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Abstract:

In approximation theory, linear positive operators of general additive form are generally studied on the positive half-axis. In this study, the Szász–Kantorovich–Chlodovsky type operator is defined on intervals extending over the entire real axis. Certain parts of this work, which were previously presented at a conference, have been used in the present research only as needed. The approximation properties are examined by means of a new Lipschitz-type function [XX]. The operator is also studied using Peetre’s K-functional. Approximation and the rate of approximation in weighted spaces are investigated. Graphs of two different functions are plotted for two different values of b_s, and the corresponding numerical tables are prepared.

Keywords:

Approximation,Szász -Mirakyan-Kantorovich Operators,Chlodovsky,weighted approximation,Symmetric Intervals,Voronovskaya type theorem,Lipschitz maximal function.,

References:

Akhieser, N.I. Akhieser, Lectures on the theory of approximation. OGIZ, Moscow-Leningrad, 1947 (in Russian), Theory of approximation (in English), Translated by C.J. Hymann, Frederick Ungar Publishing Co., New York, 1956.
Aslan , R., Izgi, A. ğırlıklı Uzaylarda 𝒒 −Szász-Kantorovich-Chlodowsky OperatörlerininYaklaşımlar, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi 36(1) , (2020), 138-150.
Aslan, R. (2014). Ağırlıklı Uzaylarda Kantorovich-Chlodowsky-Szász Tipi Operatörlerin Yaklaşımı veYaklaşım Hızı. Harran Üniversitesi, Fen bilimleri Enstitüsü, Yüksek Lisans Tezi, 29s, Şanlıurfa
Altomare, F. and Campiti, M. Korovkin-type Approximation Theory and its Applications. Berlin: New York: de Gruyter, (1994).

Bawa, P., BhardwaN. j & Bhatia, S. K. (2023). Different Variants of Bernstein Kantorovich Operators and Their Applications in Sciences and Engineering Field. Chaos Theory and Applications, 5(4), 293-299, 10.51537/chaos.1320442
Bernstein, S.N. Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités, Commun. Kharkov Math. Soc. 13 (1912/1913) 1–2.
Bajpeyi, S., Baxhaku, B. & Agrawal, P. N. Exponential Sampling Type Kantorovich Max-Product Neural Network Operators. Numerical Functional Analysis and Optimization, 45(13–14), (2024) 631–650..
Bohman, H. On approximation of continuous and of analytic functions, Ark. Mat. 2 (1) (1952) 43–56.
Chlodowsky, I. Sur le développement des fonctions définies dans un intervalle infini en séries de polynomes de M. S. Bernstein. Compositio Mathematica, 4, (1937).380–393.
Çilo, A.Approximation properties and speed of approximation of Bernstein polynomials in the interval [-1,1], Harran University, Institute of Science,(2012), (In Turkish)
Çilo A.,A.Ural , Ä°zgi, A Properties of Approximation and Rate of Approximation Bernstein Polynomials in the range [ -1,1] , Conference: XXV. Ulusal Matematik Sempozyumu – NiÄŸde Ãœniversitesi, (5-8 Eylül(September),2012).
Ditzian, Z.; Totik, V. Moduli of Smoothness; Springer Series in Computational Mathematics; Springer: New York, NY, USA, 1987; Volume 9.
Gadzhiev, A.D. The convergence problem for a sequence of linear operators on unbounded sets and theorem analogous to that of P.P. Korovkin. Soviet Math. Dokl. 15, no. 5 (1974), 1433-14.
Gadzhiev, A.D. Theorems of the type P.P. Korovkin theorems.Math. Zametki 20, no. 5 (1976) , 781-786. English translation in Math. Notes 20, no. 5-6 (1976), 996-998.
Ispir, N. On modi ed Baskakov operators on weighted spaces. Turk. J.Math. 26, no. 3 (2001), 355-365.
Kantorovich, L.V. Sur certains développements suivant les polynômes de la forme de s. Bernstein, I, II, CR Acad. URSS 563(568): (1930)595–600.
Karaisa, A. ,Aral, A. 2016. Some Approximation Properties of Kantorovich Variant of Chlodowsky Operators Based on 𝑞-integer, 65,97-119 Ankara
Korovkin, P.P. On convergence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR 90 (1953) 961–964.
Mursaleen, M., Alotaibi, A., Ansari, K.J.: On a Kantorovich variant of Szász-Mirakjan operators. J. Funct. Spaces 2016(1035253), 9 (2016). 10.1155/2016/1035253
Ozarslan ,M. A. And Aktuglu, H. Local approximation for certain King type operators, Filo mat. 27 (2013) 173–181.
Peetre, J. A Theory of Interpolation of Normed Spaces; Notas de Matemática; Instituto de Matemática Pura e Aplicada (IMPA): Rio de Janeiro, Brazil, 1963; Volume 39, pp. 1–86.
Szász, 0. Generalization of S. Bernstein’s polynomials to the infinite interval, J. Res. Nat. Bur. of Standards 45 (1950), 239-245.
Taşdelen ,F,F. ; Aktaş, R, Altn, A,: Kantorovich type of Szász operators including Brenke-type polynomials. In: Abstract and Applied Analysis, vol. 2012. Hindawi (2012)
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Yılmaz, R., Izgi, A. Simetrik Aralıkta Szász Kantorovich Operatörlerinin Yaklaşım Özellikleri (Approximation Properties of Szász -Kantoroovich Operators in Symmetric Intervals) V. INTERNATIONAL FIRAT SCIENTIFIC RESEARCH CONGRESS December 5-7 ,2025 ELAZIG,TURKIYE, (CONFERENCE BOOK).
Yılmaz. R, Simetrik Aaralıkta Szász -Kantorovich Operatörlerinin Yaklaşım Özelliklleri (Approximation Properties Of Szász -Kantorovich Operators In A Symmetrical Interval), Harran Üniversitesi Lisansüstü Eğitim Enstitüsü , 2026.(56 page)

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Abstract:

In the progress of energy-efficient digital multiplication systems, approximate multipliers have been proven to be a good solution to attain high energy efficiency with acceptable computational precision. This paper proposes a 22 nm FinFET-based approximate Modified Radix-8 Booth multiplier which is based on Modified Radix-8 Booth recoding, selective partial-product approximation, controlled truncation, and an optimized reduction and accumulation network to minimize arithmetic complexity and switching activity. This architecture was modeled in VHDL and designed using an ASIC design flow using a 22 nm standard-cell library. Post-layout evaluation showed about 63.4% silicon area reduction, 55.1% propagation delay reduction, and 65.6% power consumption reduction when compared with an exact Booth multiplier with lower Power–Delay Product (PDP) and Area–Power Product (APP). The application-level validation with representative image processing operations resulted in a PSNR of 41.2 dB and SSIM of 0.995, which validated the proposed approximation strategy to maintain high computational quality. The proposed multiplier is well suited for low-power digital signal processing, multimedia processing, and embedded VLSI systems as it gives an effective trade-off between implementation efficiency and arithmetic accuracy.

