Archive

Abstract:

Four concepts of supra fuzzy pairwise 𝑇_𝟎 bitopological spaces are introduced and studied in this paper. We also establish some relationships among them and study some other properties of these spaces.

Keywords:

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

Refference:

I. Abd EL-Monsef, M.E. and A. E. Ramadan. 1987. On fuzzy supra topological spaces. Indian J. Pure and Appl. Math. 18(4), 322-329
II. Abu Sufiya, A.S., A. A. Fora and M.W. Warner. 1994. Fuzzy separation axioms and fuzzy continuity in fuzzy bitopological spaces. Fuzzy Sets and Systems 62: 367-373.
III. Ali, D. M. A note on T0 and R0 fuzzy topological spaces, Proc. Math. Soc. B. H. U. Vol. 3, 165-167, 1987.
IV. Ali, D. M. Some remarks on α−T0, α−T1,α−T2 fuzzy topological spaces. The Journal of fuzzy Mathematics, Los Angeles, Vol. 1, No. 2, 311-321, 1993.
V. Amin, R.M., Ali, D. M., Hossain, M. S. On T0 fuzzy bitopological spaces. Journal of Bangladesh Academy of Sciences, Vol. 38, No. 2, 209-217, 2014.
VI. Azad, K. K. 1981. On Fuzzy semi-continuity, Fuzzy almost continuity an fuzzy weakly continuity. J. Math. Anal. Appl. 82(1): 14-32.
VII. Chang, C. L. 1968. Fuzzy topological spaces . J. Math. Anal. Appl. 24: 182- 192.
VIII. Hossain, M. S. and Ali, D. M. On T0 fuzzy topological spaces, J. Math and Math. Sci. Vol. 24, 95-102, 2009.
IX. Hossain, M. S. and Ali, D. M. On T1 fuzzy topological spaces, Ganit.J. Math and Math. Sci. Vol. 24, 99-106, 2004.
X. Kandil, A. and M. EL-Shafee, 1991. Separation axioms for fuzzy bitopological spaces. J. Ins. Math. Comput. Sci. 4(3): 373-383.
J. Mech. Cont.& Math. Sci., Vol.-15, No.-11, November (2020) pp 1-11
MD. Hannan Miah et al
11
XI. Kandil, A., A.A. Nouh and S. A. El-Sheikh. 1999. Strong and ultra separation axioms on fuzzy bitopological spaces. Fuzzy Sets and Systems. 105: 459-467.
XII. Lowen, R. 1976. Fuzzy topological spaces and fuzzy compactness. J. Math. Anal. Appl. 56: 621-633.
XIII. Mashour, A. S. ,Allam, A.A., Mahmoud, F. S. and Khedr, F. H. 1983: On supra topological spaces, Indian J. Pure and Appl. Math. 14(4), 502-510
XIV. Mukherjee, A. Completely induced bifuzzy topological spaces, Indian J. pure App. Math,. 33(6)(2002), 911-916.
XV. Nouh, A. A. on separation axioms in fuzzy bitopological spaces, Fuzzy sets and systems, 80 (1996), 225-236.
XVI. Srivastava, A. K. and Ali, D. M. A comparison of some FT2 concepts, Fuzzy sets and systems 23, 289-294, 1987.
XVII. Wong, C. K. Fuzzy points and local properties of Fuzzy topology; J. Math. Anal. Appl. 46:316-328,1974.
XVIII. Wong , C.K . Fuzzy topology: Product and quotient theorem, J. Math. Anal., 45(1974), 512-521.
XIX. Zadeh, L. A. 1965. Fuzzy sets. Information and Control 8: 338-353.

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Abstract:

In this paper, a transversal vibration of an axially moving beam under the influence of viscous damping has been studied. The axial velocity of the beam is assumed to be positive, constant and small compared to wave-velocity. The beam is moving in a positive horizontal direction between the pair of pulleys and the length between the two pulleys is fixed. From a physical viewpoint, this model describes externally damped transversal motion for a conveyor belt system. The beam is assumed to be externally damped, where there is no restriction on the damping parameter which can be sufficiently large in contrast to much research material. The straightforward expansion method is applied to obtain approximated analytic solutions. It has been shown that the obtained solutions have not been broken out for any parametric values of the small parameter 𝜀. The constructed solutions are uniform and have been damped out. Even though there are several secular terms in the solutions, but they are small compared to damping.

