Archive

Abstract:

Power transformers play an important role in the efficient delivery of power to consumers. Their failure leads to significantly higher losses and maintenance costs. Therefore, it is essential to have an optimal maintenance strategy in place for the transformers. However, to design an effective maintenance strategy, real failure data of the transformers need to be collected and studied to identify the failure patterns. To facilitate the analysis presented in this paper, five years of real failure data of a transformer system is collected from a power distribution company. The best-fit distribution for the failure times data of the system is found using AIC, BIC, and LKV values. Useful reliability parameters of the system are evaluated using the Maximum Likelihood Estimation and Rank Regression Method. Life data analysis is performed to estimate the reliable life, mean time to failure, and remaining lifetime of the entire system and its subsystems.

Keywords:

Best-fit distribution,Maximum likelihood estimation,Rank regression,reliability,Transformer,

Refference:

I. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. 10.1109/TAC.1974.1100705
II. Chen, T., Tang, W., Lu, Y., and Tu, X. (2014). Rank regression: an alternative regression approach for data with outliers. Shanghai Archives of Psychiatry, 26(5), 310-315. 10.11919/j.issn.1002-0829.214148
III. Cheng, J., Cho, S., Tan, Y.P., and Hu, G. (September 11-14, 2023). Deep learning-enabled statistical model estimation for power transformers with censoring and truncation problems. Asia Pacific Conference of the PHM society, Tokyo, Japan. 10.36001/phmap.2023.v4i1.3762
IV. El-Bassiouny, A., El-Shimy, M., and Hamouda, R. (2019). Probabilistic analysis of the reliability performance for power transformers in Egypt. Journal of Renewable Energy and Sustainable Development, 5(2), 46-56.
V. Jagtap, H.P., Bewoor, A.K., Kumar, R., Ahmadi, M.H., El Haj Assad, M., and Sharifpur, M. (2021). RAM analysis and availability optimization of thermal power plant water circulation system using PSO. Energy Reports, 7, 1133–1153. 10.1016/j.egyr.2020.12.025
VI. Kumar, A., Garg, R., and Barak, M.S. (2022). Performance analysis of computer systems with Weibull distribution subject to software upgrade and load recovery. Life Cycle Reliability and Safety Engineering, 12, 51–63. 10.1007/s41872-022-00211-5
VII. Maihulla, A.S., Yusuf, I., and Bala S.I. (2023). Weibull comparison based on reliability, availability, maintainability, and dependability (RAMD) analysis. Reliability: Theory & Applications, 1(72), 120-132.
VIII. Mirzai, M., Gholami, A., and Aminifar, F. (2006). Failures analysis and reliability calculation for power transformers, Journal of Electrical Systems, 2(1), 1–12.
IX. Myung, I.J. (2003). Tutorial on maximum likelihood estimation. Journal of Mathematical Psychology, 47(1), 90–100. 10.1016/S0022-2496(02)00028-7
X. Nabila Al Balushi. (2021). A review of the reliability analysis of the complex industrial systems, Advances in Dynamical Systems and Applications, 16(1), 257-297.
XI. Nabila Al Balushi, Rizwan, S.M., Taj, S.Z., and Waleed Al Khairi. (2023). Reliability analysis of power transformers of a power distribution company. International Journal of System Assurance Engineering and Management. 10.1007/s13198-023-02042-8
XII. Oliveira Neto, A.B., Costa, E.G., Moraes, V.S., and Ferreira, T.V. (August 27-September 01, 2017). Methodology for reliability analysis of power transformers based on failure data. The 20th International Symposium on High Voltage Engineering, Buenos Aires, Argentina.
XIII. Padmavathi, N., Rizwan, S.M., Pal, A., and Taneja, G. (2012). Reliability analysis of an evaporator of a desalination plant with online repair and emergency shutdowns. Aryabhatta Journal of Mathematics & Informatics, 4(1), 1-12.
XIV. Schwarz, G.E. (1978). Estimating the dimension of a model. Annals of Statistics, 6 (2), 461–464. 10.1214/aos/1176344136
XV. Seyedi, H., Fotuhi, M., and Sanaye-Pasand, M. (2006). An extended Markov model to determine the reliability of protective system, 2006 IEEE Power India Conference. 10.1109/POWERI.2006.1632549
XVI. Singla, S., Mangla, D., Panwar, P., and Taj, S.Z. (2024). Reliability optimization of a degraded system under preventive maintenance using genetic algorithm. Journal of Mechanics of Continua and Mathematical Sciences, 19(1), 1-14.
XVII. Taj, S.Z., and Rizwan, S.M. (2021). Estimation of reliability indices of a complex industrial system using best–fit distribution for repair/restoration times. International Journal of Advanced Research in Engineering and Technology, 12(2), 132-146.
XVIII. Taj, S.Z., Rizwan, S.M., Alkali, B.M., Harrison, D.K., and Taneja, G. (2020). Three reliability models of a building cable manufacturing plant: a comparative analysis. International Journal of Systems Assurance Engineering and Management. 10.1007/s13198-020-01012-8
XIX. Tang, S., Hale, C., and Thaker, H. (2014). Reliability modelling of power transformers with maintenance outage. Systems Science & Control Engineering, 2(1), 316–324. 10.1080/21642583.2014.901930
XX. Vahidi, F., and Tenbohlen, S. (November 2014). Statistical failure analysis of European substation transformers. Conference: 6. ETG-Fachtagung Diagnostik elektrischer Betriebsmittel.
XXI. Wei, X., Wang, Z., and Guo, J. (2022). Reliability assessment of transformer insulating oil using accelerated life testing. Scientific Reports, 12. 10.1038/s41598-022-26247-2
XXII. Yaqoob Al Rahbi, Rizwan, S.M., Alkali, B.M., Cowell, A. and Taneja, G. (2019). Reliability analysis of a rodding anode plant in aluminium industry with multiple units’ failure and single repairman. International Journal of System Assurance Engineering and Management, 10, 97-109. 10.1007/s13198-019-00771-3