Keywords:

Radix-8,Booth Recoding,truncation,approximate,image processing,

References:

I. Akbari, Omid, et al. “Dual-Quality 4:2 Compressors for Utilizing in Dynamic Accuracy Configurable Multipliers.” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 25, no. 4, 2017, pp. 1352–1361. 10.1109/tvlsi.2016.2643003.
II. Anchula, Sathish, et al. “Analysis of Approximate Multipliers Using FinFET.” 2025 International Conference on Electronics, Computing, Communication and Control Technology (ICECCC), IEEE, 2025, pp. 1–7.
III. Antelo, Elisardo, et al. “Improved 64-Bit Radix-16 Booth Multiplier Based on Partial Product Array Height Reduction.” IEEE Transactions on Circuits and Systems. I, Regular Papers, vol. 64, no. 2, 2017, pp. 409–418. 10.1109/tcsi.2016.2561518.
IV. Boopathy, E. Veera, and K. Kalirajan. “VLSI Implementation of Power-Aware Image Processing Using Hybrid Baugh-Booth Approximate Multiplier-Based MAC in Conviformer Architecture.” European Physical Journal Plus, vol. 141, no. 9, 2026. 10.1140/epjp/s13360-026-08302-3.
V. Chakraborty, Adrija, et al. “Energy Efficient Approximate Multiplier for Image Processing Applications.” Results in Engineering, vol. 25, no. 103798, 2025, p. 103798. 10.1016/j.rineng.2024.103798.
VI. Cui, Xiaoping, et al. “A Modified Partial Product Generator for Redundant Binary Multipliers.” IEEE Transactions on Computers. Institute of Electrical and Electronics Engineers, vol. 65, no. 4, 2016, pp. 1165–1171. 10.1109/tc.2015.2441711.
VII. George, Rachana, et al. “Fast Approximate Booth Multiplier for Error Resilient Applications.” International Journal of Signal and Imaging Systems Engineering, vol. 13, no. 2, 2024, pp. 95–108. 10.1504/ijsise.2024.142338.
VIII. Haq, Shams Ul, and Vijay Kumar Sharma. “Review of the Nanoscale FinFET Device for the Applications in Nano-Regime.” Current Nanoscience, vol. 19, no. 5, 2023, pp. 651–662. 10.2174/1573413719666221206122301.
IX. Kalaiselvi, C. M., and R. S. Sabeenian. “A Modular Technique of Booth Encoding and Vedic Multiplier for Low-Area and High-Speed Applications.” Scientific Reports, vol. 13, no. 1, 2023, p. 22379. 10.1038/s41598-023-49913-5.
X. Momeni, Amir, et al. “Design and Analysis of Approximate Compressors for Multiplication.” IEEE Transactions on Computers. Institute of Electrical and Electronics Engineers, vol. 64, no. 4, 2015, pp. 984–994. 10.1109/tc.2014.2308214.
XI. Pogue, Trevor E., and Nicola Nicolici. “Fast Inner-Product Algorithms and Architectures for Deep Neural Network Accelerators.” IEEE Transactions on Computers. Institute of Electrical and Electronics Engineers, 2023, pp. 1–14. 10.1109/tc.2023.3334140.
XII. Rao, E. Jagadeeswara, and P. Samundiswary. “High-Speed and Low-Power Recursive Rounding Based Approximate Multipliers for Error-Resilience Applications.” Wireless Personal Communications, vol. 136, no. 2, 2024, pp. 773–791. 10.1007/s11277-024-11283-0.
XIII. Sakthimohan, M., et al. “Enhanced FPGA Linear Phase FIR Filter with Amalgam Multiplier.” International Journal of Electronics, vol. 111, no. 10, 2024, pp. 1653–1678. 10.1080/00207217.2024.2349972.
XIV. Sayadi, Ladan, et al. “Two Efficient Approximate Unsigned Multipliers by Developing New Configuration for Approximate 4:2 Compressors.” IEEE Transactions on Circuits and Systems. I, Regular Papers, vol. 70, no. 4, 2023, pp. 1649–1659. 10.1109/tcsi.2023.3242558.
XV. Silvano, Cristina, et al. “A Survey on Deep Learning Hardware Accelerators for Heterogeneous HPC Platforms.” ACM Computing Surveys, vol. 57, no. 11, 2025, pp. 1–39. 10.1145/3729215.

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Abstract:

This article is devoted to deriving certain transformation identities in the theory of q-basic series and q-basic bilateral series. First, we use the symmetric Bailey transform and the Karlsson–Minton summation identity to establish several transformation identities. In the second part, we derive several useful special cases of these transformations. These findings unify and generalize existing results, extending the known results on series and transformation formulas.

Keywords:

Bailey's transform,Karlsson-Minton summation formula,q-basic hypergeometric series.,

References:

I. Andrews, George E., and Bruce C. Berndt. Ramanujan’s Lost Notebook, Part I. Springer, 2005. 10.1007/0-387-28124-X.
II. Karp, Dmitry B., and Elena G. Prilepkina. “Extensions of Karlsson-Minton Summation Theorem and Some Consequences of the First Miller-Paris Transformation.” Integral Transforms and Special Functions, 2018. 10.1080/10652469.2018.1526793.
III. Kaur, H., and A. K. Shrivastav. “Certain q-Series by using ₂Ψ₂ Basic Bilateral Hypergeometric Identity.” Journal of Information and Computational Science, vol. 10, no. 9, pp. 638–643, 2020. 10.12733/JICS.2020.V10I9.535569.13059
IV. Kaur, H., and A. K. Shrivastav, "On certain transformations for mock theta functions," Journal of Critical Reviews, vol. 7, no. 13, pp. 3927-3932, 2020. 10.31838/jcr.07.13.590.
V. Kaur, H., and A. K. Shrivastav, "Summation formulae involving basic hypergeometric and truncated basic hypergeometric functions," Journal of Mathematical Sciences and Computational Mathematics, vol. 1, no. 4, pp. 456-461, 2020. 10.15864/jmscm.1403.
VI. Kaur, K., P. Wadhwa, H. Kaur, and A. K. Shrivastav, "On identities for basic hypergeometric series through WP-bailey's pairs," Journal of Critical Reviews, vol. 7, no. 19, pp. 3669-3674, 2020. 10.31838/jcr.07.19.437.
VII. Shrivastav, A. K., H. Kaur, “On transformations formulae and certain transformations,” Journal of Physics: Conference Series, vol. 1818, Art. no. 012222, 2021. 10.1088/1742-6596/1818/1/012222.
VIII. Shrivastav, A. K., and A. N. Herbert, "On transformation formulae for basic hypergeometric functions by using WP-bailey's pairs," International Journal of Mathematics Trends and Technology, vol. 57, no. 2, pp. 122-127, 2018. 10.14445/22315373/IJMTT-V57P518
IX. Shrivastav, A. K., and A. N. Herbert, "On bailey's transform and transformation formulae for basic hypergeometric functions," Journal of Computer and Mathematical Sciences, vol. 9, no. 7, pp. 880-885, 2018. 10.29055/JCMS%2F824
X. Shrivastav, A. K., A. N. Herbert, and H. Kaur, "Certain rogers-ramanujan type multi-sum identities and ratio of infinite products," South East Asian Journal of Mathematics and Mathematical Sciences, vol. 15, no. 2, pp. 85-96, 2019. https://rsmams.org/journals/seajmams/article/349.
XI. Shrivastav, A. K., et al., "Multi-sum identities involving q-basic series," Journal of Computational Analysis and Applications, vol. 33, no. 6, pp. 17-23, 2024. https://eudoxuspress.com/index.php/pub/article/view/674.
XII. Shrivastav, A. K., Bajaj, S., Sharma, A., Kaur, H., Kaur Dhaliwal, R., & Budhiraja, R., “Analysis of q-Mittag–Leffler Function by using q-Fractional Operators,” Boletim Da Sociedade Paranaense De Matemática, 44(12), pp. 1-9, 2026.
https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/85030
XIII. Wadhwa, P., and A. K. Shrivastav, "An aspect of basic (q-) integral for q-basic series," Advances in Nonlinear Variational Inequalities, vol. 26, no. 2, pp. 41-45, 2023. 10.52783/anvi.v26.i2.261

