. Alsubaie, S. Momani, M. Albdareen, F. Zouidi, S. M. Eldin, H. Jahanshahi. : ‘A numerical confirma-tion of a fractional-order COVID-19 model’s efficiency’. Symmetry. Vol. 14, p. 2583, 2022. 10.3390/sym14122583
VIII. I. M. Batiha, J. Oudetallah, A. Ouannas, A. A. Al-Nana, I. H. Jebril. : ‘Tuning the fractional-order PID-Controller for blood glucose level of diabetic patients’. International Journal of Advances in Soft Computing and its Applications. Vol. 13, pp. 1–10, 2021. https://www.i-csrs.org/Volumes/ijasca/2021.2.1.pdf
IX. I. M. Batiha, N. Djenina, A. Ouannas, T. E. Oussaeif. : ‘Fractional-order SEIR Covid-19 model: discretization and stability analysis’. In: D. Zeidan, J. C. Cortes, A. Burqan, A. Qazza, J. Merker, G. Gharib.: ‘Mathematics and Computation’. Springer, Singapore, Vol. 418, 2023.
X. I. M. Batiha, S. A. Njadat, R. M. Batyha, A. Zraiqat, A. Dababneh, S. Momani. : ‘Design fractional-order PID controllers for single-joint robot arm model’. International Journal of Advances in Soft Computing and its Applications. Vol. 14, pp. 96-114, 2022. 10.15849/IJASCA.220720.07
XI. J. Arleback, T. Kawakami. : ‘Advancing and Consolidating Mathematical Modelling’. Springer, Berlin, 2023
XII. J. Cha. : ‘Numerical simulation of chemical propulsion systems: survey and fundamental mathematical modeling approach’. Aerospace. Vol. 10, p. 839, 2023. 10.3390/aerospace10100839
XIII. M. Almuzini, I. M. Batiha, S. Momani. : ‘A study of fractional-order monkeypox mathematical model with its stability analysis’. International Conference on Fractional Differentiation and its Applications, Ajman, UAE, 2023. 10.1109/ICFDA58234.2023.10153214.
XIV. M. H. Kutner, C. J. Nachtsheim, J. Neter, W. Li. : ‘Applied Linear Statistical Models’. McGraw Hill, New York, 2005.
XV. M. T. Shatnawi, A. A. Khennaoui, A. Ouannas, G. Grassi, A. V. Radogna, A. Bataihah, I. M. Batiha. : ‘A multistable discrete memristor and its application to discrete-time FitzHugh–Nagumo model’. Electronics. Vol. 12, p. 2929, 2023. 10.3390/electronics12132929
XVI. N. A. Gershenfeld. : ‘The Nature of Mathematical Modeling’. Cambridge University Press, Cambridge, 1999.
XVII. N. C. Atuegwu, L. R. Arlinghaus, X. Li, E. B. Welch, B. A. Chakravarthy, J. C. Gore, T. E. Yankeelov. : ‘Integration of diffusion-weighted MRI data and a simple mathematical model to predict breast tumor cellularity during neoadjuvant chemotherapy’. Magnetic Resonance in Medicine. Vol. 66, pp. 1689-1696, 2011. 10.1002/mrm.23203
XVIII. N. Djenina, A. Ouannas, I. M. Batiha, G. Grassi, T. E. Oussaeif, S. Momani. : ‘A novel fractional-order discrete SIR model for predicting COVID-19 behavior’. Mathematics. Vol. 10, p. 2224, 2022. 10.3390/math10132224
XIX. O. Sharomi, A. Gumel. : ‘Curtailing smoking dynamics: a mathematical modelling approach’. Applied Mathematics and Computation. Vol. 195, pp. 475-499, 2008. 10.1016/j.amc.2007.05.012
XX. R. McPhee, M. Scott Poole. : ‘Mathematical modeling in communication research: an overview’. Annals of the International Communication Association. Vol. 5, pp. 159-191, 1981.
XXI. S. Belkhir, F. Thomas, B. Roche. : ‘Darwinian approaches for cancer treatment: benefits of mathematical modeling’. Cancers. Vol. 13, p. 4448, 2021. 10.3390/cancers13174448
XXII. S. Coles, J. Bawa, L. Trenner, P. Dorazio. : ‘An Introduction to Statistical Modeling of Extreme Values’. Springer, London, 2001.
XXIII. S. Coles, S. Coles. : ‘An introduction to statistical modeling of extreme values’. Basics of Statistical Modelling. Vol. 13, pp. 18-44, 2001.
XXIV. T. Hamadneh, A. Hioual, O. Alsayyed, Y. A. Al-Khassawneh, A. Al-Husban, A. Ouannas. : ‘The FitzHugh–Nagumo model described by fractional difference equations: stability and numerical simulation’. Axioms. Vol. 12, pp. 806, 2023. 10.3390/axioms12090806
XXV. T. H. Shahraiyni, S. Sodoudi. : ‘Statistical modeling approaches for PM10 prediction in urban areas; a review of 21st-century studies’. Atmosphere. Vol. 7, p. 15, 2016. 10.3390/atmos7020015
XXVI. T. Roos, P. Myllymaki, H. Tirri. : ‘A statistical modeling approach to location estimation’. IEEE Transactions on Mobile Computing. Vol. 1, pp. 59-69, 2002. 10.1109/TMC.2002.1011059
XXVII. V. Cristini, J. Lowengrub. : ‘Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach’. Cambridge University Press, Cambridge, 2010.