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Abstract:

This paper presents a novel approach for solving 2D mathematical models arising in applied sciences, specifically focusing on 2-dimensional time-fractional order Klein-Gordon (TFKGE) and sine-Gordon equations (TFSGE) using the Sumudu transform-homotopy perturbation method (STHPM). The amalgamation of the Sumudu transform with the homotopy perturbation method provides an effective analytical technique for tackling these time-fractional order partial differential equations. The solutions obtained illustrate the precision and efficiency of the method, offering valuable insights for modelling complex physical systems. In this study, we also solve the same numerical problems using the variational iteration method and perform a comparative analysis of the results. This study advances the application of fractional calculus methods to challenging problems in theoretical and applied physics.

Keywords:

Homotopy Perturbation Method,Klein-Gordon Equation,Sine-Gordon Equation,Sumudu Transform,Test Examples,Variational Iteration Method,

Refference:

I. Atangana Abdon and Adem Kılıçman. “The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations.” Abstract and Applied Analysis 2013 (2013): 1-12. 10.1155/2013%2F737481.
II. Belayeh W. G., Mussa Y. O., Gizaw A.K., “Approximate analytic solutions of two-dimensional nonlinear Klein-Gordon equation by using the reduced differential transform method.” Mathematical Problems in Engineering, 2020(1), 2020. 10.1155/2020/5753974.
III. Belgacem Fethi Bin Muhammed, Karaballi, Ahmed Abdullatif “Sumudu transform fundamental properties investigations and applications.” Journal of Applied Mathematics and Stochastic Analysis, 2006(6), (2006) pp. 1-23. 10.1155/JAMSA/2006/91083.
IV. Chang, Chih-Wen, Kuo Chia-Chen “A lie-group approach for solving backward two-dimensional nonlinear Klein-Gordon equation.” Procedia Engineering, 79, (2014), pp. 590-598. 10.1016/j.proeng.2014.06.384.
V. Deresse, Alemayehu Tamirie. “Application of iterative three-dimensional Laplace transform method for 2-dimensional non linear Klein Gordon equation.” Trends in sciences, (2023), 20(3). 10.48048/tis.2023.4410.
VI. Deresse Alemayehu Tamirie, Mussa Yesuf Obsie and Gizaw Ademe Kebede. “Analytical solution of two-dimensional sine-Gordon equation”, Advances in Mathematical Physics, 2021 (2021), issue 1, 2021. 10.1155/2021/6610021.
VII. El-Sayed M.A., Elsaid A., I.L. El-Kalla, D. Hammad, “A homotopy perturbation technique for solving partial differential equations of fractional order in finite domains.” Applied Mathematics and Computation, 218(17), (2012), pp. 8329–8340. 10.1016/j.amc.2012.01.057.
VIII. Gill V., Dubey R.S., “New analytical method for Klein-Gordon equations arising in quantum field theory.” European Journal of Advances in Engineering and Technology, 5( 8), (2018), pp. 649-655.
IX. Gupta P.K., Singh M., “Homotopy perturbation method for fractional Fornberg-Whitham equation.” Computer and Mathematics with Applications, 61(2), , 2011, pp. 250-254. 10.1016/j.camwa.2010.10.045.
X. He, Ji-Huan, “Homotopy perturbation technique”, Computer Methods in Applied Mechanics and Engineering, 178(3-4), (1999), pp. 257–262. 10.1016/S0045-7825(99)00018-3.
XI. He Ji-Huan, “Some applications of nonlinear fractional differential equations and their approximations.” Bulletin of Science, Technology & Society, 15(2), , 1999, pp. 86–90.
XII. He Ji-Huan,“A coupling method of a homotopy technique and a perturbation technique for non-linear problems.” International Journal of Non-Linear Mechanics, 35(1), (2000), pp. 37–43. 10.1016/S0020-7462(98)00085-7.