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Abstract:

This article develops a time-truncated Skip Lot Sampling Plan of model R (SkSP-R) assuming that the product lifetime follows a Type II Generalized Half-Logistic Distribution (Type II GHLD). The distributional properties of Type II GHLD were briefly discussed. The percentiles of the Type II GHLD are used in the preparation of skip lot sampling plan of SkSP-R model for a life test. A reference single sampling plan is used to determine the minimum sample size required to ensure the specific percentile life of the product. The parameters of the sampling plan are estimated using a two-point approach, specifically the Limiting Quality Level (LQL) and Acceptable Quality Level (AQL). The Operating Characteristic (OC) values and Average Sample Number (ASN) values are calculated for the estimated plan parameters using OC function and ASN of the SkSP-R plan, the applicability of the proposed sampling plan is illustrated with a real-data example.

Keywords:

Type II Generalized Half-Logistic Distribution,Percentiles,SkSP–R,Life Test,Skip Lot Sampling.,

References:

I. Aslam, M., Balamurali, S., Azam, M., & Jun, C.-H. (2014). Skip-lot sampling plan of type SkSP-2 with two-stage group acceptance sampling plan as reference plan, Communications in Statistics — Simulation and Computation, 43(4), 777–789. 10.1080/03610918.2012.715224
II. Aslam, M., Balamurali, S., Jun, C.-H., & Ahmad, M. (2013). Optimal design of skip lot group acceptance sampling plans for the Weibull distribution and the generalized exponential distribution, Quality Engineering, 25(3), 1-10. 10.1080/08982112.2013.794834
III. Aslam, M., Balamurali, S., Jun, C.-H. & Ahmad, M. (2010). Optimal designing of a skip-lot sampling plan by two-point method, Pakistan Journal of Statistics, 26(4), 585-592.
IV. Aslam, M., Balamurali, S., Jun, C.-H., & Hussain, B. (2015). Design of SkSP-R variables sampling plans, Revista Colombiana de Estadística, 38(2), 413-429. 10.15446/rce.v38n2.51669.
V. Aslam, M., Srinivasa Rao, G., Khan, N., & Jun, C.-H. (2014). SkSP-V sampling plan for the exponentiated Weibull distribution, Journal of Testing and Evaluation, 42(3), 687-694. 10.1520/JTE20130051.
VI. Balamurali, S., & Jun, C.-H. (2011). A new system of skip-lot sampling plans having a provision for reducing normal inspection, Applied Stochastic Models in Business and Industry, 27(3), 348–363. 10.1002/asmb.844.
VII. Balamurali, S., Aslam, M., & Jun, C.H. (2014). A new system of skip-lot sampling plans including resampling, The Scientific World Journal, 192412, 10.1155/2014/192412.
VIII. Carr, W. E. (1982). Sampling Plan Adjustment for Inspection Error and Skip-Lot Plan. Journal of Quality Technology, 14(3), 105–116. 10.1080/00224065.1982.11978802.
IX. Dodge, H. F. (1955). Skip-lot sampling plan. Industrial Quality Control, 11(5), 3-5.
X. Hussain, J., Balamurali, S., & Aslam, M. (2020). Design of SkSP-R plan for popular statistical distributions, Journal of Modern Applied Statistical Methods, 19(1), eP2860. 10.22237/jmasm/1608552240.
XI. Jilani, Sd., Rao, G. S., & Rao, A. V. (2024). Designing of multiple dependent state sampling plan for Type-II generalized half logistic distribution. Research in Mathematics, 11(1). 10.1080/27684830.2024.2326706.

XII. Kantam, R. R. L., Ramakrishna, V., and Ravikumar, M. S. (2014). Estimation and testing in type II generalized half logistic distribution, Journal of Modern Applied Statistical Methods, 12(1), 198-206. 10.22237/jmasm/1398917760.
XIII. Krishnamoorthy, K., Mathew, T., & Mukherjee, S. (2008). Normal-based methods for a gamma distribution. Technometrics, 50(1), 69-78. 10.1198/004017007000000353.
XIV. P. Umamaheswari, K. P. Veerakumari, and S. Suganya. (2022). Construction and Selection of Skip Lot Sampling Plan of type Sksp-V for life tests based on Percentiles of Exponentiated Rayleigh Distribution. Reliability: Theory & Applications, 4(71), 123-131. 10.24412/1932-2321-2022-471-123-131.
XV. P. Umamaheswari., K. Pradeepa Veerakumari, and S.Suganya. (2023). Selection procedure for skip lot sampling plan of type SkSP-R based on percentiles of exponentiated Rayleigh distribution, Reliability: Theory &Applications, 1(72), 432-439. 10.24412/1932-2321-2023-172-432-439.
XVI. Parker, R. D., & Kessler, L. (1981). A Modified Skip-Lot Sampling Plan. Journal of Quality Technology, 13(1), 31–35. 10.1080/00224065.1981.11980983.
XVII. Perry, R. L. (1973). Skip-Lot Sampling Plans. Journal of Quality Technology, 5(3), 123–130. 10.1080/00224065.1973.11980585.
XVIII. Rao, G.S., Jilani, S.D. & Rao, A.V. (2021). Designing of multiple dependent state repetitive sampling plan for type-II generalized half logistic distribution. Int J Syst Assur Eng Manag 12, 1397–1409. 10.1007/s13198-021-01338-x.
XIX. Rao, G. S., Jilani, S., & Rao, A. V. (2020). Group acceptance sampling plans for resubmitted lots under Type II generalized half logistic distribution, Journal of Scientific Research, 12(3), 311-325. 10.3329/jsr.v12i3.44406.
XX. Reddy MR, Rao BS, Rosaiah K. (2024). Acceptance Sampling Plans based on Percentiles of Exponentiated Inverse Kumaraswamy Distribution. Indian Journal of Science and Technology. 17(16), 1681-1689. 10.17485/IJST/v17i16.222.
XXI. Tripathi, H., Al-Omari, A. I., & Alomani, G. A. (2022). A SkSP-R plan under the assumption of Gompertz distribution, Applied Sciences, 12(12), 6131. 10.3390/app12126131.

