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Abstract:

In today's world, communication is essential for various aspects of life. From military operations and medical systems to community networks, communication plays a crucial role in ensuring the smooth functioning of these applications. With the advancement of technology, communication has become more efficient and has significantly reduced the barriers of distance, bringing people and nations closer together. One of the key components of modern communication systems is microstrip devices. These devices are used in a wide range of applications, including filters, diplexers, and triplexers. Filters are used to selectively allow certain frequencies to pass through while blocking others, making them essential for signal processing and interference reduction in communication systems. Diplexers and triplexers are used to combine or separate multiple signals, allowing for more efficient use of the available frequency spectrum. This article aims to provide an overview of the state-of-the-art microstrip devices used in communication systems. It will review previous studies and advancements in the field, providing insights into the latest developments and technologies. By understanding the current state of research and development in microstrip devices, engineers and researchers can gain valuable knowledge to improve the performance and efficiency of communication systems. Furthermore, the article will explore the potential applications of microstrip devices in various communication systems, such as satellite communications, wireless networks, and radar systems. Understanding the capabilities and limitations of these devices will be crucial for optimizing their performance in different scenarios. Overall, this article will serve as a comprehensive resource for anyone interested in the role of microstrip devices in communication systems. Delving into the scope of filters, diplexers, and triplexers, will provide valuable insights into the advancements and potential future developments in this important area of technology.

Keywords:

Microstrip,Bandpass Filter,Diplexer,Triplexer,

Refference:

I. A. Al-ghoul and T. F. Skaik, “Design of UMTS/LTE Diplexer and DCS/UMTS/LTE Triplexer for Mobile Communication Systems,” Islamic University of Gaza, 2013.
II. A. B. Yousif, “Design of Microstrip Diplexer Filters for Wireless Applications,” University of Technology, 2020.
III. A. E. Ammar, N. M. Mahmoud, M. A. Attia, and A. H. Hussein, “Efficient diplexer with high selectivity and low insertion loss based on SOLR and DGS for WiMAX,” Prog. Electromagn. Res. C, vol. 116, pp. 171–180, 2021, doi: 10.2528/PIERC21090104.
IV. A. El-Tokhy, R. Wu, and Y. Wang, “Microstrip triplexer using a common triple-mode resonator,” Microw. Opt. Technol. Lett., vol. 60, no. 7, pp. 1815–1820, 2018, doi: 10.1002/mop.31244.
V. A. Kumar and D. K. Upadhyay, “A compact planar diplexer based on via-free CRLH TL for WiMAX and WLAN applications,” Int. J. Microw. Wirel. Technol., vol. 11, no. 2, pp. 130–138, 2019, doi: 10.1017/S1759078718001496.
VI. A. Rezaei and L. Noori, “Miniaturized microstrip diplexer with high performance using a novel structure for wireless L-band applications,” Wirel. Networks, vol. 26, no. 3, pp. 1795–1802, 2020, doi: 10.1007/s11276-018-1870-5.
VII. A. Rezaei and L. Noori, “Novel low-loss microstrip triplexer using coupled lines and step impedance cells for 4G and WiMAX applications,” Turkish J. Electr. Eng. Comput. Sci., vol. 26, no. 4, pp. 1871–1880, 2018, doi: 10.3906/elk-1708-48.
VIII. A. Rezaei, S. I. Yahya, L. Nouri, and M. H. Jamaluddin, “Design of a low-loss microstrip diplexer with a compact size based on coupled meandrous open-loop resonators,” Analog Integr. Circuits Signal Process., vol. 102, no. 3, pp. 579–584, 2020, doi: 10.1007/s10470-020-01625-w.
IX. A. Rezaei, S. I. Yahya, S. Moradi, and M. H. Jamaluddin, “A compact microstrip triplexer with a novel structure using patch and spiral cells for wireless communication applications,” Prog. Electromagn. Res. Lett., vol. 86, pp. 73–81, 2019, doi: 10.2528/pierl19060104.
X. C. Jayanth, P. Peter, and B. Santhosh, “Optical Triplexer and Diplexer Filter Using Two-Dimensional Photonic Crystal,” Journal of Optics (2023): 1-8.‏