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Abstract:

Local workshops generate large quantities of industrial lathe waste steel fibers, which the steel manufacturing industries find difficult to recycle because of their sharp edges. The utilization of lathe waste steel fibers as fiber reinforcement is sustainable in concrete because these fibers have the same properties as steel fibers. Furthermore, using combinations of ductile and elastic fibers improves strain capacity and resistance to pre- and post-cracking. This research employs hybrid fiber reinforcement technology, utilizing industrial lathe waste steel fibers and glass fibers in varying proportions, to bridge the micro and macro cracks in concrete specimens. This research was done to examine the physical (workability) and mechanical properties (compressive and flexural strength) of hybrid fiber-reinforced concrete. In this research different mixtures of hybrid fiber-reinforced concrete were cast and designated as M0, M1, M2, M3, M4, M5, and M6. The mixtures included lathe waste steel fibers at 0%, 0.50%, 1%, 1.5%, 2%, 2.5%, and 3%, and glass fibers at 0%, 0.15%, 0.25%, 0.45%, 0.60%, 0.75%, and 0.90%, respectively. The ASTM-standardised protocols were followed for all laboratory testing. The physical property results showed a decrease in the workability of concrete mixes as the percentage of lathe waste steel and glass fiber increased. This suggests that a higher percentage of lathe waste steel and glass fibers leads to a lower slump value. Consequently, the mechanical property results showed a gradual enhancement in the compressive and flexural strengths of hybrid fiber-reinforced concrete up to 2.5% lathe waste steel fibers and 0.75% (M5). Further incorporation causes a reduction in strength. The physical examination of fractured samples of hybrid fiber-reinforced concrete confirms that the lathe waste steel fibers yield a maximum strain before breaking down in the concrete matrix. Furthermore, lathe waste steel fibers broke rather than being pulled out, indicating a good bond with the concrete. It is recommended that up to 2.5% lathe waste steel fibers and 0.75% of glass fibers by the total weight of the concrete can be used as hybrid fiber reinforcement for optimum strength achievement.

Keywords:

Lathe waste Steel Fibers,Glass Fibers,Hybrid Fiber Reinforced Concrete,Workability,Compressive Strength,Flexural Strength,Mechanical and Physical Properties,

Refference:

I. Ahmad, Fawad, Mohammed Saleh Nusari, and Mohammad Nizamuddin Inamdar. “A leap towards environmental and economic friendly concrete having locally available lathe waste steel fibers as fiber reinforcement.” AIP Conference Proceedings. Vol. 2854. No. 1. AIP Publishing, 2023. 10.1063/5.0162507

II. Ahmad, Jawad, and Zhiguang Zhou. “Mechanical properties of natural as well as synthetic fiber reinforced concrete: a review.” Construction and Building Materials 333 (2022): 127353. 10.1016/j.conbuildmat.2022.127353

III. Ahmad, Jawad, et al. “Glass fibers reinforced concrete: Overview on mechanical, durability and microstructure analysis.” Materials 15.15 (2022): 5111. 10.3390/ma15155111

IV. Ali, Mujahid, et al. “Experimental and analytical investigation on the confinement behavior of low strength concrete under axial compression.” Structures. Vol. 36. Elsevier, 2022. 10.1016/j.istruc.2021.12.038
V. Amer, Omar Alsanusi, Prasad Rangaraju, and Hassan Rashidian-Dezfouli. “Effectiveness of binary and ternary blended cements of class C fly ash and ground glass fibers in improving the durability of concrete.” Journal of Sustainable Cement-Based Materials 11.2 (2022): 127-136. 10.1080/21650373.2021.1899085