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Abstract:

Ethiopia banned internal combustion engine (ICE) vehicle imports in early 2024, promoting electric vehicles (EVs) and imposing a 15% import duty, compared to 60-100% for ICEs. Within one year, EVs registered in Ethiopia numbered 115,000, with targets of 500,000 by 2030. Despite the rapid rise in registrations, the supporting regulatory, training, supply chain, and grid connection infrastructures lag, creating several challenges and research issues. This study employs a convergent parallel mixed-method design to examine Ethiopia’s EV transition through the tripartite themes of policy, social acceptance, and technical specifications. Specifically, the study distributes questionnaires to 422 respondents and conducts 130 semi-structured interviews while analyzing policy documents. Six proxy indicators are normalized to form a Composite Social Acceptance Index (CSAI), ranging from 0 to 100. A Monte Carlo simulation is performed to forecast the hourly load of 50,000, 150,000, and 250,000 EVs in Addis Ababa using 10,000 iterations under three charging demand management scenarios: uncontrolled, off-peak incentives, and smart charging. The identified policy gaps include documentation problems during battery certification, lack of EV-specific insurance, and driver training, while the technical specifications section addresses the charging infrastructure’s impact on the grid. The CSAI scores for EV owners and non-owners are 72.3 and 38.4, respectively. The Monte Carlo results show that the peak demand for 250,000 EVs using uncontrolled charging would increase by 9.3%. Off-peak and smart charging incentives would reduce the increase by 35% and 52%, respectively. Overall, this study contributes to a better understanding of EV adoption and demonstrates how the CSAI and Monte Carlo methods could be useful in other data-scarce African countries.

Keywords:

Electric vehicles,Ethiopia,policy gaps,supply chain,social acceptance,charging load forecasting,Monte Carlo simulation,driver training,

References:

I. A. S. Sinija, and Vinod Kumar K P. “Consumer Adoption Trends of Electric Vehicles: A Secondary Data Analysis of Global Markets.” Journal of Emerging Technologies and Innovative Research, vol. 12, no. 11, Jan. 2025. 10.56975/jetir.v12i11.571295.
II. Berhane, Kiros, et al. “Health Effects of Environmental Exposures, Occupational Hazards and Climate Change in Ethiopia: Synthesis of Situational Analysis, Needs Assessment and the Way Forward.” The Ethiopian Journal of Health Development = Ya’Ityopya Tena Lemat Mashet, vol. 30, no. 1 Spec Iss, Jan. 2016. https://ejhd.org/index.php/ejhd/article/view/455.

III. Creswell, John W., and Vicki L. “Plano Clark. Designing and Conducting Mixed Methods Research.” SAGE Publications, 2017, https://books.google.com.et/books?id=eTwmDwAAQBAJ.
IV. Emole, Emmanuel Onuoha, and Rupert Avis. “Causes and Consequences of Air Pollution in Ethiopia. Institute of Development Studies.”, 1 Aug. 2025. 10.19088/k4dd.2025.075.
V. Gerber Machado, Pedro, et al. “Electric Vehicles Adoption: A Systematic Review (2016–2020).” WIREs Energy and Environment, vol. 12, no. 5, May 2023. 10.1002/wene.477.
VI. Harnaningrum, Rizky Novera, et al. “Factors Influencing Consumer Adoption of Electric Vehicles: A Literature Review.” Priviet Social Sciences Journal, vol. 6, no. 2, Feb. 2026, pp. 597–614, 10.55942/pssj.v6i2.1588.
VII. Janasak, Keith M. “Challenges Faced In Electric Vehicle Adoption.” Institute Of Electrical Electronics Engineers, 2024, 10.1109/rams51492.2024.10457699.
VIII. Li, Lili, et al. “Development of Electric Vehicles: Opportunities and Challenges for Power Grid Companies.” Institute Of Electrical Electronics Engineers, 2012, pp. 1–7, 10.1109/ciced.2012.6508460.
IX. Oxford Analytica. “Incentives May Fuel East Africa Green Transport Growth.” Emerald Expert Briefings, Emerald, 23 May 2024, 10.1108/oxan-db287210.
X. Pamidimukkala, Apurva, et al. “Barriers and Motivators to the Adoption of Electric Vehicles: A Global Review.” Green Energy and Intelligent Transportation, vol. 3, no. 2, Jan. 2024, p. 100153, 10.1016/j.geits.2024.100153.
XI. “Political Economy.” Law Ethiopia, www.lawethiopia.com/index.php?view=article&id=2087%3Aproclamation-no-600&catid=218. Accessed 14 Oct. 2026.
XII. Qian, Kejun, et al. “Modeling of Load Demand Due to EV Battery Charging in Distribution Systems.” IEEE Transactions on Power Systems, vol. 26, no. 2, May 2011, pp. 802–810, 10.1109/tpwrs.2010.2057456.
XIII. Ramli, R., et al. “Forecasting Demand for Green Vehicles.” IET Conference Proceedings, vol. 2023, no. 11, Sept. 2023, pp. 312–316, 10.1049/icp.2023.1797.
XIV. Solomon, Abel. “Directive Issued to Determine Electric Vehicle Charging System (EVCS) (Directive No. 1034/2024).” Ministry of Justice, 2024, justice.gov.et/en/directives/directive-issued-to-determine-electric-vehicle-charging-system-evcs-directive-no-1034-2024/.Accessed 14 Oct. 2026.

XV. Thompson, Avery. “Identifying Factors Influencing Electric Vehicle Adoption in Sub-Saharan Africa.” Scilight, vol. 2024, no. 52, Dec. 2024, 10.1063/10.0034793.
XVI. Toolib, Siti Norhidayah, et al. “Factors Influencing Electric Vehicle Adoption: A Conceptual Paper.” European Proceedings of Finance and Economics, vol. 1, 18 Aug. 2023, pp. 849–857. 10.15405/epfe.23081.77.
XVII. Tripathi, Shashi Kant, et al. “Ranking the Performance Outcomes of Electric Vehicle Adoption Due to Its Enablers for Achieving SDGs and Net-Zero Emissions.” Management of Environmental Quality: An International Journal, vol. 36, no. 6, Apr. 2025, pp. 1329–1351. 10.1108/meq-08-2024-0326.
XVIII. Truby, Jon, et al. “Regulatory Options for Vehicle Telematics Devices: Balancing Driver Safety, Data Privacy and Data Security.” International Review of Law, Computers & Technology, vol. 38, no. 1, Sept. 2023, pp. 86–110. 10.1080/13600869.2023.2242671.
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XX. Yao, Zhaosheng, and Mengqi Li. Smart Orderly Charging of Electric Vehicles Based on Demand-Side Management.” Applied Energy Innovation Institute, 2 Mar. 2021. 10.46855/energy-proceedings-7183

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Abstract:

Here we study the new concept of a doubly isolated edge geodetic set for a connected graph 𝐺 = (𝑉, 𝐸) of order 𝑛 ≥ 3 . The edge geodetic set 𝑆 ⊆ 𝑉 of a connected graph 𝐺 is said to be a doubly isolated edge geodetic set if the induced subgraphs < 𝑆 > and < 𝑉(𝐺) − 𝑆 > have at least one isolated vertex. The doubly isolated edge geodetic number is the minimum cardinality of a doubly isolated edge geodetic set of G and is denoted by 𝑔1𝑑𝑖(𝐺). The doubly isolated edge geodetic number of some standard graphs, Cartesian product, and corona graphs is determined. It is shown that for any three positive integers 𝑎, 𝑏 and 𝑐 with 𝑎 ≤ 𝑏 ≤ 𝑐 there exists a connected graph 𝐺 of order 𝑛 with 𝑔(𝐺) = 𝑎, 𝑔1(𝐺) = 𝑏 and 𝑔1𝑑𝑖(𝐺) = 𝑐.