XI. C. Sangdao, “Simulation of Triplexer Design for Improving Insertion Loss and Isolation,” in 17th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, ECTI-CON 2020, 2020, pp. 603–606, doi: 10.1109/ECTI-CON49241.2020.9158285.
XII. C. W. Tang and M. G. Chen, “Packaged microstrip triplexer with star-junction topology,” Electronics Letters, vol. 48, no. 12, pp. 699-701, 2012.
XIII. D. A. Letavin, “Microstrip diplexer implemented on high-pass and low-pass filters,” in International Conference of Young Specialists on Micro/Nanotechnologies and Electron Devices, EDM, 2018, vol. 2018-July, pp. 199–202, doi: 10.1109/EDM.2018.8435001.
XIV. D. K. Choudhary and R. K. Chaudhary, “Compact Lowpass and Dual-Band Bandpass Filter with Controllable Transmission Zero/Center Frequencies/Passband Bandwidth,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 67, no. 6, pp. 1044–1048, 2020, doi: 10.1109/TCSII.2019.2931446.
XV. D. Sen, E. Dillibabu, and M. Ramesh, “Design of compact inline triplexer for multi band receiver,” 2018, doi: 10.1109/IMaRC.2018.8877199.
XVI. F. Fouladi and A. Rezaei, “A six-channel microstrip diplexer for multi-service wireless communication systems,” Eng. Rev., vol. 41, no. 3, 2021, doi: 10.30765/ER.1556.
XVII. H. A. Hussein, Y. S. Mezaal, and B. M. Alameri, “Miniaturized microstrip diplexer based on fr4 substrate for wireless communications,” Elektron. ir Elektrotechnika, vol. 27, no. 5, pp. 34–40, 2021, doi: 10.5755/j02.eie.28942.
XVIII. H. Tizyi, F. Riouch, A. Tribak, A. Najid, and A. Mediavilla, “Microstrip diplexer design based on two square open loop bandpass filters for RFID applications,” Int. J. Microw. Wirel. Technol., vol. 10, no. 4, pp. 412–421, 2018, doi: 10.1017/S1759078718000314.
XIX. H. X. Xu, G. M. Wang, C. X. Zhang, and J. G. Liang, “Novel design of compact microstrip diplexer based on fractal-shaped composite right/left handed transmission line,” Journal of Infrared and Millimeter Waves, vol. 30, no. 5, pp. 390-396, 2011.
XX. H.-X. Xu, G.-M. Wang, and H.-P. An, “Hilbert fractal curves form compact diplexer,” Microw. & RF, vol. 49, no. 8, pp. 92-95, 2010.
XXI. J. H. Song, K. S. Lee, and Y. Oh, “Triple wavelength demultiplexers for low-cost optical triplexer transceivers,” Journal of Lightwave Technology, vol. 25, no. 1, pp. 350-358, 2007.
XXII. J. Konpang and N. Wattikornsirikul, “An analysis of high selectivity and harmonic suppression based on stepped-impedance resonator structure for dual-mode diplexer,” Prog. Electromagn. Res. C, vol. 112, pp. 45–54, 2021, doi: 10.2528/PIERC21032102.
XXIII. J. Liu et al., “New design of a compact 6-pole reconfigurable narrowband triplexer based on common net-type resonator,” 2018, doi: 10.1109/ASEMD.2018.8558973.
XXIV. J. Liu, T. Su, H. Lv, L. Lin, and B. Wu, “Six-channel diplexer using stub-loaded stepped impedance resonators,” Appl. Comput. Electromagn. Soc. J., vol. 37, no. 10, pp. 1582–1587, 2019, [Online]. Available: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85074453270&partnerID=40&md5=1cfa615441d068f8c9ed93e35a37884d.
XXV. J. S. G. Hong and M. J. Lancaster, “Microstrip filters for RF/microwave applications,” John Wiley & Sons, 2004.‏
XXVI. J. Xu, et al., “Diplexer-integrated spdt switches with multiple operating modes using common fractal stub-loaded resonator,” IEEE Transactions on Microwave Theory and Techniques, vol. 69, no. 2, pp. 1464-1473, 2020, doi: 10.1109/TMTT.2019.2892732.
XXVII. J. Xu, F. Liu, Z. Y. Feng, and Y. F. Guo, “Diplexer-Integrated SPDT Switches with Multiple Operating Modes Using Common Fractal Stub-Loaded Resonator,” IEEE Trans. Microw. Theory Tech., vol. 69, no. 2, pp. 1464–1473, 2021, doi: 10.1109/TMTT.2020.3039603.
XXVIII. J. Xu, Z. Y. Chen, and H. Wan, “Lowpass-bandpass triplexer integrated switch design using common lumped-element triple-resonance resonator technique,” IEEE Trans. Ind. Electron., vol. 67, no. 1, pp. 471–479, 2020, doi: 10.1109/TIE.2019.2898579.
XXIX. J. Zhou, J. L. Li, C. G. Sun, H. Li, and S. S. Gao, “A novel microstrip diplexer based on coupled line,” Electromagnetics, vol. 38, no. 2, pp. 87–95, 2018, doi: 10.1080/02726343.2018.1436668.
XXX. J.-G. Liang, W.-L. Chen, and G.-M. Wang, “Harmonics suppression microstrip diplexer for 3G wireless communication system using fractal‐shaped geometry,” Microwave and Optical Technology Letters, vol. 49, no. 12, pp. 2973-2975, 2007.
XXXI. K. Al-Majdi and Y. S. Mezaal, “Microstrip diplexer for recent wireless communities,” Period. Eng. Nat. Sci., vol. 10, no. 1, pp. 387–396, 2022, doi: 10.21533/pen.v10i1.2664.