VI. Benemaran, Reza Sarkhani, Mahzad Esmaeili-Falak, and Morteza Sadighi Kordlar. “Improvement of recycled aggregate concrete using glass fiber and silica fume.” Multiscale and Multidisciplinary Modeling, Experiments and Design 7.3 (2024): 1895-1914. 10.1007/s41939-023-00313-2

VII. Bijo, M. D., and Sujatha Unnikrishnan. “Mechanical strength and impact resistance of hybrid fiber reinforced concrete with coconut and polypropylene fibers.” Materials Today: Proceedings 65 (2022): 1873-1880. 10.1016/j.matpr.2022.05.048

VIII. Celik, Ali İhsan, et al. “Performance assessment of fiber-reinforced concrete produced with waste lathe fibers.” Sustainability 14.19 (2022): 11817. 10.3390/su141911817

IX. Chellapandian, M., Arunachelam, N., Maheswaran, J. and Kumar, N.P., 2024. Shear behavior of low-cost and sustainable bio-fiber based engineered cementitious composite beams–experimental and theoretical studies. Journal of Building Engineering, 84, p.108497. 10.1016/j.jobe.2024.108497

X. Chen, Boyu, et al. “Evolution law of crack propagation and crack mode in coral aggregate concrete under compression: Experimental study and 3D mesoscopic analysis.” Theoretical and Applied Fracture Mechanics 122 (2022): 103663. 10.1016/j.tafmec.2022.103663

XI. Courland, Robert. Concrete planet: the strange and fascinating story of the world’s most common man-made material. Rowman & Littlefield, 2022. 10.1007/s10745-013-9576-x
XII. Dharek, Manish S., et al. “Biocomposites and Their Applications in Civil Engineering—An Overview.” Smart Technologies for Energy, Environment and Sustainable Development, Vol 1: Select Proceedings of ICSTEESD 2020 (2022): 151-165. 10.1007/978-981-16-6875-3_13

XIII. Gencel, Osman, et al. “A detailed review on foam concrete composites: Ingredients, properties, and microstructure.” Applied Sciences 12.11 (2022): 5752. 10.3390/app12115752

XIV. Golewski, Grzegorz Ludwik. “The phenomenon of cracking in cement concretes and reinforced concrete structures: the mechanism of cracks formation, causes of their initiation, types and places of occurrence, and methods of detection—a review.” Buildings 13.3 (2023): 765. 10.3390/buildings13030765

XV. Heidari, Ali, and Farid Naderi Shourabi. “Mechanical properties of ultra-high performance concrete based on reactive powder concrete: Effect of sand-to-cement ratio, adding glass fiber and calcium carbonate.” Construction and Building Materials 368 (2023): 130108. 10.1016/j.conbuildmat.2022.130108

XVI. Huang, Yitao, et al. “Strengthening of concrete structures with ultra high performance fiber reinforced concrete (UHPFRC): A critical review.” Construction and Building Materials 336 (2022): 127398. 10.1016/j.conbuildmat.2022.127398

XVII. Khoso, Salim, et al. “Experimental study of the effect of lathe steel fiber on the mechanical properties of concrete.” Webology (ISSN: 1735-188X) 19.2 (2022). https://www.webology.org/abstract.php?id=1908

XVIII. Lee, Ming-Gin, et al. “Mechanical properties of high-strength pervious concrete with steel fiber or glass fiber.” Buildings 12.5 (2022): 620. 10.3390/buildings12050620

XIX. Li, Zongjin, et al. Advanced concrete technology. John Wiley & Sons, 2022. 10.1002/9781119806219

XX. Lilargem Rocha, Diego, et al. “A review of the use of natural fibers in cement composites: concepts, applications and Brazilian history.” Polymers 14.10 (2022): 2043. 10.3390/polym14102043

XXI. Los Santos-Ortega, Jorge, et al. “Mechanical and Environmental Assessment of Lathe Waste as an Addiction to Concrete Compared to the Use of Commercial Fibers.” Materials 16.17 (2023): 5740. 10.3390/ma16175740

XXII. Maiti, Saptarshi, et al. “Sustainable fiber‐reinforced composites: a Review.” Advanced Sustainable Systems 6.11 (2022): 2200258. 10.1002/adsu.202200258