Keywords:

Cartesian product,Corona,Edge geodetic set,Extreme vertex,Full vertex,Isolate edge geodetic number,Support vertex.,

References:

I. A. P. Santhakumaran, J. John. : ‘Edge geodetic number of a graph’. Journal of Discrete Mathematical Sciences and Cryptography. Vol. 10, No. 3, pp. 415-432, 2007. 10.1080/09720529.2007.10698129

II. D. Antony Xavier, A. Arokiaraj, E. Thomas. : ‘Doubly Geodetic Number of a Graph’. IOSR Journal of Mathematics. Vol. 12, Issue 5, Ver. IV, pp. 13-17, 2016.    10.9790/5728-1205041317.

III. F. Buckley, F. Harary. : ‘Distance in Graphs’. Addison-Wesley, Redwood City, CA, 1990. (Book)

IV. F. Buckley, F. Harary, L. V. Quintas. : ‘Extremal results on the geodetic number of a graph’. Computing Research Laboratory, New Mexico State University Vol. A(2), pp. 17-26, 1988.
https://books.google.co.in/books?id=6bhyHAAACAAJ

V. F. Harary. : ‘Graph Theory’. Addison-Wesley, 1969. (Book)

VI. F. Harary, L. Emmanuel, T. Constantine. : ‘The geodetic number of a graph’. Mathematical and Computer Modelling. Vol. 17, No. 11, pp. 89-95, 1993. 10.1016/0895-7177(93)90259-2

VII. G. Chartrand, P. Zhang. : ‘Introduction to Graph Theory’. Tata McGraw-Hill Pub. Co. Ltd., 2006. (Book)

VIII. G. Chartrand, F. Harary, P. Zhang. : ‘On the geodetic number of a graph’. Networks. Vol. 39, pp. 1-6, 2002. 10.1002/net.10007

IX. G. Chartrand, E. M. Palmer, P. Zhang. : ‘The geodetic number of a graph: A survey’. Congr. Numerantium. Vol. 156, pp. 37-58, 2002. 10.1016/0895-7177(93)90259-2

X. K. L. Bhavyavenu, V. M. Goudar. : ‘Doubly connected geodetic number of graphs’. Malaya Journal of Matematik. Vol. 6, No. 3, pp. 626-631, 2018.    10.26637/MJM0603/0025

XI. K. L. Bhavyavenu, V. M. Goudar. : ‘Doubly connected geodetic number on operations in graphs’. Journal of Engineering and Applied Sciences. Vol. 13, No. 12, pp. 4330-4335, 2018. 10.3923/jeasci.2018.4330.4335

XII. X. X. Lenin Xaviour, S. V. Ashwin Prakash. : ‘Isolate Geodetic Number of a Graph’. Journal of Applied Science and Computations. Vol. 5, No. 11, pp. 755-765, 2018.
https://www.researchgate.net/publication/344390328_Isolate_Geodetic_Number_of_a_Graph

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Abstract:

This investigation examines passive control tactics for administering base pressure at Mach M = 1.8. Because the base pressure in the separated section is reduced and below the back pressure, it contributes a sizable portion of the total drag. Hence, we must restrain or regulate this parameter. Consequently, we use base drag to extend the range of aerospace vehicles and save energy. We select expansion levels to expose the nozzle to both adverse and favorable pressure conditions, allowing us to evaluate the control mechanism's efficacy. We select three cavity geometries to evaluate the flow-regulation mechanism by placing the cavities at various positions across a range of duct sizes. The simulated results show that the cavity is effective only when the viscous layer exiting the nozzle enters the cavity; otherwise, the control is ineffective, regardless of whether the reattachment point occurs before or after the cavity. The present investigation shows that the cavity is most effective when located 8.5 mm from the base; however, at other cavity locations, its effectiveness is negligible except at NPRs 3 and 5. At these two NPRs, the exiting flow is associated with oblique shock waves and an adverse pressure gradient, which reduces base pressure.

Keywords:

Triangular Cavity,Base Flow,Area Ratio,Supersonic Mach Number,Duct Size,

References:

I. Aabid, Abdul, et al. “Numerical Simulation of Suddenly Expanded Flow at Mach 2.2.” International Journal of Engineering and Advanced Technology, vol. 8, no. 3, 2019, pp. 457–62, https://www.researchgate.net/publication/331466434_Numerical_Simulation_of_Suddenly_Expanded_Flow_at_Mach_22.
II. Akhtar, Mohammad Nishat, et al. “Effects of Micro Jets on the Flow Field of the Duct with Sudden Expansion.” International Journal of Innovative Technology and Exploring Engineering, vol. 8, no. 9S2, 2019, pp. 636–40, 10.35940/ijitee.i1129.0789s219.
III. Akhtar, Mohammad Nishat, et al. “Numerical Simulations of a CD Nozzle and the Influence of the Duct Length.” International Journal of Innovative Technology and Exploring Engineering, vol. 8, no. 9S2, 2019, pp. 622–30, 10.35940/ijitee.i1127.0789s219.
IV. Arabi, Abderraouf, et al. “Pressure Recovery Model for Gas–liquid Two-Phase Flow Across Sudden Expansions.” Experimental and Computational Multiphase Flow, vol. 6, no. 1, 2024, pp. 14–27, 10.1007/s42757-023-0160-3.
V. Arabi, Abderraouf, et al. “Identifying the Intermittent Flow Sub-Regimes Using Pressure Drop Time Series Fluctuations.” Experimental and Computational Multiphase Flow, vol. 6, no. 1, 2024, pp. 28–40, 10.1007/s42757-022-0153-7.
VI. Baig, Maughal Ahmed Ali, et al. “Control of Base Flows with Micro Jets.” International Journal of Turbo and Jet Engines, vol. 28, no. 1, 2011, pp. 59–69, 10.1515/tjj.2011.009.
VII. Davletshin, I. A., et al. “Heat Transfer and Flow Structure in a Plane Diverging Channel.” International Journal of Heat and Mass Transfer, vol. 189, 2022, article 122744. 10.1016/j.ijheatmasstransfer.2022.122744.
VIII. Davletshin, I. A., et al. “Secondary Flows in a Flat Diffuser and Their Significance for the Formation of a Turbulence Field.” Thermophysics and Aeromechanics, vol. 30, no. 6, 2024, pp. 995–1011, 10.1134/S0869864323060033.
IX. Golubkina, I. V., and A. N. Osiptsov. “Compressible Gas-Droplet Flow and Heat Transfer Behind a Condensation Shock in an Expanding Channel.” International Journal of Thermal Sciences, vol. 179, 2022, article 107576, 10.1016/j.ijthermalsci.2022.107576.
X. Khan, Ambareen, et al. “Comprehensive CFD Analysis of Base Pressure Control Using Quarter Ribs in Sudden Expansion Duct at Sonic Mach Numbers.” International Journal of Thermofluids, vol. 24, 2024, article 100908. 10.1016/j.ijft.2024.100908.
XI. Khan, Ambareen, et al. “Passive Control of Base Pressure: A Review.” Applied Sciences, vol. 11, no. 3, 2021, article 1334. 10.3390/app11031334.
XII. Khan, Ambareen, et al. “Experimental Investigation of Suddenly Expanded Flow at Sonic and Supersonic Mach Numbers Using Semi-Circular Ribs: A Comparative Study Between Experimental, Single Layer, Deep Neural Network (SLNN and DNN) Models.” The European Physical Journal Plus, vol. 138, no. 4, 2023, article 314. 10.1140/epjp/s13360-023-03853-1.
XIII. Khan, Ambareen, et al. “Numerical Simulation of Suddenly Expanded Flow from Converging Nozzle at Sonic Mach Number.” Proceedings of International Conference of Aerospace and Mechanical Engineering 2019, Springer, 2020, pp. 349–59. 10.1007/978-981-15-4756-0_29.
XIV. Khan, Ambareen, et al. “Effect of Ribs in a Suddenly Expanded Flow at Sonic Mach Number.” Heliyon, vol. 10, no. 9, 2024, article e30313. 10.1016/j.heliyon.2024.e30313.
XV. Khan, S. A., et al. “Passive Control of Base Drag Employing Dimple in Subsonic Suddenly Expanded Flow.” International Journal of Mechanical and Mechatronics Engineering, vol. 18, no. 3, 2018, pp. 69–74, https://www.researchgate.net/publication/326684003_Passive_control_of_base_drag_employing_dimple_in_subsonic_suddenly_expanded_flow.
XVI. Khan, Sher Afghan, et al. “CFD Analysis of Human Powered Submarine to Minimize Drag.” International Journal of Mechanical and Production Engineering Research and Development, vol. 8, no. 3, 2018, pp. 1057–66, 10.24247/ijmperdjun2018111.
XVII. Khan, Sher Afghan, and E. Rathakrishnan. “Nozzle Expansion Level Effect on Suddenly Expanded Flow.” International Journal of Turbo and Jet Engines, vol. 23, no. 4, 2006, pp. 233–58, 10.1515/tjj.2006.23.4.233.
XVIII. Khan, Sher Afghan, et al. “Passive Control of Base Drag in Compressible Subsonic Flow Using Multiple Cavity.” International Journal of Mechanical and Production Engineering Research and Development, vol. 8, no. 4, 2018, pp. 39–44. 10.24247/ijmperdaug20185.
XIX. Kim, Yongchan, et al. “Base Flow and Drag Characteristics of a Supersonic Vehicle with Cold and Hot Jet Flows of Nozzles.” Aerospace, vol. 10, no. 10, 2023, article 836. 10.3390/aerospace10100836.
XX. Kopparthy, Saketh, et al. “Numerical Investigations of Turbulent Single-Phase and Two-Phase Flows in a Diffuser.” International Journal of Multiphase Flow, vol. 130, 2020, article 103333. 10.1016/j.ijmultiphaseflow.2020.103333.
XXI. Lee, Shibo, et al. “A Review of Flow Control Strategies for Supersonic/Hypersonic Fluid Dynamics.” Aerospace Research Communications, vol. 2, 2024, article 13149. 10.3389/arc.2024.13149.
XXII. Pakhomov, M. A., and V. I. Terekhov. “Gas-Droplet Flow Structure and Heat Transfer in an Axisymmetric Diffuser with a Sudden Expansion.” Journal of Applied Mechanics and Technical Physics, vol. 61, no. 5, 2020, pp. 787–97. 10.1134/S0021894420050132.
XXIII. Pakhomov, Maksim A., and Viktor I. Terekhov. “Modeling of Turbulent Heat-Transfer Augmentation in Gas-Droplet Non-Boiling Flow in Diverging and Converging Axisymmetric Ducts with Sudden Expansion.” Energies, vol. 15, no. 16, 2022, article 5861. 10.3390/en15165861.
XXIV. Pandey, K. M., and E. Rathakrishnan. “Annular Cavities for Base Flow Control.” International Journal of Turbo and Jet Engines, vol. 23, no. 2, 2006, pp. 113–27. 10.1515/TJJ.2006.23.2.113.
XXV. Rashid, Shagufta, et al. “Review of Wave Drag Reduction Techniques: Advances in Active, Passive, and Hybrid Flow Control.” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 236, no. 14, 2022, pp. 2851–84. 10.1177/09544100211069796.
XXVI. Rehman, Shafiqur, and S. A. Khan. “Control of Base Pressure with Micro-Jets: Part I.” Aircraft Engineering and Aerospace Technology, vol. 80, no. 2, 2008, pp. 158–64. 10.1108/00022660810859373.
XXVII. Salem, Khaled M., et al. “Modeling Two-Phase Gas-Solid Flow in Axisymmetric Diffusers Using Cut Cell Technique: An Eulerian-Eulerian Approach.” Boundary Value Problems, vol. 2024, no. 1, 2024, article 150. 10.1186/s13661-024-01955-y.
XXVIII. Shakirov, R. R., et al. “Kinematic Structure of Flow and the Heat Transfer in Flat Diffuser and Confuser Channels.” Thermophysics and Aeromechanics, vol. 29, no. 5, 2023, pp. 759–64. 10.1134/S08698643220500146.

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Abstract:

Over the past few decades, the night-time use of digital devices has increased significantly among the young adult population While most of the existing studies examine only sleep outcomes associated with night-time digital use. This study aims to investigate three interconnected domains --sleeping habits, cognitive function, and physiological well-being within a single framework, providing a holistic understanding of digital nocturnality among young adults. The study was conducted among 180 young adults aged 20–39 years residing in semi-urban areas of Bhubaneswar, Odisha. Participants were selected using simple random sampling. Data were collected using validated tools, including the Sleep Hygiene Index (SHI), Karolinska Sleepiness Scale (KSS), Stroop Test, and Digital Wellbeing/App Tracker. Descriptive statistics and correlation analysis, were used for data interpretation. Findings revealed that about half of the participants spent 1-2 hours of night-time digital activity (49.44%). Based on the Spearman correlation test, there was a significant positive relationship between night-time digital activity and physiological sleepiness (ρ=0.215, p=0.0037) and a moderate positive relationship with poor sleep hygiene (ρ=0.504, p<0.001). No significant relationship existed between night-time digital activity and cognitive wellbeing (ρ=-0.051, p=0.494). Night time digital engagement was significantly associated with sleep habits and physiological well-being of young adults. Results of this study have highlighted the potential adverse effects of digital nocturnality.