XXXII. K. D. Xu, M. Li, Y. Liu, Y. Yang, and Q. H. Liu, “Design of Triplexer Using E-Stub-Loaded Composite Right-/Left-Handed Resonators and Quasi-Lumped Impedance Matching Network,” IEEE Access, vol. 6, pp. 18814–18821, 2018, doi: 10.1109/ACCESS.2018.2819641.
XXXIII. M. A. Sazali, N. A. Shairi, and Z. Zakaria, “Hybrid microstrip diplexer design for multi-band WiMAX application in 2.3 and 3.5 GHz bands,” Int. J. Electr. Comput. Eng., vol. 8, no. 1, pp. 576–584, 2018, doi: 10.11591/ijece.v8i1.pp576-584.
XXXIV. M. Hayati, A. R. Zarghami, S. Zarghami, and S. Alirezaee, “Designing a miniaturized microstrip lowpass-bandpass diplexer with wide stopband by examining the effects between filters,” AEU – Int. J. Electron. Commun., vol. 139, p. 153912, 2021, doi: https://doi.org/10.1016/j.aeue.2021.153912.
XXXV. M. Q. Dinh and M. Thuy Le, “Triplexer-Based Multiband Rectenna for RF Energy Harvesting from 3G/4G and Wi-Fi,” IEEE Microw. Wirel. Components Lett., vol. 31, no. 9, pp. 1094–1097, 2021, doi: 10.1109/LMWC.2021.3095074.
XXXVI. P. H. Deng, S. W. Lei, W. Lo, and M. W. Li, “Novel Diplexer and Triplexer Designs Avoiding Additional Matching Circuits Outside Filters,” IEEE Access, vol. 8, pp. 14714–14723, 2020, doi: 10.1109/ACCESS.2020.2966262.
XXXVII. S. Ben Haddi, A. Zugari, and A. Zakriti, “Low Losses and Compact Size Microstrip Diplexer Based on Open-Loop Resonators with New Zigzag Junction for 5G Sub-6-GHz and Wi-Fi Communications,” Prog. Electromagn. Res. Lett., vol. 102, pp. 109–117, 2022, doi: 10.2528/PIERL21120305.
XXXVIII. S. H. Esmaeli and S. H. Sedighy, “A compact size, high isolation and low insertion loss microstrip diplexer,” J. Circuits, Syst. Comput., vol. 27, no. 13, 2018, doi: 10.1142/S0218126618502110.
XXXIX. T. H. Le, X. W. Zhu, C. Ge, and T. V. Duong, “A Novel Diplexer Integrated with a Shielding Case Using High Q -Factor Hybrid Resonator Bandpass Filters,” IEEE Microw. Wirel. Components Lett., vol. 28, no. 3, pp. 215–217, 2018, doi: 10.1109/LMWC.2018.2804174.
XL. T. Upadhyaya, J. Pabari, V. Sheel, A. Desai, R. Patel, and S. Jitarwal, “Compact and high isolation microstrip diplexer for future radio science planetary applications,” AEU – Int. J. Electron. Commun., vol. 127, 2020, doi: 10.1016/j.aeue.2020.153497.