XIII. He Ji-Huan, “Application of homotopy perturbation method to nonlinear wave equations.” Chaos, Solitons and Fractals, 26(3), , 2005, pp. 695–700. 10.1016/j.chaos.2005.03.006.
XIV. Hosseininia M., Heydari M.H., Ghaini F.M.M., Avazzadeh Z., “A wavelet method to solve nonlinear variable order time fractional 2D Klein-Gordon equation.” Computers & Mathematics with Applications, 78(15), (2019), pp. 3713-3730. 10.1016/j.camwa.2019.06.008.
XV. Ibrahim W., Tamiru M., “Solutions of three dimensional non-linear Klein-Gordon equations by using quadruple Laplace transform.” International Journal of Differential Equations, 2022(1), 2022. 10.1155/2022/2544576.
XVI. Kang X., Feng W., Cheng K., Guo, C., “An efficient finite difference scheme for the 2D sine-Gordon equation.” Arxiv, 10(6), (2017), pp. 2998-3012.
XVII. Karbalaie Abdolamir, Montazeri Mohammad Mehdi, and Muhammed Hamed Hamid “Exact Solution of Time-Fractional Partial Differential Equations Using Sumudu Transform.” WSEAS Transactions on Mathematics archive 13 (2014): 142-151.
XVIII. Khader M., “Application of homotopy perturbation method for solving nonlinear fractional heat-like equations using sumudu transform.” Scientia Iranica, 24(2), , (2017), pp. 648-655.
XIX. Li Demei, Lai Huilin, Shi Baochang “Mesoscopic simulation of the (2+1)-dimensional wave equation with non-linear damping and source terms using the lattice Boltzmann BGK model.” MDPI, 21(4), 2019.
XX. Li, X, “Mesh less numerical analysis of a class of nonlinear generalized Klein-Gordon equation with a well shaped moving least square approximation”, Applied Mathematical Modelling, 48, , (2017), pp. 153-182. 10.1016/j.apm.2017.03.063.
XXI. Liu W., Sun J., Wu B. , “Space–time spectral method for the two-dimensional generalized sine-Gordon equation.” Journal of Mathematical Analysis and Applications, 427(2), (2015), pp. 787-804, 10.1016/j.jmaa.2015.02.057.
XXII. Maitama S., Zhao W., “Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences.” Journal of Applied Mathematics and Computational Mechanics, 20(1), (2021), pp. 71-82. 10.17512/jamcm.2021.1.07.
XXIII. Singh Brajesh Kumar, Kumar Parmod, “Fractional variational iteration method for solving fractional partial differential equations with proportional Delay.” International Journal of Differential Equations, 2017(1), (2017), 10.1155/2017/5206380.
XXIV. Singh Inderdeep, Kumari Umesh “Elzaki Transform Homotopy Perturbation Method for Solving Two-dimensional Time-fractional Rosenau-Hyman Equation.” Matematika, Malaysian Journal of Industrial and Applied Mathematics, 39(2), (2023), pp. 159–171. https://matematika.utm.my/index.php/matematika/article/view/1463.
XXV. Singh P., Sharma D., “On the problem of convergence of series solution of non-linear fractional partial differential equation.” In: AIP Conference Proceeding, 1860: 020027, 2017. 10.1063/1.4990326.
XXVI. Watugala G.K, “Sumudu transform- a new integral transform to solve differential equations and control engineering problems.” International Journal of Mathematical Education in Science and Technology, 24(1), (1993), pp. 35-43. 10.1080/0020739930240105.
XXVII. Yıldırım Ahmet, “Analytical approach to fractional partial differential equations in fluid mechanics by means of the homotopy perturbation method.” International Journal of Numerical Methods for Heat & Fluid Flow, 20(2), (2010), pp. 186-200. 10.1108/09615531011016957.
XXVIII. Yousif Eltayeb A., Hamed Sara H. “Solution of nonlinear fractional differential equations using the homotopy perturbation sumudu transform method”, Applied Mathematical Sciences, 8(44), 2014, pp. 2195-2210.