Keywords:

Digital nocturnality,night-time screen exposure,sleep quality,cognitive function,sleep hygiene,physiological well-being,young adults.,

References:

I. Alam, M., Abbas, K., Sharf, Y., & Khan, S. (2024). Impacts of blue light exposure from electronic devices on circadian rhythm and sleep disruption in adolescent and young adult students. Chronobiology in Medicine, 6(1), 39–46.
II. Brautsch, L. A. S., Lund, L., Andersen, M. M., Jennum, P., Folker, A. P., & Andersen, S. (2023). Digital media use and sleep in late adolescence and young adulthood: A systematic review. Sleep Medicine Reviews, 68, 101742. 10.1016/j.smrv.2022.101742
III. Deivendran, G., Kanagaraj, T. S., Leelabai, B. S., Kannan, P., Srinivasan, Y., Ayyavoo, S., & Periasamy, P. (2025). Impact of excessive screen time on sleep quality and sleep disturbances among young adults: A cross-sectional study. Journal of Pharmacy & Bioallied Sciences, 17(2), 53–55. 10.1556/2006.4.2015.010
IV. Demirci, K., Akgönül, M., & Akpınar, A. (2015). Relationship of smartphone use severity with sleep quality, depression, and anxiety in university students. Journal of Behavioral Addictions, 4(2), 85–92.
V. Devi, M., Tomy, C., Olickal, J., Rose, B. M., & Thankappan, K. R. (2025). Prevalence of smartphone addiction and its associated factors among college students aged 18–23 years in Kerala, India: A cross-sectional study. Cureus, 17(11), e97301. 10.7759/cureus.97301

VI. Dissing, A. S., Andersen, T. O., Jensen, A. K., Lund, R., & Rod, N. H. (2022). Nighttime smartphone use and changes in mental health and wellbeing among young adults: A longitudinal study based on high-resolution tracking data. Scientific Reports, 12, 8013.
VII. Dresp-Langley, B., & Hutt, A. (2022). Digital addiction and sleep. International Journal of Environmental Research and Public Health, 19(11), 6910. 10.3390/ijerph19116910
VIII. Fiore, M., Arena, D., Crisafi, V., Grieco, V., Palella, M., Timperanza, C., Conti, A., Cuffari, G., & Ferrante, M. (2025). Digital devices use and sleep in adolescents: An umbrella review. International Journal of Environmental Research and Public Health, 22(10), 1517. 10.3390/ijerph22101517
IX. Grzelak, A. (2024). Managing blue light exposure: Impacts on sleep quality and circadian health. Quality in Sport.
X. Höhn, C., Hahn, M. A., Gruber, G., Pletzer, B., Cajochen, C., & Hoedlmoser, K. (2024). Effects of evening smartphone use on sleep and declarative memory consolidation in male adolescents and young adults. Brain Communications, 6(3), fcae173. 10.1093/braincomms/fcae173
XI. Karila, L., Scher, N., Draghi, C., Lichte, D., Darmon, I., Boudabous, H., Lamallem, H., Bauduceau, O., Bollet, M., & Toledano, A. (2025). Understanding problematic smartphone and social media use among adults in France: Cross-sectional survey study. JMIR Mental Health, 12, e63431. 10.2196/63431
XII. Khan, M. D., Junaidi, S., & Dalbah, M. I. (2026). Digital engagement and sleep dysregulation in young adults: A narrative review. Cureus, 18(3), e105030. 10.7759/cureus.105030
XIII. Khan, S., Siddiqui, A., Husain, F., & Zubair, M. Y. (2025). A narrative review of digital screen time and sleep quality among young adults in India. International Journal of Research in Medical Sciences, 13(12), 5610–5616. 10.18203/2320-6012.ijrms20254006
XIV. Kumar, V. A., Chandrasekaran, V., & Brahadeeswari, H. (2019). Prevalence of smartphone addiction and its effects on sleep quality: A cross-sectional study among medical students. Industrial Psychiatry Journal, 28(1), 82–85. 10.4103/ipj.ipj_56_19
XV. Liebig, L., Balogh, E., Birkás, B., Faubl, N., Zelko, E., Gräfe, W., Pieper, S., Gottschall, M., & Riemenschneider, H. (2026). Nighttime screen use, sleep quality, and smartphone addiction symptoms among medical students: An international cross-sectional study. Frontiers in Psychiatry, 17, 1735186. 10.3389/fpsyt.2026.1735186
XVI. Maurya, C., Muhammad, T., Maurya, P., & Dhillon, P. (2022). The association of smartphone screen time with sleep problems among adolescents and young adults: Cross-sectional findings from India. BMC Public Health, 22, 1686. 10.1186/s12889-022-14076-x

XVII. Sohn, S. Y., Krasnoff, L., Rees, P., Kalk, N. J., & Carter, B. (2021). The association between smartphone addiction and sleep: A UK cross-sectional study of young adults. Frontiers in Psychiatry, 12, 629407. 10.3389/fpsyt.2021.629407
XVIII. Soumya Sonalika, Jacqueline D. M. Williams, Sikandar Kumar, (2026), DIGITAL DETOXIFICATION: EVALUATING INTERVENTION STRATEGIES FOR ADOLESCENTS. J. Mech. Cont.& Math. Sci., Vol.-20, No.-3, March (2025) pp 166-179. 10.26782/jmcms.2025.03.00011
XIX. Warsaw, R. E., Jones, A., Rose, A. K., Newton-Fenner, A., Alshukri, S., & Gage, S. H. (2021). Mobile technology use and its association with executive functioning in healthy young adults: A systematic review. Frontiers in Psychology, 12, 643542. 10.3389/fpsyg.2021.643542

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Abstract:

Epidemiological surveillance data collected during the early stage of an outbreak are rarely free of doubt: case counts are revised, contact-tracing records are incomplete, and a share of reports remain formally unclassified, a pattern documented explicitly during the 2014–2016 West Africa Ebola outbreak, when the World Health Organization stopped consistently reporting probable and suspected case counts because of high reclassification rates. Fuzzy and intuitionistic fuzzy differential equations model vagueness in such parameters but cannot separately track how much of the uncertainty is indeterminate rather than simply "false." This paper develops a Susceptible–Infected–Recovered (SIR) epidemic model in which the transmission rate and the recovery rate are represented as single-valued triangular neutrosophic numbers, so that truth, indeterminacy, and falsity in the parameter estimates are carried independently through the dynamics. We recall the algebra of triangular neutrosophic numbers and their (α,β,γ)-cuts, define the model through the generalized Hukuhara neutrosophic derivative, prove existence and uniqueness for the resulting family of classical systems, and prove in closed form that the epidemic peak and the final attack rate are monotonic in the transmission and recovery rates, which is what rigorously justifies reading the computed cut families as genuine bounds. A corner-point (α, β, γ)-cut solution procedure is proposed and solved with an adaptive Runge–Kutta scheme on parameters grounded in published country-level reproduction-number estimates from the West Africa Ebola outbreak. Truth-, indeterminacy-, and falsity-cut families are all computed numerically, showing how the epidemic peak, its timing, the final attack rate, and the effective reproduction number widen or narrow independently along each of the three membership dimensions, and that the indeterminacy- and falsity-cut bounds diverge from one another even at matched confidence levels a distinction no fuzzy or intuitionistic fuzzy model can represent. The results indicate that the neutrosophic formulation keeps the full three-way structure of the uncertainty in the surveillance data while remaining computationally no more demanding than a comparable fuzzy model, and that it collapses to the classical deterministic SIR model at the maximal-confidence limit of every cut, giving a consistent basis for comparison with existing crisp and fuzzy epidemic models.