XLI. X. Bi, Q. Ma, C. Ning, and Q. Xu, “A Compact Switchable Filtering Diplexer Based on Reused L-Shaped Resonator,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 65, no. 12, pp. 1934–1938, 2018, doi: 10.1109/TCSII.2018.2810066.
XLII. X. Guan, M. Xu, B. Ren, W. Liu, X. Zhang, and B. Zhao, “High Isolated and Wide Stopband Switchable Diplexer with Inserted Lowpass Filter,” 2020. 10.1109/CSRSWTC50769.2020.9372460.
XLIII. X. Guan, W. Liu, B. Ren, H. Liu, and P. Wen, “A Novel Design Method for High Isolated Microstrip Diplexers without Extra Matching Circuit,” IEEE Access, vol. 7, pp. 119681–119688, 2019, doi: 10.1109/ACCESS.2019.2936553.
XLIV. Y. Chu, K. Ma, and Y. Wang, “A novel triplexer based on SISL platform,” IEEE Trans. Microw. Theory Tech., vol. 67, no. 3, pp. 997–1004, 2019, doi: 10.1109/TMTT.2019.2892732.
XLV. Y. F. Tsao, T. J. Huang, H. T. Hsu, and C. W. Wu, “Planar Diplexer Design Using Hairpin Resonators Loaded with External Capacitors for Improvement of Isolation and Stopband Rejection Levels,” in 2019 49th European Microwave Conference, EuMC 2019, 2019, pp. 368–371, doi: 10.23919/EuMC.2019.8910892.
XLVI. Y. S. Mezaal and H. T. Eyyuboglu, “A new narrow band dual-mode microstrip slotted patch bandpass filter design based on fractal geometry,” in 2012 7th International Conference on Computing and Convergence Technology (ICCCT), IEEE, 2012, pp. 1180–1184.
XLVII. Y. S. Mezaal, H. H. Saleh, and H. Al-saedi, “New compact microstrip filters based on quasi fractal resonator,” Adv. Electromagn., vol. 7, no. 4, pp. 93–102, 2018.
XLVIII. Y. S. Mezaal, S. A. Hashim, A. H. Al-fatlawi, and H. A. Hussein, “New microstrip diplexer for recent wireless applications,” Int. J. Eng. Technol., vol. 7, no. 3.4 Special Issue 4, pp. 96–99, 2018, [Online]. Available: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85082370717&partnerID=40&md5=29671327ca11331ef98fa39d8d95a883.
XLIX. Y. Shi, J. Chen, and H. Xu, “Silicon-based on-chip diplexing/triplexing technologies and devices,” Science China Information Sciences, vol. 61, pp. 1-15, 2018.
L. Zhang, L., Liu, D., Jiang, H., & Dai, D. First demonstration of an on-chip quadplexer for passive optical network systems. Photonics Research, vol.9, no.5, pp.757-763, 2021.

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Abstract:

Nowadays Polymeric materials reinforced with synthetic fibers play an incredible role in almost all spheres of day-to-day life due to their elevated stiffness, outstanding strength-to-weight ratio, and electrical, thermal, and wear properties. The accumulation of micro-fillers or particulates in polymeric components reinforced with fibers made from synthetic materials may enhance their properties compared to fiber-reinforced composites. Solid particle erosion of engineering components made up of polymer composites is a major industrial problem, and it is significantly affected by the components' mechanical characteristics and their working environment. Therefore, it's essential to research the polymer composites' solid particle erosion properties. One area that has attracted less research attention is the impact of particle fillers and E-glass fiber reinforcing on erosion wear characteristics. Because of its significance to science and industry, research in this area is especially needed about particle fillers. Furthermore, to properly design a machine or structural component and use materials that will increase wear resistance, one must have a thorough grasp of how every system variable affects wear rate. In this research article, to estimate the erosion damage induced by solid particle impact on composites without conducting the experiment on an air jet erosion test rig, a theoretical model is proposed. The successful implementation of this theoretical model can reduce the experimentation cost with good quantitative accuracy.