Keywords:

Moving beam,Viscous Damping,Secular terms,Eigen functions,Straight-forward expansion method,

Refference:

I. A. Maitlo, S. Sandilo, A. H. Sheikh, R. Malookani, and S. Qureshi, “On aspects of viscous damping for an axially transporting string,” Sci. int. (Lahore)., Vol. 28, No. 4, pp. 3721–3727, (2016).
II. Darmawijoyo, W. T. van Horssen, and P. Clément, “On a Rayleigh wave equation with boundary damping,” Nonlinear Dyn., Vol. 33, No. 4, pp. 399–429, (2003).
III. K. Marynowski and T. Kapitaniak, “Zener internal damping in modelling of axially moving viscoelastic beam with time-dependent tension,” Int. J. Non. Linear. Mech., Vol. 42, No. 1, pp. 118–131, ( 2007)
J. Mech. Cont.& Math. Sci., Vol.-15, No.-11, November (2020) pp 12-22
Khalid H. Malik et al
22
IV N. Gaiko, “On transverse vibrations of a damped traveling string with boundary damping”. ENOC 2014.
V R. A. Malookani, S. Dehraj, and S. H. Sandilo, “Asymptotic approximations of the solution for a traveling string under boundary damping,” J. Appl. Comput. Mech., Vol. 5, No. 5, pp. 918–925, (2019)
VI S. Dehraj, R. A. Malookani, and S. H. Sandilo, “On Laplace transforms and (in) stability of externally damped axially moving string”. Journal of Mechanics of Continua and Mathematical Sciences., Vol. 15, No. 8, pp. 282–298, (2020).
VII. S. H. Sandilo and W. T. van Horssen, “On Boundary Damping for an Axially Moving Tensioned Beam,” J. Vib. Acoust., Vol. 134, No. 1, (2011).
VIII. S. H. Sandilo, R. A. Malookani, and A. H. Sheikh, “On vibrations of an axially moving beam under material damping,” IOSR J. Mech. Civ. Eng., Vol. 13, No. 05, pp. 56–61.
IX. Sunny Kumar Aasoori, Rajab A. Malookani, Sajad H. Sandilo, Sanaullah Dehraj, A.H. Sheikh, : ON TRANSVERSAL VIBRATIONS OF AN AXIALLY MOVING STRING UNDER STRUCTURAL DAMPING, J. Mech. Cont. & Math. Sci., Vol.-15, No.-8, August (2020) pp 93-108.
X. T. Akkaya and W. T. van Horssen, “On the transverse vibrations of strings and beams on semi-infinite domains,” Procedia IUTAM, Vol. 19, pp. 266–273, (2016).
XI. W. T. Van Horssen, “On the weakly damped vibrations of a string attached to a spring-mass -dashpot system,” J. Vib. Control., Vol. 9, No. 11, pp. 1231–1248, (2003).

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Abstract:

This research analyzes the design and simulation of a mobile robot using Extended Kalman Filter (EKF) and Unscented Kalman filter (UKF). The mobile platform has a differential configuration, where each track of a wheel is associated with an encoder. The EKF and UKF methods are used to integrate the measurements of a novel odometric system based on the optical mice and the measurements of a localization system based on a map of geometric beacons. Two different types of simulations have been performed for validating the results, either using the mouse-based odometric system or using the conventional wheel encoder-based odometric system, to compare and evaluate the errors made by each system.

Keywords:

Extended Kalman Filter,Unscented Kalman Filter,localization, odometry,encoder,optical mouse sensor,

Refference:

I. Antonelli,G. and S.Chiaverini,. Linear estimation of the physical odometric parametric parameters for differential-drive mobile robots. Springer Netherlands, Auton Robots, 23:59-68. 2007.
II. B. Subhojyoti, K. Amit, and P. Gupta, “On the noise and power performance of a shoe-mounted multi-IMU inertial positioning system,” in Proceedings of the International Conference on Indoor Positioning and Indoor Navigation (IPIN 2017), Sapporo, Japan, September 2017.
III. Cui, M., Liu, W., Liu, H., et al.: Extended state observer-based adaptive sliding mode control of differential-driving mobile robot with uncertainties. Nonlinear Dyn. 83(1–2), 667–683 (2016)
IV. Chen, X. et al. A novel UKF based scheme for GPS signal tracking in high dynamic environment. Proc. of 3rd International Symposium on Systems and Control in Aeronautics and Astronautics (ISSCAA), Harbin, 2010, pp. 202-206.
V. Cimino, Mauro, and Prabhakar R. Pagilla. “Location of optical mouse sensors on mobile robots for odometry.” 2010 IEEE International Conference on Robotics and Automation. IEEE, 2010.
VI. Denis F. Wolf, Gaurav S. Sukhatme, “Mobile robot simultaneous localization and mapping in dynamic environments,” Autonomous Robots, vol. 19, no. 1, pp. 53-65, July 2005.
VII. Dahmen, H.; Mallot, H.A. Odometry for ground moving agents by optic flow recorded with optical mouse chips. Sensors 2014, 14, 21045–21064.
VIII. Dong, W.: Tracking control of multiple-wheeled mobile robots with limited information of a desired trajectory. IEEE Trans Robot. 28(1), 262–268 (2012)
IX. Doh NL, Choset H and Chung WK . “Relative localization using path odometry information”, Autonomous Robots. 21: 143-154.(2006)
X. F. Wang, Y. Lin, T. Zhang, and J. Liu, “Particle filter with hybrid proposal distribution for nonlinear state estimation,” Journal of Computers, vol. 6, no. 11, pp. 2491–2501, 2011.
XI. Houshangi, Nasser, and Farouk Azizi. “Mobile Robot Position Determination Using Data Integration of Odometry and Gyroscope.” 2006 World Automation Congress.
XII. Iman Abdalkarim Hasan, Nabil Hassan Hadi, : ADAPTIVE PI-SLIDING MODE CONTROL OF NON-HOLOMONIC WHEELED MOBILE ROBOT, J. Mech. Cont.& Math. Sci., Vol.-15, No.-2, February (2020) pp 236-25.
XIII. Kim, S.; Lee, S. Robust velocity estimation of an omnidirectional mobile robot using a polygonal array of optical mice. In Proceedings of the IEEE International Conference on Information and Automation, Changsha, China, 20–23 June 2008; pp. 713–721.
XIV. Lee D and Chung W (2006) Discrete-Status-Based Localization for Indoor Service Robots, IEEE Transactions on Industrial Electronics. 53: 1737-1746.
XV. Lee, Wei-chen, and Cong-wei Cai. “An orientation sensor for mobile robots using differentials.” International Journal of Advanced Robotic Systems 10.2 (2013): 134.
XVI. Pozna, C., Troester, F., Precup, R.-E., Tar, J.K., Preitl, S.: On the design of an obstacle avoiding trajectory: method and simulation. Math. Comput. Simul. 79(7), 2211–2226 (2009).
XVII. Rao S K, Kumar D V A N R and Raju K P 2013 Combination of pseudo-linear estimator and modified gain bearings-only extended Kalman filter for passive target tracking in abnormal conditions. Ocean Electron. (SYMPOL) p 3–8.
XVIII. Sousa, A.j., P.j. Costa, A.p. Moreira, and A.s. Carvalho. “Self Localization of an Autonomous Robot: Using an EKF to Merge Odometry and Vision Based Landmarks.” 2005 IEEE Conference on Emerging Technologies and Factory Automation.
XIX. S. Kosanam and D. Simon, “Kalman filtering with uncertain noise covariances,” in Proceedings of the Intelligent Systems and Control (ISC ’04), pp. 375–379, Honolulu, Hawaii, USA, 2004.
XX. Tovar, Benjamin, and Todd Murphey. “Trajectory Tracking among Landmarks and Binary Sensor-beams.” 2012 IEEE International Conference on Robotics and Automation (2012)
XXI. TesliÄ , Luka, Igor Å krjanc, and Gregor KlanÄ ar. “EKF-Based Localization of a Wheeled Mobile Robot in Structured Environments.” Journal of Intelligent & Robotic Systems 62.2 (2010):187-203.
XXII. Ullah, I., Ullah, F., Ullah, Q., Shin, S.: Integrated tracking and accident avoidance system for mobile robots. Int. J Integrated Control Autom. Syst. 11(6), 1253–1265 (2013)
XXIII. Uyulan, C., Erguzel, T. and Arslan, E., 2017, September. Mobile robot localization via sensor fusion algorithms. In 2017 Intelligent Systems Conference (IntelliSys) (pp. 955-960). IEEE.
XXIV. Wang, Z.P., Ge, S.S., Lee, T.H.: Adaptive neural network control of a wheeled mobile robot violating the pure nonholonomic constraint. In: Proceeding of the IEEE International Conference on Decision and Control, p. 51985203 (2004).
XXV. Younus Kawther K, Nabil H Hadi, : OPTIMUM PAATH TRACKING AND
CONTROL FOR A WHEELED MOBILE ROBOT (WMR), J. Mech. Cont.& Math. Sci., Vol.-15, No.-1, January (2020) pp 73-95.

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Abstract:

In this paper, carrier's generation-based graphene with applicability for wavelength division multiplexing (WDM) systems have been produced via an illumination of graphene by 980 nm. This technique allowed for servicing of a greater number of channels in a WDM system, and the carriers were able to travel in an optical channel with high data rate. Eight carriers, having a frequency spacing (FS) of 25 GHz and full-width at half-maximum (FWHM) of 500 MHz, were created. These generated carriers were separately modulated with eight optical quadrature phase shift keying (QPSK) signals and subsequently optically multiplexed and transmitted to an optical fiber channel. At the receiver side, the received signal was demultiplexed, and the performance of the system was analyzed via calculating the error vector magnitude and constellation diagram of the entire system. Opti System version 17.1 and Matlab software are used for demonstration of WDM system and carrier generation.