Keywords:

neutrosophic differential equations; neutrosophic numbers; (α,β,γ)-cut; generalized Hukuhara derivative; SIR epidemic model; epistemic uncertainty.,

References:

I. Abdy, M., Side, S., Annas, S., Nur, W., Sanusi, W. "An SIR Epidemic Model for COVID-19 Spread with Fuzzy Parameter: the Case of Indonesia." Advances in Difference Equations, Vol. 2021 (2021), Art. 105. 10.1186/s13662-021-03263-6
II. Acharya, A., Mahato, S., Sil, N., Mahata, A., Mukherjee, S., Mahato, S. K., Roy, B. "An Intuitionistic Fuzzy Differential Equation Approach for the Lake Water and Sediment Phosphorus Model." Healthcare Analytics, Vol. 5 (2024), Art. 100294. 10.1016/j.health.2024.100294
III. Acharya, A., Mahata, A., Mukherjee, S., Biswas, M. A., Das, K. P., Mondal, S. P., Roy, B. "A Neutrosophic Differential Equation Approach for Modelling Glucose Distribution in the Bloodstream Using Neutrosophic Sets." Decision Analytics Journal, Vol. 8 (2023), Art. 100264. 10.1016/j.dajour.2023.100264
IV. Acharya, A., Mahata, A., Karak, M., Sil, N., Mukherjee, S., Mondal, S. P., Roy, B. "Stability Analysis of Diabetes Mellitus Model in Neutrosophic Fuzzy Environment." Franklin Open, Vol. 8 (2024), Art. 100144. 10.1016/j.fraope.2024.100144
V. Alamin, A., Mondal, S. P., Alam, S., Ahmadian, A., Salahshour, S., Salimi, M. "Solution and Interpretation of Neutrosophic Homogeneous Difference Equation." Symmetry, Vol. 12(7) (2020), 1091. 10.3390/sym12071091
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IX. Biswas, S., Moi, S., Pal, S. "Second-Order Neutrosophic Boundary-Value Problem." Complex & Intelligent Systems, Vol. 7(2) (2021), pp. 1079–1098. 10.1007/s40747-020-00260-x
X. Chalco-Cano, Y., Roman-Flores, H. "On New Solutions of Fuzzy Differential Equations." Chaos, Solitons & Fractals, Vol. 38 (2008), pp. 112–119. 10.1016/j.chaos.2006.10.043
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XII. Garske, T., Cori, A., Ariyarajah, A., et al. "Heterogeneities in the Case Fatality Ratio in the West African Ebola Outbreak 2013–2016." Philosophical Transactions of the Royal Society B, Vol. 372 (2017), 20160308. 10.1098/rstb.2016.0308
XIII. Kaleva, O. "Fuzzy Differential Equations." Fuzzy Sets and Systems, Vol. 24 (1987), pp. 301–317. 10.1016/0165-0114(87)90029-7
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XV. Kumar, Ch. Shashi, Rao, T. S. N., Naresh, M., Rao, V. V. "Neutrosophic Bipolar Soft Topological Compact Spaces." International Journal of Mechanical Engineering, Vol. 7(1) (2022), pp. 2607–2613. [DOI not assigned by publisher]
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XVII. Mahata, A., Acharya, A., Sil, N., Smarandache, F., Paul, S., Mukherjee, S., Biswas, M. A., Roy, B. "Dynamics of a SEIR Epidemic Model Utilizing Intuitionistic Fuzzy Set." OPSEARCH (2026, in press). [DOI to be confirmed by authors on acceptance]
XVIII. Mazandarani, M., Xiu, L. "A Review on Fuzzy Differential Equations." IEEE Access, Vol. 9 (2021), pp. 62195–62211. 10.1109/ACCESS.2021.3074245
XIX. Meltzer, M. I., Atkins, C. Y., Santibanez, S., et al. "Estimating the Future Number of Cases in the Ebola Epidemic -Liberia and Sierra Leone, 2014–2015." MMWR Supplements, Vol. 63(3) (2014), pp. 1–14. [CDC report; no DOI assigned]
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XXI. Momena, A. F., Haque, R., Rahaman, M., Salahshour, S., Mondal, S. P. "The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy." Logistics, Vol. 8(1) (2024), 18. 10.3390/logistics8010018
XXII. Rao, Y. S., Ch. Shashi Kumar, Rao, T. S. N., Rao, V. V. "Single Valued Neutrosophic Detour Distance." Journal of Critical Reviews, Vol. 7(8) (2020). [DOI not assigned by publisher]
XXIII. Sarkar, N., Sen, M. "A Hybrid Daubechies Wavelet Collocation Approach for a Fractional-Order SIR Epidemic Model with Delay Effects." Scientific Reports (2025, in press). [DOI to be confirmed by authors on acceptance]
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XXVI. Sumathi, I. R., Sweety, C. A. C. "New Approach on Differential Equation via Trapezoidal Neutrosophic Number." Complex & Intelligent Systems, Vol. 5(4) (2019), pp. 417–424. 10.1007/s40747-019-0117-3
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Abstract:

Reliability assessment and maintenance optimization are crucial for improving the productivity, availability, and profitability of continuous manufacturing systems. Paper manufacturing plants are particularly vulnerable to equipment failures because production depends on the uninterrupted operation of interconnected subsystems. Existing studies have extensively applied continuous-Time Markov Chains (CTMC) and optimization techniques for reliability analysis; however, limited attention has been given to integrating the Regenerative Point Graphical Technique (RPGT) with CTMC and Grey Wolf Optimization (GWO) for repairable manufacturing systems incorporating active redundancy and preventive maintenance. This study proposes a reliability model for a paper manufacturing plant consisting of a pulp preparation unit, two identical paper machines operating under active redundancy, and a cutting and packaging unit supported by a single repair facility, significantly enhancing system performance. The Grey Wolf Optimizer is used to resolve the optimal failure, repair, and preventive maintenance parameters that maximize system profit while improving operational performance. Numerical and sensitivity analysis demonstrate that active redundancy and a cutting and packaging unit supported by a single repair facility. The system behavior is analyzed by developing Chapman-Kolmogorov differential equations and steady-state probability equations. Performance measures, including steady-state availability, repair facility busy period, and long-run profit, are analytically evaluated. The proposed framework provides an effective decision-support tool for reliability-centered maintenance planning and optimization in paper manufacturing and other continuous process industries. Numerical and sensitivity analysis demonstrate that the proposed framework significantly improves system availability, reduces the repair facility busy period, and increases long-run profit through the optimal selection of failure, restore, and precautionary maintenance parameters.

Keywords:

Reliability assessment; Paper manufacturing system; Regenerative Point Graphical Technique (RPGT); Continuous-Time Markov Chain (CTMC); Grey Wolf Optimizer; Active redundancy; Preventive maintenance; Profit Optimization.,

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