Keywords:

Erosion,Erosion Modeling,Air-jet erosion test rig,Operating Parameters,Theoretical Model,

Refference:

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Abstract:

In order to improve the welfare of newborns, this study investigates the use of sound-recognition-based artificial intelligence (AI) approaches to the interpretation and monitoring of infant screams. Crying has long been a problem because it is the primary means of communication between infants and caregivers. The limitations of conventional interpretation techniques are discussed. These limitations include the subjective nature of interpretation and the inability to detect subtle variations in crying patterns. The goal of the research is to categorize crying patterns based on the cries of male and female infants and identify noises that are a sign of distress. The study utilized the Mel Frequency Cepstral Coefficients (MFCC) method to extract features from internet-sourced MP3 and WAV audio data. The technique successfully captured the unique qualities of each crying sound using various machine-learning models, including Random Forest and XGBoost. These models outperformed others with accuracy rates of 94.5% and 94.2%, respectively. These findings show how well these algorithms perform in correctly categorizing various newborn cries. The findings of this study establish the platform for possible Internet of Things (IoT) and healthcare framework implementations targeted at supporting parents in caring for their newborns by offering an insightful understanding of the distinctive vocalizations connected with weeping.

Keywords:

infant cry interpretation,machine learning,artificial intelligence,infant monitoring,real-time systems,privacy concerns,XGBoost,

Refference:

I. A. Bashiri and R. Hosseinkhani, : ‘Infant crying classification by using genetic algorithm and artificial neural network.’ Acta Medica Iranica, 531-539 (2020).
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Abstract:

This article provides an overview of cloud computing and fog computing, as well as a discussion of the potential applications of these technologies in Iraq. The ability of cloud computing to provide scalable and adaptable computer resources on demand has led to a significant uptick in interest in this computing model all around the world. However, fog computing improves cloud computing by moving computation to devices that are positioned on the edge of a network. This research investigates the up-to-date applications of cloud computing and fog computing in Iraq, as well as the challenges that have been faced and the potential applications of these technologies in the future, particularly in the areas of agriculture, transportation, and healthcare. The use of questionnaires in research will be the topic of discussion in this study. This is made up of two different parts that work separately. In the first part of our survey, we ask respondents questions about their level of expertise with direct and indirect cloud on object and fog computing. The remaining aspects of the investigation are dissected in Part 2 of the study. These inquiries are in accordance with concerns regarding the complexity of the implementation process, the size and culture of an organization, practicability, compliance with legislation, compatibility with current systems, and support from the government. The final open-ended inquiry of the survey will assist us in compiling a wide variety of opinions on the types of cloud-on-object and fog computing services that are required by the Iraqi government.

Keywords:

Cloud of Thing,Fog Computing,Governmental support,Administrative Informatics Sustainability,

Refference:

I. D. G. Bonett, T. A. Wright, “Cronbach’s alpha reliability: Interval estimation, hypothesis testing, and sample size planning,” Journal of Organizational Behavior 36, no. 1, pp. 3-15, 2015.
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III. F. F. S. Al-Bajjari, “A model for adopting cloud computing in government sector: Case study in Iraq” (Master’s thesis, Çankaya Üniversitesi).
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V. H. F. Atlam, R. J. Walters, & G. B. Wills, “Fog computing and the internet of things: A review,” Big Data and Cognitive Computing, vol. 2, no. 2, pp.10, 2018.
VI. J. K. Ali, Y. S. Miz’el, “A new miniature Peano fractal-based bandpass filter design with 2nd harmonic suppression,” In 2009 3rd IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications, 2009.
VII. M. Amini, A. Bakri, “Cloud computing adoption by SMEs in Malaysia: A multi-perspective framework based on DOI theory and TOE framework,” Journal of Information Technology & Information Systems Research (JITISR), vol. 9, no. 2, pp. 121-135, 2015.
VIII. M. S. Shareef, Y. S. Mezaal, N. H. Sultan, S. K. Khaleel, A. A. Al-Hillal, H. M. Saleh, … & K. Al-Majdi, “Cloud of Things and fog computing in Iraq: Potential applications and sustainability,” Heritage and Sustainable Development, vol. 5, no. 2, pp. 339-350, 2023.
IX. T. Abd, Y. S. Mezaal, M. S. Shareef, S. K. Khaleel, H. H. Madhi, & S. F. Abdulkareem, “Iraqi e-government and cloud computing development based on unified citizen identification,” Periodicals of Engineering and Natural Sciences, vol. 7, no. 4, pp. 1776-1793, 2019.
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XIV. Y. S. Mezaal, S. F. Abdulkareem, “New microstrip antenna based on quasi-fractal geometry for recent wireless systems,” In 2018 26th Signal Processing and Communications Applications Conference (SIU), 2018.