Keywords:

WDM system,Graphene-based carrier,Frequency spacing (FS),Quadrature phase shift keying (QPSK),Error vector magnitude (EVM),Eye diagram,

Refference:

I. Amulya Boyina, Praveen Kumar Kancherla, : Active Coplanar Wave guide Fed Switchable Multimode Antenna Design and Analysis, J. Mech. Cont.& Math. Sci., Vol.-14, No.-4, July-August (2019) pp 188-196.
II. A. Bekkali, C. Ben Naila, K. Kazaura, K. Wakamori, and M. Matsumoto, “Transmission analysis of OFDM-based wireless services over turbulent radio-on-FSO links modeled by Gamma-Gamma distribution,” IEEE Photonics J., vol. 2, no. 3, pp. 510–520, Jun. 2010.
III. A. Hammoodi, L. Audah, and M. A. Taher, “Green Coexistence for 5G Waveform Candidates: A Review,” IEEE Access, vol. 7, pp. 10103-10126, 2019
IV. A. Hraghi, M. E. Chaibi, M. Menif, and D. Erasme, “Demonstration of 16QAM-OFDM UDWDM transmission using a tunable optical flat comb source,” journal of lightwave technology, vol. 35, pp. 238-245, 2016
V. A. M. Jaradat, J. M. Hamamreh, and H. Arslan, “Modulation Options for OFDM-Based Waveforms: Classification, Comparison, and Future Directions,” IEEE Access, vol. 7, pp. 17263-17278, 2019
VI. A. Mostafa and S. Hranilovic, “In-field demonstration of OFDM-over-FSO,” IEEE Photon. Technol. Lett., vol. 24, no. 8, pp. 709–711, Apr. 2012.
VII. Al Naboulsi M, Sizun H, De Fornal F. Fog attenuation prediction for optical and infrared waves. Opt Eng. 2004;43(2):319–29.
VIII. Amphawan A, Chaudhary S, Chan V. 2 × 20 Gbps-40 GHz OFDM Ro-FSO transmission with mode division multiplexing. J Eur Opt Soc-Rapid Public. 2014;9:14041.
IX. Amphawan A, Chaudhary S, Chan VWS. 2 × 20 Gbps-40 GHz OFDM Ro-FSO transmission with mode division multiplexer. Europ Opt Soc Rap Public. 2014;9:14041.
X. C. B. Naila, K. Wakamori, M. Matsumoto, A. Bekkali, and K. Tsukamoto, “Transmission analysis of digital TV signals over a radio-on-FSO channel,” IEEE Commun. Mag., vol. 50, no. 8, pp. 137–144, Aug. 2012.
XI. Chaudhary S, Amphawn A. 4 × 2.5Gbps=10Gbps RO-FSO transmission system by incorporating hybrid WDM-MDM of spiral phased LG-HG Modes. International Conference on internet applications, protocols and services, 978-967-0910-06-2. 2015.
XII. CH. S. N. Sirisha Devi, B. Vijayakumar, Sudipta Ghosh, : CACHING AND NETWORK RELATED SOLUTIONS FOR: 4G TO 5G TECHNOLOGY IN WIRELESS COMMUNICATIONS, J.Mech.Cont.& Math. Sci., Vol.-14, No.2, March-April (2019) pp 402-426
XIII. E. Wong, “Next-generation broadband access networks and technologies,” J. Lightwave Technol., vol. 30, no. 4, pp. 597–608, Feb. 2012.
XIV. Foschini GJ. Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas. Bell Labs Tech J. 1996;1:41–59.
XV. Gupta MS. What is RF? Microwave Magazine, IEEE. 2002 August 6;12:16.10.
XVI. Haykin S. Communication system, 4th, 2000. “Pass Band Data Transmissions”, McMaster University, John Wiley & Sons, Inc., “PassBand Data Transmissions”, chapter 6, ISBN 0-471-17869-1.
XVII. K. Kazaura et al., “RoFSO: A universal platform for convergence of fiber and free-space optical communication networks,” IEEE Commun. Mag., vol. 48, no. 2, pp. 130–137, Feb. 2010.
XVIII. K. Mori, H. Takara, and S. Kawanishi, “Analysis and design of supercontinuum pulse generation in a single-mode optical fiber,” J. Opt. Soc. Amer. B, vol. 18, no. 12, pp. 1780–1792, 2001
XIX. M. Matsumoto et al., “Experimental investigation on a radio-on-free-space optical system suitable for provision of ubiquitous wireless services,” PIERS Online, vol. 6, no. 5, pp. 400–405, 2010.
XX. M. S. Chowdhury, M. Kavehrad, W. Zhang, and P. Deng, “Combined CATV and very-high-speed data transmission over a 1550-nm wavelength indoor optical wireless link,” in Proc. SPIE OPTO, 2014, Art ID. 901009.
XXI. N. Madamopoulos et al., “Applications of large-scale optical 3D-MEMS switches in fiber-based broadband-access networks,” Photon. Netw. Commun., vol. 19, no. 1, pp. 62–73, Feb. 2010.
XXII. Polla DL, Wolfson MB, “RF MEMS integration present & futuretrends”, Radio-Frequency Integration Technology, RFIT, 2009.
XXIII. Refa HH, SIuss JJ, Jr., Refai HH, “The transmission of multiple RF signals in free-space optics using wavelength division multiplexing” Proceedings of SPIE Vol 0.5793, 2005.
XXIV. S. E. Alavi et al., “W-band OFDM for radio-over-fibre direct-detection link enabled by frequency nonupling optical upconversion,” IEEE Photon. J., vol. 6, no. 6, Dec. 2014, Art ID. 7903908.
XXV. Wake D, Nkansh A, Gomes NJ, Senior Member IEEE. Radio over fiber link design for next generation wireless systems. J Light Wave Technol. 2010;28(16):2456–64.