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Abstract:

The present work in bio-inspired robotics explores the design and implementation of a novel-legged robotic system featuring a modified Peaucellier-Lipkin mechanism with three control points for a single degree of freedom. The emphasis is placed on the robot’s adaptability to various walking gaits in different environments. The paper delves into the robot’s design, construction, and control system, which includes the application of PID control for enhanced stability and efficiency in mimicking biological locomotion. The primary aim is to demonstrate a robot capable of adjusting its form and function for diverse operational challenges, enhancing robotic mobility. The design also addresses repeatability issues, ensuring consistent performance across various tasks and conditions, contributing to the robot’s reliability and practical applicability in real-world scenarios.

Keywords:

Biological locomotion,Peaucellier-Lipkin mechanism,PID controller repeatability,Robotic mobility,

Refference:

I. Alexeev, L., Dobra, A., & Lovasz, E.: “Walking Robot with Modified Jansen Linkage.” In Machine and Industrial Design in Mechanical Engineering, Mechanisms and Machine Science 109, Springer Nature Switzerland, 2022, Ch. 58, p. 577. 10.1007/978-3-030-88465-9_58

II. Bhavsar, Keval, Dharmik Gohel, Pranav Darji, Jitendra Modi, and Umang Parmar.: ‘Kinematic Analysis of Theo Jansen Mechanism-Based Eight-Leg Robot’. In Advances in Fluid Mechanics and Solid Mechanics: Proceedings of the 63rd Congress of ISTAM 2018, pp. 75-82. Singapore: Springer Singapore, 2020. 10.1007/978-981-32-9971-9_30

III. Chen, X., Wang, L. Q., Ye, X. F., Wang, G., & Wang, H. L.: “Prototype Development and Gait Planning of Biologically Inspired Multi-Legged Crablike Robot.” Mechatronics, 2013, 23(4), pp. 429-444. 10.1016/j.mechatronics.2013.03.006

IV. Chwila, S., Zawiski, R., and Babiarz, A.: ‘Developing and Implementation of the Walking Robot Control System’. In Man-Machine Interactions 3, Springer International Publishing, pp. 97-105, 2014. 10.1007/978-3-319-02309-0_10

V. Desai, Shivamanappa G., Anandkumar R. Annigeri, and A. TimmanaGouda.: ‘Analysis of a New Single Degree-of-Freedom Eight Link Leg Mechanism for Walking Machine’. Mechanism and Machine Theory, Vol. 140, pp. 747-764, 2019. 10.1016/j.mechmachtheory.2019.06.002

VI. Gao, H., Kareem, A., Jawarneh, M., Ofori, I., Raffik, R., and Kishore, K.H.: ‘[Retracted] Metaheuristics Based Modeling and Simulation Analysis of New Integrated Mechanized Operation Solution and Position Servo System’. Mathematical Problems in Engineering, 2022(1), p. 1466775. 10.1155/2022/1466775

VII. Ghassaei, Amanda, Professors Phil Choi, and Dwight Whitaker.: “The Design and Optimization of a Crank-Based Leg Mechanism.” Pomona, USA (2011).