XXIII. Mujalli, Mohammed A., et al. “Evaluation of the tensile characteristics and bond behaviour of steel fiber-reinforced concrete: An overview.” Fibers 10.12 (2022): 104. 10.3390/fib10120104

XXIV. Naveen, M., K. Hemalatha, and V. Srinivasa Reddy. “Evaluation of Ductility of Hybrid Reinforced Concrete Beams Made with Glass Fiber-Reinforced Polymer Rebar.” International Conference on Recent Advances in Civil Engineering. Singapore: Springer Nature Singapore, 2022. 10.1007/978-981-99-2676-3_51

XXV. Paktiawal, Ajmal, and Mehtab Alam. “Experimental evaluation of sorptivity for high strength concrete reinforced with zirconia rich glass fiber and basalt fiber.” Materials Today: Proceedings 49 (2022): 1132-1140. 10.1016/j.matpr.2021.06.008

XXVI. Palanisamy, Eswaramoorthi, and Murugesan Ramasamy. “Dependency of sisal and banana fiber on mechanical and durability properties of polypropylene hybrid fiber reinforced concrete.” Journal of Natural Fibers 19.8 (2022): 3147-3157. 10.1080/15440478.2020.1840477

XXVII. Rahman, Saadman Sakib, Sumi Siddiqua, and Chinchu Cherian. “Sustainable applications of textile waste fiber in the construction and geotechnical industries: A retrospect.” Cleaner Engineering and Technology 6 (2022): 100420. 10.1016/j.clet.2022.100420.

XXVIII. Shahid, M. A., et al. “Mechanical Experiments on Concrete with Hybrid Fiber Reinforcement for Structural Rehabilitation. Materials 2022, 15, 2828.” (2022). 10.3390/ ma15082828

XXIX. Shcherban’, Evgenii M., et al. “Analytical Review of the Current State of Technology, Structure Formation, and Properties of Variatropic Centrifugally Compacted Concrete.” Materials 17.8 (2024): 1889. 10.3390/ma17081889
XXX. Tawfik, Maged, et al. “Mechanical properties of hybrid steel-polypropylene fiber reinforced high strength concrete exposed to various temperatures.” Fibers 10.6 (2022): 53. 10.3390/fib10060053

XXXI. Vairagade, Vikrant S., and Shrikrishna A. Dhale. “Hybrid fiber reinforced concrete–a state of the art review.” Hybrid Advances 3 (2023): 100035. 10.1016/j.hybadv.2023.100035

XXXII. Van der Merwe, Johann Eduard. “Evaluation of concrete tensile strength as a function of temperature.” Construction and Building Materials 329 (2022): 127179. 10.1016/j.conbuildmat.2022.127179

XXXIII. Xiao, Jianzhuang, et al. “Pore structure characteristics, modulation and its effect on concrete properties: A review.” Construction and Building Materials 397 (2023): 132430. 10.1016/j.conbuildmat.2023.132430

XXXIV. Zhang, Baifa, et al. “Compressive behaviours, splitting properties, and workability of lightweight cement concrete: the role of fibers.” Construction and Building Materials 320 (2022): 126237. 10.1016/j.conbuildmat.2021.126237

XXXV. Zhang, Wei, et al. “Reliability-based analysis of the flexural strength of concrete beams reinforced with hybrid BFRP and steel rebars.” Archives of Civil and Mechanical Engineering 22.4 (2022): 171. 10.1007/s43452-022-00493-7

XXXVI. Zhao, Chenggong, et al. “Research on different types of fiber reinforced concrete in recent years: An overview.” Construction and Building Materials 365 (2023): 130075. DOI:10.1016/j.conbuildmat.2022.130075

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Abstract:

The research paper probes into coconut fibre used as lightweight aggregate in concrete for thermal conditioning, specifically on durability. The durability properties of coconut fibre and coconut fibre lightweight aggregate concrete were examined on the thermal conditioning. The use of coconut fibre aggregate in construction was tested and verified. It ascertained the moisture content and water absorption capacity found to be 4.20% and 24% respectively. These values can be compared to the conventional aggregate used in normal times. The density of coconut fibre was found to be in the range of 550 -650 kg/m³. They are within the specified limits of lightweight aggregate standards. The study conducted a related hydration test on coconut fibre fines with cement. The coconut fibre-cement ratio has been optimized to satisfy the criteria of structural lightweight concrete for insulation and thermal conditioning to ensure durability. The experiments for long-term investigation continued for 365 days on the compressive strength of coconut fibre aggregate concrete for three different curing conditions.