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Abstract:

Pervious concrete technology is a special and reliable way of fulfilling increasing specifications for the climate. Pervious concrete is important in restoring groundwater, minimize erosion and converging flood water by absorbing rainwater and allowing it to seep through the land. Pervious concrete is comprised of coarse aggregate, Portland cement and chemical admixtures and is a building substance. It is somewhat different from standard concrete since there are little to no fine aggregates. The main objective of this project work is to study the densification and splitting tensile strength with the infiltration rate of pervious concrete. Also to do water quality test of rainwater after passing from 3 inches of the charcoal layer. The results concluded Compressive and splitting stability of Pervious concrete shows an extensive increment in strength when 2% of Ta titanium Dioxide is replaced by cement at the curing age of 7, 14 and 28 days.  At 28 Days mean compressive and splitting tensile strength (Having Strength Enhancement Admixture) comes up to be 2104.5psi and 531.4 psi respectively which is considerable for Pervious concrete.  From the infiltration rate test it can be concluded that as the percentage of gravel increases in the concrete mix, the permeability or infiltration rate increases. Infiltration rate ranges from 838.5 in/hr to 927.8 in/hr for the two concrete mixes M1 (1:0:2.5) and M2 (1:0:3) respectively. From the water quality test it can be concluded that when rainwater is passed from a 3inches layer of charcoal the PH value increase from 4.47 to 5.77 which can be used for cleaning and bathing in our houses. Hence it is recommended that 100% reduction of sand from concrete give significant mechanical strength and an increase of infiltration rate can be proposed for the roadway of parking and walking track. Also after passing rainwater from 3 inches layer it can be recommended for cleaning and Bathing Purposes.

Keywords:

Pervious concrete,strength enhancement admixture,Full sand Reduction,Mechanical Properties,Infiltration Rate test,Rainwater,water quality test using charcoal,

Refference:

I. A. Nagaraju, S.Vijaya Bhaskar Reddy, : EFFECT OF BINDER CONTENT ON SUPER PLASTICIZER DOSAGE FOR SELF-COMPACTING CONCRETE, J. Mech. Cont.& Math. Sci., Vol.-15, No.-4, April (2020) pp 36-46
II. Adil Afridi, Atif Afridi, Farhan Zafar, : A REVIEW OF PERVIOUS CONCRETE PAVEMENT & TEST ON GEO TEXTILE, J. Mech. Cont.& Math. Sci.,Vol.-13, No.-5, November-December (2018) pp 114-126 .
III. Anderson, I.A., Suozzo, M. and Dewoolkar, M. M. (2013). “Laboratory & Field Evaluations of Pervious Concrete.” Transportation Research Center, University of Vermont.
IV. Ajamu, S.O., Jimoh, A.A. and Oluremi, J.R. (2012). “Evaluation of Structural Performance of Pervious Concrete in Construction.” International Journal of Engineering and Technology, 2(5), 829-836.
V. Arhin, S.A., Madhi, R. and Khan, W. (2014). “Optimal Mix Designs for Pervious Concrete for an Urban Area.” International Journal of Engineering Research & Technology, 3(12), 4250.
VI. Balaji, M.H., Amarnaath, M.R., Kavin, R.A. and Pradeep, S. J. (2015). “Design of Eco Friendly Pervious Concrete.” International Journal of Civil Engineering and Technology, 6(2), 22-29.
VII. Chopra, M. and Wanielista, M. (2007). “Performance Assessment of Portland Cement Pervious Pavement.” Stormwater Management Academy, University of Central Florida.
VIII. Crouch, L. K., Cates, M. A., Dotson, V., J., Honeycutt, K. R., and Badoe, D. A. (2003) “Measuring the Effective Air Void Content of Portland Cement Pervious Pavements.” Cement, Concrete and Aggregates, 25(1), 16-20.
IX. Crouch, L. K., Pitt, J., and Hewitt, R. (2007). “Aggregate Effects on Pervious Portland cement Concrete Static Modulus of Elasticity.” Journal of Materials in Civil Engineering, 19(7), 561-568.
X. Ghafoori, N. (1995). “Development of No-Fines Concrete Pavement Applications.” Journal of Transportation Engineering, 126(3), 283-288.
XI. Ghafoori, N., and Dutta, S. (1995). “Laboratory Investigation of Compacted No-Fines Concrete for Paving Materials.” Journal of Materials in Civil Engineering, 7(3), 183-191
XII. Jain, A.K. and Chouhan, J.S. (2011). “Effect of Shape of Aggregate on Compressive Strength and Permeability Properties of Pervious Concrete.” International Journal of Advanced Engineering Research and Studies, 1(1), 120-126.
XIII. McCain, G. N. and Dewoolkar, M. M. (2009). “Porous Concrete Pavements: Mechanical and Hydraulic Properties.” School of Engineering, University of Vermont.
XIV. McCain, G.N. and Dewoolkar, M.M. (2010). “A Laboratory study on the effect of winter surface application on the hydraulic conductivity of porous concrete pavements.” TRB Annual Meeting, CD-ROM., Washington D.C.
XV. McCain, G. N. and Dewoolkar, M. M. (2009). “Strength and Permeability Characteristics of Porous Concrete Pavements.” School of Engineering, University of Vermont.
XVI. Neptune, A.I. (2008). “Investigation of the Effects of Aggregate Properties and Gradation on Pervious Concrete Mixtures.” Final Report, Civil Engineering, Clemson University.
XVII. Offenberg, M. (2005) “Producing Pervious Pavements.” Concrete International, 50-54.
XVIII. Patil, P. and Murnal, S.M. (2014). “Study on the Properties of Pervious Concrete.” International Journal of Engineering Research & Technology, 3(5), 819-822.
XIX. Schaefer, V., Wang, K., Suleimman, M. and Kevern, J. (2006). “Mix Design Development for Pervious Concrete in Cold Weather Climates.” Final Report, Civil Engineering, Iowa State University.
XX. Shah, D.S., Pitroda, J. and Bhavsar, J.J. (2013). “Pervious Concrete: New Era for Rural Road Pavement.” International Journal of Engineering Trends and Technology, 4(8), 3495-3499.
XXI. Singer, D.F. (2012). “An Examination of the Influence of Cement Paste on Pervious Concrete Mixtures.” Final Report, Civil Engineering, Clemson University.
XXII. Sriravindrarajah, R., Wang, N.D.H. and Ervi, L.J.W. (2012). “Mix Design for Pervious Recycled Aggregate Concrete.” International Journal of Concrete Structures and Materials, 6(4), 239-246.
XXIII. Tennis, P. D., Leming, M. L., and Akers, D. J. (2004) “Pervious Concrete Pavements,” Portland Cement Association, Skokie, Illinois, and National Ready Mixed Concrete Association, Silver Spring, Maryland.