VIII. Giesbrecht, Daniel. Design and Optimization of a One-Degree-of-Freedom Eight-Bar Leg Mechanism for a Walking Machine. MS thesis, 2010. http://hdl.handle.net/1993/3922

IX. Haidar, A. M., C. Benachaiba & M. Zahir.: “Software Interfacing of Servo Motor with Microcontroller.” Journal of Electrical Systems, vol. 9, (1) pp. 84-99, 2013. https://ro.uow.edu.au/eispapers/468/

X. Janson, T. The Great Pretender. Uitgeverij, 2007.

XI. Jaichandar, K., Mohan Rajesh, E., Martínez-García, E., and Le Tan-Phuc.: ‘Trajectory Generation and Stability Analysis for Reconfigurable Klann Mechanism Based Walking Robot’. Robotics, Vol. 5, No. 3, pp. 1-12, 2016. https://doi.org/10.3390/robotics5030013

XII. Jaichandar, K., Rajesh Elara M., Martínez-García E., & Tan-Phuc L.: “Synthesizing Reconfigurable Foot Traces Using a Klann Mechanism.” Robotica, 35(1), 2015. Cambridge University Press. https://doi.org/10.1017/S0263574715000089

XIII. Kajita, Shuuji, and Bernard Espiau.: ‘Legged Robot’. Springer Handbook of Robotics. Berlin/Heidelberg, Germany: Springer, pp. 361-389, 2008.

XIV. Khaled, Nassim.: “Acceleration Based Approach for Position Control.” IOP Conference Series: Materials Science and Engineering, Vol. 717, No. 1, IOP Publishing, 2020. 10.1088/1757-899X/717/1/012020

XV. Kim, D.H.: ‘Design and Tuning Approach of 3-DOF Emotion Intelligent PID (3-DOF-PID) Controller’. In 2012 Sixth UKSim/AMSS European Symposium on Computer Modeling and Simulation, IEEE, pp. 74-77, November 2012. https://doi.org/10.1109/EMS.2012.93

XVI. Klann, J.C.: Patent No. 6.260.862, USA, 2001. https://patents.google.com/patent/US6260862B1/en

XVII. Krishnamurthy, Balachandar, Sabari Senbagarajan, and Lokesh Mahendran.: ‘Design and Fabrication of Spider Bot’. AIP Conference Proceedings, Vol. 2946, No. 1, AIP Publishing, pp. 1-5, 2023. https://doi.org/10.1063/5.0178024

XVIII. McCarthy, J. M., and Kevin Chen.: Design of Mechanical Walking Robots. MDA, Press, 2021. https://www.google.co.in/books/edition/Design_of_Mechanical_Walking_Robots/-gfozgEACAAJ?hl=te

XIX. Papoutsidakis, M., Chatzopoulos, A., Symeonaki, E., and Tseles, D.: ‘Methodology of PID Control – A Case Study for Servomotors’. International Journal of Computer Applications, Vol. 179, No. 30, pp. 30-33, 2018. 10.5120/ijca2018916689

XX. Sheba, J.K., Martínez-García, E., Elara, M.R., and Tan-Phuc, L.: ‘Design and Evaluation of Reconfigurable Klann Mechanism Based Four-Legged Walking Robot’. In 2015 10th International Conference on Information, Communications and Signal Processing (ICICS), IEEE, pp. 1-5, December 2015. 10.1109/ICICS.2015.7459939

XXI. Sun, Jiefeng, and Jianguo Zhao.: ‘An Adaptive Walking Robot with Reconfigurable Mechanisms Using Shape Morphing Joints’. IEEE Robotics and Automation Letters, Vol. 4, No. 2, pp. 724-731, 2019. 10.3390/robotics5030013

XXII. Sutyasadi, P., and Parnichkun, M.: ‘Gait Tracking Control of Quadruped Robot Using Differential Evolution Based Structure Specified Mixed Sensitivity H∞ Robust Control’. Journal of Control Science and Engineering, 2016(1), p. 8760215, 2016. 10.1155/2016/8760215

XXIII. Vanitha, U., Premalatha, M., Nithinkumar, S., and Vijayaganapathy, S.: ‘Mechanical Spider Using Klann Mechanism’. Scholarly Journal of Engineering and Technology, Vol. 3, No. 9, pp. 737-740, December 2015. chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://saspublishers.com/media/articles/SJET39737-740.pdf

XXIV. Visioli, Antonio. Practical PID Control. Springer Science & Business Media, 2006. https://www.google.co.in/books/edition/Practical_PID_Control/ymyAY01bEe0C?hl=te&gbpv=0

XXV. Zielinska, Teresa.: “Development of Walking Machines; Historical Perspective.” International Symposium on History of Machines and Mechanisms: Proceedings HMM2004. Springer Netherlands, 2004. 10.1016/S0957-4158(01)00017-4

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Abstract:

Life tables are used in many fields in demographic and health research They represent an important indicator of death in society. There are two types of life tables; complete life tables are based on the age at death based on single-age categories and are obtained using a comprehensive survey method. The second type is the abbreviated life tables which are based on the age at death of five-year age groups and are obtained by the sample survey method. In this research, the survival function was estimated for the data obtained from the Central Statistical Organization, social and Economic Survey of the Family in Iraq (IHSES II) using parametric methods (the principle of Maximizing Entropy method (POME), and maximum likelihood method (MLE)), as well as the use of A non-parametric approach, the kernel smoothing method (KS), the compared between the estimation methods using (RMSE) and (MAPE). One of the most important conclusions was the emergence of a preference for the (POME) method for the five-age groups, but in the case of the single-age groups, the (KS) method is the best.

Keywords:

life tables,the principle of maximum entropy method,kernel smoothing method.,

Refference:

I. Calot, Gérard, and Jean-Pierre Sardon. Calculation of Eurostat’s Demographic Indicators. 2004.

II. Central Statistical Organization, Ministry of Planning. Iraqi Household Social and Economic Survey (IHSES II, 2012) Tables Report. Central Statistical Organization Press, 2014. www.cost.gov.iq.

III. Chen, Dong-Guk, and Ying-Chung Lio. “A Note on the Maximum Likelihood Estimation for the Generalized Gamma Distribution Parameters under Progressive Type-Ⅱ Censoring.” International Journal of Intelligent Technologies and Applied Statistics, vol. 2(2), 2009, pp. 145-152.

IV. Cropper, William H. Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking. Oxford UP, 2004. “The Road to Entropy: Rudolf Clausius.”

V. Jaynes, E. T. Probability Theory in Science and Engineering. No. 4, Socony Mobil Oil Company Field Research Laboratory, 1959.

VI. Jowitt, P. W. “The Extreme-Value Type-1 Distribution and the Principle of Maximum Entropy.” Journal of Hydrology, vol. 42, no. 1-2, 1979, pp. 23-38. 10.1016/0022-1694(79)90004-0

VII. Lagos Álvarez, B., Ferreira, G., and Valenzuela Hube, M. “A Proposed Reparameterization of Gamma Distribution for the Analysis of Data of Rainfall-Runoff Driven Pollution.” Proyecciones (Antofagasta), vol. 30, no. 3, 2011, pp. 415-439. https://www.scielo.cl/pdf/proy/v30n3/art09.pdf

VIII. Qamruz, Z., and Karl, P. “Survival Analysis Medical Research.” InterStat, 2011, http://interstat.statjournals.net/YEAR/2011/abstracts/1105005.php.

IX. Qiao, H., and C. P. Tsokos. “Nonparametric Approach to Reliability Analysis.” Proceedings of SOUTHEASTCON’94, April 1994, pp. 231-235. IEEE.

X. Rao, B. L. S. P. Nonparametric Functional Estimation. Academic Press, 1983.

XI. Reshi, J. A., Ahmed, A., and Mir, K. A. “Some Important Statistical Properties, Information Measures, and Estimations of Size Biased Generalized Gamma Distribution.” Journal of Reliability and Statistical Studies, 2014, pp. 161-179.

XII. Roshani, S., Yahya, S. I., Mezaal, Y. S., Chaudhary, M. A., Al-Hilali, A. A., Mojirleilani, A., & Roshani, S. (2023). Design of a compact quad-channel microstrip diplexer for L and S band applications. Micromachines, 14(3), 553.
XIII. Roshani, S., Yahya, S. I., Alameri, B. M., Mezaal, Y. S., Liu, L. W., & Roshani, S. (2022). Filtering power divider design using resonant LC branches for 5G low-band applications. Sustainability, 14(19), 12291.

XIV. Singh, V. P., and Fiorentino, M. “A Historical Perspective of Entropy Applications in Water Resources.” Entropy and Energy Dissipation in Water Resources, 1992, pp. 21-61. https://link.springer.com/chapter/10.1007/978-94-011-2430-0_2
XV. Singh, V. P., and Guo, H. “Parameter Estimation for 3-Parameter Generalized Pareto Distribution by the Principle of Maximum Entropy (POME).” Hydrological Sciences Journal, vol. 40, no. 2, 1995, pp. 165-181. 10.1080/02626669509491402

XVI. Sulaiman, Abbas Najm, and Ebtihal Hussein Farhan. “Estimation of the Survival Function for Complete Real Data of Lung Cancer Patients.” Ibn Lahitham Journal of Pure and Applied Sciences, vol. 27, no. 3, 2014, pp. 531-541. https://jih.uobaghdad.edu.iq/index.php/j/article/view/318

XVII. S. A. AbdulAmeer et al., “Cyber Security Readiness in Iraq: Role of the Human Rights Activists,” International Journal of Cyber Criminology, vol. 16, no. 2, pp. 1–14-1–14, 2022.