Keywords:

Durability,Volume of Permeable Voids,Resistance,Rapid Chloride Penetrability,Residual Strength,

Refference:

I. Alabadan BA, Njoku C, Yusuf M O,: ‘The potentials of Groundnut shell as has concrete admixtures”, Agricultural Engineering International: the CIGR Ejournal, Vol.VIII , 2006, P-48-53
II. Bentur A, Igarashi S, and Kovler K,: “Prevention of autogenous shrinkage in high-strength concrete by internal curing using wet LWA”, Cement and Concrete Research,31 , 2001, P- 13-18
III. BS 8110, Structural use of concrete Part 1, Code of practice for design and construction, British Standard Institution,London.
IV. Coatanlem P, Jauberthie R, and Rendell F,: “Lightweight wood chipping concrete durability”, Construction and Building Materials, 20, 2006. P- 778-781, 10.1016/j.conbuildmat.2005.01.057
V. Geiver RL, Souza MR, Moslerni AA, and Sirnatupang MH,: “Carbon dioxide application for rapid production of cement particleboard”, Proceedings, Inorganic-Bonded Wood and Fiber Composite Materials, Editor Moslemi AA, Forest Products Society, Madison, Wis., Vol. 3, 1992, P- 179-184, 10.1007/BF00771364
VI. Hall C, and Yau MHR,: “Water movement in porous materials—IX. The water, sorptivity of concretes”, Building and Environment, 22, 1987, P- 77-82, 10.1016/0360-1323(87)90044-8
VII. Haque MN, Al-Khaiat H, and Kayali O,: “Strength and durability of LWC” Cement and Concrete Composites, Vol. 11, Issue. , 2004, P-26-31, https://doi.org/10.1061/(ASCE)0899-1561(1999)11:3(2
VIII. IS: 2386 (Part I)-1963, Indian Standard Methods of Test for Aggregate for Concrete, Part I Particle size and shape.
IX. Maiti S, Dey S, Purakayastha S, and Ghosh B,: “Physical and thermochemical characterization of rice husk char as a potential biomass energy source”, Bioresource Technology, 97, 2007, P-2065-2070, doi.org/10.1016/j.biortech.2005.10.005
X. Mannan MA and Ganapathy C,: “Concrete from an agricultural waste-oil palm shell (OPS)”, Building and Environment,39, 2004, P-441-448, https://doi.org/10.1016/j.buildenv.2003.10.007
XI. Mathur VK.,: “Composite materials from local resources”, Construction and Building Materials, 20,2008, P-470-477 , https://doi.org/10.1016/j.conbuildmat.2005.01.031
XII. Mindess S, Young JF, and Darwin D,: “Concrete”, 2nd edition, Prentice-Hall , USA.
XIII. Neville AM, and Brooks JJ,: “Concrete Technology”, Pearson Education Asia Pvt Ltd, Singapore.
XIV. Olanipekun EA, Olusola KO, and Ata O,: “A comparative study of concrete properties using coconut shell and palm kernel shell as coarse aggregate”, Building and Environment, 41, 2017, P-297-301, https://doi.org/10.1016/j.buildenv.2005.01.029
XV. Paramasivam P, and Loke YO,: “Study of sawdust concrete”, International Journal of LWC, Volume 2, Issue 1, March 1980, Pages 57-61, https://doi.org/10.1016/0262-5075(80)90008-1
XVI. Rossignolo JA, and Agnesini MVC,: “Durability of polymer- modified LWA concrete”, Cement and Concrete Composites, Volume 249, 20 July 2020, 118764, https://doi.org/10.1016/j.conbuildmat.2020.118764
XVII. Teo DCL, Mannan MA, Kurian VJ, and Ganapathy C,:“LWC made from oil palm shell (OPS): Structural bond and durability properties”, Building and Environment, Volume 42, Issue 7, July 2007, Pages 2614-2621, https://doi.org/10.1016/j.buildenv.2006.06.013
XVIII. Warner B, Quirke D, and Longmore C,: “A review of the future prospects for the world coconut industry and past research in coconut production and product”, Project No. PLIA/2007/019, Final Report, September Australian Centre for International Agricultural Research, 2007, P-206-230, 2007
XIX. Weigler H, and Karl S.,: “Structural LWA concrete with reduced density LWA foamed concrete”, International Journal of Lightweight Concrete, 2, Vol. 2, 1980, P-101-104.

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