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Abstract:

This work provides a theoretical framework to investigate the shear wave propagation properties within an Electrostrictive cylindrical layered structure. The structure is made up of a concentric, Functionally Assessed Electrostrictive Material (FAEM) cylindrical layer of limited width and an inadequately bonded Electrostrictive material cylinder. The FAEM layer has a constant functional gradient in the radial direction, and flaws at the interface are taken seriously, mirroring actual circumstances involving structural and electrical degradation. The fundamental electromechanical connected Bessel's equations are used to simplify field differential equations by mathematical modifications. Relationships for shear wave propagation under electrically short and open circumstances are established analytically. The acquired findings are verified against predefined standards and a particular issue instance. The impact of variables on the phase velocity of shear waves, including functional range and imperfection parameters, is shown through numerical simulations and graphical displays. The research also establishes boundaries for electrically short and open circumstances, taking into account the shear defect that exists between the inner and outer cylindrical layers.

Keywords:

Shear Wave Propagation,Cylinder,Electrostrictive Materials,Functional Assessment,

Refference:

I. Chaudhary, S., Sahu, S.A., Singhal, A. and Nirwal, S., 2019. Interfacial imperfection study in a pres-stressed rotating multiferroic cylindrical tube with wave vibration analytical approach. Materials Research Express, 6(10), p.105704.

II. Della Schiava, N., Thetpraphi, K., Le, M.Q., Lermusiaux, P., Millon, A., Capsal, J.F. and Cottinet, P.J., 2018. Enhanced figures of merit for a high-performing actuator in electrostrictive materials. Polymers, 10(3), p.263.

III. Di Stefano, S., Miller, L., Grillo, A. and Penta, R., 2020. Effective balance equations for electrostrictive composites. Zeitschrift für angewandte Mathematik und Physik, 71, pp.1-36.

IV. Liang, C., Yaw, Z. and Lim, C.W., 2023. Thermal strain energy induced wave propagation for imperfect FGM sandwich cylindrical shells. Composite Structures, 303, p.116295.

V. Luo, H., Tao, M., Wu, C. and Cao, W., 2023. Dynamic response of an elliptic cylinder inclusion with imperfect interfaces subjected to plane SH wave. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 9(1), p.24.

VI. Manduca, A., Bayly, P.V., Ehman, R.L., Kolipaka, A., Royston, T.J., Sack, I., Sinkus, R. and Van Beers, B.E., 2021. MR elastography: Principles, guidelines, and terminology. Magnetic resonance in medicine, 85(5), pp.2377-2390.
VII. Marino, A., Genchi, G.G., Sinibaldi, E. and Ciofani, G., 2017. Piezoelectric effects of materials on bio-interfaces. ACS Applied Materials & interfaces, 9(21), pp.17663-17680.

VIII. Ming, T., Hao, L., Rui, Z. and Gongliang, X., 2023. Dynamic response of an elliptic cylinder inclusion with imperfect interfaces subjected to plane SH wave (No. EGU23-7726). Copernicus Meetings.

IX. Pankaj, K.K., Sahu, S.A. and Kumari, S., 2020. Surface wave transference in a piezoelectric cylinder coated with reinforced material. Applied Mathematics and Mechanics, 41, pp.123-138.

X. Reijmers, J.J., Kaminski, M.L. and Stapersma, D., 2022. Analytical formulations and comparison of collapse models for risk analysis of axisymmetrically imperfect ring-stiffened cylinders under hydrostatic pressure. Marine Structures, 83, p.103161.

XI. Ryu, J. and Jeong, W.K., 2017. Current status of musculoskeletal application of shear wave elastography. Ultrasonography, 36(3), p.185.

XII. Singhal, A., Baroi, J., Sultana, M. and Baby, R., 2022. Analysis of SH-waves propagating in multiferroic structure with interfacial imperfection. Mechanics Of Advanced Composite Structures, 9(1), pp.1-10.

XIII. Trujillo, D.P., Gurung, A., Yu, J., Nayak, S.K., Alpay, S.P. and Janolin, P.E., 2022. Data-driven methods for discovery of next-generation electrostrictive materials. npj Computational Materials, 8(1), p.251.

XIV. Uchino, K., 2017. The development of piezoelectric materials and the new perspective. In Advanced Piezoelectric Materials (pp. 1-92). Woodhead Publishing.

XV. Wijeyewickrema, A.C. and Leungvichcharoen, S., 2022. Effect of imperfect contact on the cloaking of a circular elastic cylinder from antiplane elastic waves. Mechanics Research Communications, 124, p.103964.