XVIII. Tarrad , K. M. et al., “Cybercrime Challenges in Iraqi Academia: Creating Digital Awareness for Preventing Cybercrimes,” International Journal of Cyber Criminology, vol. 16, no. 2, pp. 15–31-15–31, 2022.

XIX. Tan, P., and C. Drossos. “Invariance Properties of Maximum Likelihood Estimators.” Mathematics Magazine, vol. 48, no. 1, 1975, pp. 37-41.

XX. United Nations. MORT PAK for Windows, version 4.3, New York, 2013.

XXI. Y. S. Mezaal, & Ali, J. K. (2016). Investigation of dual-mode microstrip bandpass filter based on SIR technique. PLoS one, 11(10), e0164916.
XXII. Yahya, Salah I., et al. “A New Design method for class-E power amplifiers using artificial intelligence modeling for wireless power transfer applications.” Electronics 11.21 (2022): 3608.

XXIII. Y. S. Mezaal, K. Al-Majdi, A. Al-Hilalli, A. A. Al-Azzawi, and A. A. Almukhtar, “New miniature microstrip antenna for UWB wireless communications,” Proceedings of the Estonian Academy of Sciences, vol. 71, no. 2, pp. 194-202, 2022.
XXIV. Y. S. Mezaal , H. A. Hussein, and B. M. Alameri, “Miniaturized microstrip diplexer based on fr4 substrate for wireless communications,” Elektronika Ir Elektrotechnika, vol. 27, no. 5, pp. 34-40, 2021.

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Abstract:

A_G = (N, A, σ, μ) be a anti fuzzy graph. A partition of N(A_G) Π = {D₁, D_{2, ….,} D_k} is a regular anti fuzzy partial domatic partition of A_G if (i) for each D_i, < D_i > is an anti fuzzy regular and (ii) D_i is an anti fuzzy dominating set of G_A. The maximum fuzzy cardinality of a regular anti fuzzy partial domatic partition of A_G is called the regular anti fuzzy partial domatic number [RAPDN]of A_G and it is denoted by  Also these numbers are determined for various anti fuzzy graph. In this work, random r- regular anti fuzzy graph, regular partial domatic number in anti fuzzy graphs, regular partial anti domatic number in anti fuzzy graphs are introduced. Some bounds for anti fuzzy domatic numbers are discussed.

Keywords:

Anti fuzzy graph,Dominating set,Domatic number,Vertex degree,

Refference:

I. Akram, Muhammad. “Anti fuzzy structures on graphs.” Middle East Journal of Scientific Research 11.12 (2012): 1641-1648. 10.5829/idosi.mejsr.2012.11.12.131012

II. Allan, Robert B., and Renu Laskar. “On domination and independent domination numbers of a graph.” Discrete mathematics 23.2 (1978): 73-76. 10.1016/0012-365X(78)90105-X
III. Chang, Gerald J. “The domatic number problem.” Discrete Mathematics 125.1-3 (1994): 115-122. 10.1016/0012-365X(94)90151-1
IV. Cockayne, Ernest J., and Stephen T. Hedetniemi. “Towards a theory of domination in graphs.” Networks 7.3 (1977): 247-261. 10.1002/net.3230070305
V. Dharmalingam, K.M., and Valli, K., “Regular Domatic Partition in Fuzzy Graph.” World Journal of Engineering Research and Technology, 5.5 (2019), 100-107.b http://wjert.org/admin/assets/article_issue/34082019/1567157413.pdf
VI. Gani, A. Nagoor, and K. Prasanna Devi. “2-domination in fuzzy graphs.” International Journal of Fuzzy Mathematical Archive 9.1 (2015): 119-124. http://www.researchmathsci.org/IJFMAart/IJFMA-V9n1-14.pdf
VII. Haynes, Teresa W., Stephen Hedetniemi, and Peter Slater. Fundamentals of domination in graphs. CRC press, 2013. 10.1201/9781482246582
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