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Abstract:

Considering the basic role of numbers in Mathematics, Science, and Technology the author developed a new structure of numbers named as ‘Theory of Dynamics of Numbers.’ According to the Theory of Dynamics of Numbers, the author defined 0 (zero) is the starting point of any number and also defined 0 (zero) as a neutral number. The numbers can move in infinite directions from the starting point 0 (zero) and back to 0 (zero). The author has defined the three types of numbers: 1) Neutral Numbers, 2) Count Up Numbers, and 3) Count Down Numbers. These three types of numbers cover the entire numbers in the number system where there is no necessity for the concept of imaginary numbers. Introducing this new concept the author solved the quadratic equation in one unknown (say x) in the form ax² + bx + c = 0, even if the numerical value of the discriminant b² – 4ac < 0 in real numbers without using the concept of imaginary numbers. Already the author solved the quadratic equation x² + 1 = 0 and proved that  √ -1 = -1  by using the Theory of Dynamics of Numbers. The Theory of Dynamics of Numbers is a more powerful tool than that of the real and imaginary number system to explain the truth of nature.

Keywords:

Cartesian Coordinate System,Imaginary Numbers,Quadratic Equation,Rectangular Bhattacharyya’s Coordinate System,Theory of Numbers,Theory of Dynamics of Numbers.,

Refference:

I. Amelia Ethan. Exploring the Use of Number Theory in Modern Cryptography: Advancements and Applications. Department of Journalism, University of Harvard. July 2023. pp 1-6.
II. A. Harripersaud, (2021). The quadratic equation concept. American Journal of Mathematicsand Statistics, (11)3, 2021, 67-71.
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V. H. Lee Price, Frank R. Bernhart, : “Pythagorean Triples and a New Pythagorean Theorem”. arXiv:math/0701554 [math.HO]. 10.48550/arXiv.math/0701554
VI. Lucena, F. J. H., Díaz, I. A., Rodríguez, J. M. R., and Marín, J. A. M., Influencia del aula invertida en el rendimiento académico. Una revisión sistemática. Campus Virtuales, 8(1), p. 9-18, 2019.
VII. L. Nurul , H., D., (2017). : “Five New Ways to Prove a Pythagorean Theorem”. International Journal of Advanced Engineering Research and Science. Volume 4, issue 7, pp.132-137. 10.22161/ijaers.4.7.21
VIII. Makbule Gözde DİDİŞ KABAR. : A Thematic Review of Quadratic Equation Studies in The Field of Mathematics Education. Participatory Educational Research (PER)Vol.10(4), pp. 29-48, July 2023. 10.17275/per.23.58.10.4
IX. Manjeet Singh. Transformation of number system. International Journal of Advance Research, Ideas and Innovations in Technology. Volume 6, Issue 2 , 2020. pp 402-406. 10.13140/RG.2.2.33484.77442
X. M. Janani et al, : “Multivariate Crypto System Based on a Quadratic Equation to Eliminate in Outliers using Homomorphic Encryption Scheme”. Homomorphic Encryption for Financial Cryptography. pp 277–302. 01 August 2023. Springer
XI. M. Sandoval-Hernandez et al, : “The Quadratic Equation and its Numerical Roots”. International Journal of Engineering Research & Technology (IJERT). Vol. 10 Issue 06, June-2021 pp. 301-305. 10.17577/IJERTV10IS060100
XII. M. Sandoval-Hernandez, H. Vazquez-Leal, U. Filobello-Nino , Elisa De-Leo-Baquero, Alexis C. Bielma-Perez, J.C. Vichi-Mendoza , O. Alvarez-Gasca, A.D. Contreras-Hernandez, N. Bagatella-Flores , B.E. Palma-Grayeb, J. Sanchez-Orea, L. Cuellar-Hernandez. : The Quadratic Equation and its Numerical Roots’. IJERT. Volume 10, Issue 06 (June 2021), 301-305. 10.17577/IJERTV10IS060100
XIII. Peter Chew, : ‘Peter Chew Method for Quadratic Equation’ (2019). 2019 the 8th International Conference on Engineering Mathematics and Physics, Journal of Physics: Conference Series1411 (2019) 012003, IOP Publishing, 10.1088/1742-6596/1411/1/012003
XIV. Pieronkiewicz, B., & Tanton, J. (2019). Different ways of solving quadraticequations. Annales Universitatis Paedagogicae Cracoviensis Studia ad DidacticamMathematicae Pertinentia, 11, 103-125
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