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Abstract:

The permeability of the soil is one of the most important properties of an unlined earthen canal or river bed. Using fine plastic particles has experimentally proven to reduce soil permeability, but the experimental study of the effect of a variety of types of plastic fines and their percentages in riverbed soil is tedious work to do. Estimation of permeability of riverbed soil by altering it with plastic fines using Artificial Neural Networks (ANNs) may reduce this effort. Particle size distributions (PSDs) have a significant influence on the permeability of bed soils. Being able to predict the permeability of bed soil by knowing the PSDs may provide an easy approach to know the loss of water by percolation. This study has investigated the quantitative relationships between permeability and PSD indices using ANNs. The aim was to build a mathematical model capable of predicting the permeability of bed soil by PSD indices of choice. A model was built using ANNs including PSD indices as input and permeability as output. The model stated that the coefficients of curvature and uniformity (C_c) and (C_u) and effective particle size (D₅₀) may be used to predict the bed permeability. The computational model was able to predict the effect of variation of PSD indices on bed permeability, thus allowing increasing the efficiency of the river bed, to ensure maximum downstream water supply, lesser seepage and percolation and better productivity. The test result has confirmed the efficiency of the developed ANN tool in predicting the bed permeability for different PSD combinations.

Keywords:

River,permeability,plastic fines,neural network,

Refference:

I. Abdul Farhan, Farman Ullah, Fawad Ahmad, Mehr E Munir, : Effect of Thin Layer on Bearing Capacity in Layered Profile Soil, J. Mech. Cont.& Math. Sci., Vol.-14, No.-3, May-June (2019) pp 597-608.
II. Alyamani, M. S. and Şen, Z. (1993) ‘Determination of Hydraulic Conductivity from Complete Grain-Size Distribution Curves’, Ground Water. Blackwell Publishing Ltd, 31(4), pp. 551–555. doi: 10.1111/j.1745-6584.1993.tb00587.x.
III. Amini, M. et al. (2005) ‘Neural network models to predict cation exchange capacity in arid regions of Iran’, European Journal of Soil Science. Blackwell Science Ltd, 56(4), pp. 551–559. doi: 10.1111/j.1365-2389.2005.0698.x.
IV. Arkin, H. and Colton, R. R. (1956) Statistical Methods, 4th Edition. New York: Barnes and Noble Inc.
V. ASTM D854-14 (2014), “Standard Test Methods for Specific Gravity of Soil Solids by Water Pycnometer,” ASTM International, West Conshohocken, PA, 2014, 10.1520/D0854-14,www.astm.org
VI. ASTM D698-12 (2012), “Standard Test Methods for Laboratory Compaction Characteristics of Soil Using Standard Effort (12 400 ft-lbf/ft3 (600 kN-m/m3)),” ASTM International, West Conshohocken, PA, 2012, 10.1520/D0698-12E02, www.astm.org
VII. ASTM D422-63 (2007), “Standard Test Method for Particle-Size Analysis of Soils,” ASTM International, West Conshohocken, PA, 2007, 10.1520/D0422-63R07, www.astm.org
VIII. ASTM D4318-17 (2017), “Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils,” ASTM International, West Conshohocken, PA, 2017, 10.1520/D4318-17,www.astm.org
IX. ASTM D2434-68 (2006), “Standard Test Method for Permeability of Granular Soils (Constant Head) (Withdrawn 2015),” ASTM International, West Conshohocken, PA, 2006, 10.1520/D2434-68R06,www.astm.org
X. ASTM D5084-16a, (2016a), “Standard Test Methods for Measurement of Hydraulic Conductivity of Saturated Porous Materials Using a Flexible Wall Permeameter,” ASTM International, West Conshohocken, PA, 2016, 10.1520/D5084-16A,www.astm.org
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XVI. Hazen, A. (1892) Some Physical Properties of Sands and Gravels: With Special Reference to Their Use in Filtration. Available at: https://books.google.com.pk/books?id=DW1cGwAACAAJ.
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XXIX. Sarmadian, F., Mehrjardi, R. T. and Akbarzadeh, A. (2009) ‘Modeling of Some Soil Properties Using Artificial Neural Network and Multivariate Regression in Gorgan Province, North of Iran’, Australian Journal of Basic and Applied Sciences, 3(1), pp. 323–329.
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XXXII. Tizpa, P. et al. (2015) ‘ANN prediction of some geotechnical properties of soil from their index parameters’, Arabian Journal of Geosciences, 8(5), pp. 2911–2920. doi: 10.1007/s12517-014-1304-3.
XXXIII. Von Twickel, A., Büschges, A. and Pasemann, F. (2011) ‘Deriving neural network controllers from neuro-biological data: implementation of a single-leg stick insect controller’, Biological Cybernetics, 104(1), pp. 95–119. doi: 10.1007/s00422-011-0422-1.
XXXIV. Xing, L., & Pham, D. T. (1995), Neural networks for identification, prediction, and control. New York: Springer-Verlag New York, Inc.

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Abstract:

Numerical modeling of brick masonry behaviour under different performance conditions has always remained a challenging task. Several modeling strategies have been developed for masonry, in general, through the course of time that have been simplified to speed up modeling and analysis duration. This ranges from a simplified strut model to a highly discontinuous micro-scale nonlinear model. With the current advent of high-speed computing and modeling tools, more realistic numerical modeling of masonry is now possible. In this paper, the strategy adopted is based on macro-scale modeling, where isotropic material properties are considered for the homogenous continuum. ABAQUS is used as a state-of-the-art finite element-based analysis and modeling tool. The Concrete Damage Plasticity (CDP) model is used for simulating inelastic material behaviour of brick and mortar, which is available in the ABAQUS library. This material model can be used in both implicit and explicit schemes of integration but the explicit procedure is highly preferred as it overcomes the convergence issues. Various parameters required for CDP modeling of brick and mortar are adapted from literature. The model is assembled in two parts, first part is modeled for masonry with both elastic and plastic properties, while the other part simulates a rigid beam at the top of the masonry part to create a uniform in-plane shear loading effect. The masonry part has been fixed at the bottom with free vertical ends, while horizontal in-plane displacement was applied to the top rigid beam. The load-displacement curves were generated from these models for monotonic push, to compare them with the envelopes of experimental results, loaded similarly. Since brick masonry is a highly disjointed material, it is a complicated procedure to develop an exact model and predict its exact behaviour. However, the overall representative load-displacement curve developed numerically was in good agreement with the ones produced experimentally.

Keywords:

Macro-Scale,Masonry,Numerical Model,Squat Pier,Tension Stiffening,

Refference:

I. ABAQUS, (2016). “Analysis User’s Guide”, Version 6.8, Hibbitt, Karls-son & Sorensen, Inc., Pawtucket, Rhode Island, USA.
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III. ABAQUS, (2016). Analysis Example Manual, Version 6.8, Hibbitt, Karls-son & Sorensen, Inc., Pawtucket, Rhode Island, USA.
IV. Aref A.J., Dolatshahi K.M., (2013) “A three-dimensional cyclic meso-scale numerical procedure for simulation of unreinforced masonry structures”, Computers and Structures 120: 9-27.
V. Brencich A., Lagomarsino S., (1998) “A macro element dynamic model for masonry shear walls” in Pande G. et al. (ed), Computer methods in structural masonry 4. London: E&FN Span; 67-75.
VI. Backes, H. P. (1985), “Behaviour of Masonry Under Tension in the Direction of the Bed Joints”, Ph.D. thesis, Aachen University of Technology, Aachen, Germany.
VII. Belardi, A. Zhang, L. and Thomas, T.C. (1996), “Constitutive Laws of Reinforced Concrete Membrane Elements”. The 11th World Conference on Earthquake Engineering, paper No. 1208.
VIII. Calderon B., Marone P., Pagano M., (1987) “Modelli perrla verifica static degli edifici in Murature in Zona sismica”, Ingegneria sismica, n.3, pp. 19-27.
IX. Dolatshahi K.M., Aref A.J., (2011) “Two-Dimensional computational framework of meso-scale rigid and line interface elements for masonry structures”, Engineering Structures 33: 3657-67.
X. Grecchi G., (2010) “Material and structural behaviour of masonry: Simulation with a commercial code”, Master’s Dessertation, Alme Ticinensis Universitas, Universita di Pavia.
XI. Gambarotta L., Lagomarsino S., (1997) “Dynamic response of masonry panels” in Gambarotta L. (ed), Proc. of the National Conferenche “La meccanica delle murature tra teoria e progetto”, Messina (in Itallian).
XII. Ghiassi, B. Soltani, M. and Tasnimi, A.A. (2012), “A Simplified Model for Analysis of Unreinforced Masonry Shear Walls Under Combined Axial, Shear and Flexural Loading”, The International Journal of Engineering Structures, Elsevier, Volume 42, September 2012, Pages 396–409
XIII. Hemant B, Kaushik, Rai D.C., and Jain S.K., (2007), “Uniaxial Compressive Stress-Strain Model for Clay Brick Masonry”, Current Science, 92(4), Indian Academy of Sciences, Bangalore, India, 25 February 2007, pp. 497-501.
XIV. Javed M., (2006), “Seismic Risk Assessment of Unreinforced Brick Masonry Buildings System of Northern Pakistan”, Ph.D. Thesis, University of Engineering and Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan
XV. Lourenco P., (1996) “Computational strategies for masonry structures”, Ph.D. Dissertation, Netherlands: Delft University.
XVI. Masood Fawwad , Asad-ur-Rehman Khan, : Behaviour of Full Scale Reinforced Concrete Beams Strengthened with Textile Reinforced Mortar (TRM), J. Mech. Cont. & Math. Sci., Vol.-14, No.-3, May-June (2019) pp 65-82.
XVII. Mohammad Khaki, : Effect of Infilled Frame on Seismic Performance of Concrete Moment-Resisting Frame Buildings, J. Mech. Cont. & Math. Sci., Vol.-14, No.-4, July-August (2019) pp 466-480.
XVIII. Page A.W., (1978) “Finite element model for masonry”, J. Structure Div ASCE; 104(8): 1267-85.
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XXIV. van Noort J.R., (2012), “Computational Modeling of Masonry Structures”, Master thesis, Delft University of Technology, Delft, The Netherlands.
XXV. Van der Mersch, W. A. (2015), “Modeling the seismic response of an unreinforced masonry structure”, M.Sc. thesis, Delft University of Technology.

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Abstract:

Smart and cost-effective solutions for water quality monitoring are gaining attention with the recent advancement in information and communication system technology.  This paper aims at the design and development of the internet of things (IoT) based low-cost and portable water quality and quantity monitoring (WQQM) system. The proposed system not only monitors the water quality but also monitors the amount of water being utilized by the consumer. The main objective of designing WQQM is to ensure both purity and conservation of water. The water quality meter measures six qualitative parameters of water viz. potential hydrogen (pH), water temperature, atmospheric temperature, turbidity, and total dissolved solids (TDS). Whereas, the water quantity meter measures the water level and water flow to calculate the amount of water being used.  A custom printed circuit board (PCB) is designed to integrate all the sensors for quality and quantity measurement. The results generated by the WQQM system are wirelessly transferred, using Wi-Fi, to the online monitoring system.

Keywords:

IoT,water quality,water quantity,TDS,pH,turbidity,

Refference:

I. Ahmad Bilal, Ameer Hamza, Sheeraz Ahmed, Zeeshan Najam, Atif Ishtiaq, : Synthesis and Characterization of PMMA Nanofibers for Filtration of Drinking Water, J. Mech. Cont.& Math. Sci., Vol.-14, No.-4, July-August (2019) pp 102-116.
II. A.S. Rao, S. Marshall, J. Gubbi, M. Palaniswami, R. Sinnott, V. Pettigrove, “Design of Low-cost Autonomous Water Quality Monitoring System”, International Conference on Advances in Computing, Communications and Informatics (ICACCI), 2013.
III. A.N. Prasad, K.A. Mamun, F.R. Islam, H. Haqva Smart water quality monitoring system The University of the South Pacific. 2nd Asia-Pacific World congress on Computer Science and Engineering IEEE Conference (2015)
IV. Baig SA, Lou Z, Baig MA, Qasim M, Shams DF, et al. (2017) Assessment of tap water quality and corrosion scales from the selected distribution systems in northern Pakistan. Environ Monit Assess 189: 194.
V. Gray, N. F. (2008). Drinking water quality: problems and solutions. Cambridge University Press.
VI. H G Gorchev and G Ozolins. 2011. WHO guidelines for drinking-water quality.WHO chronicle 38, 3 (2011), 104–108. https://doi.org/10.1016/S1462-0758(00)00006-6
VII. Md. Omar Faruq, Injamamul Hoque Emu, Md. Nazmul Haque1, Maitry Dey, N.K. Das, Mrinmoy Dey Design and implementation of a cost-effective water quality evaluation system IEEE Region 10 Humanitarian Technology Conference, Dhaka, Bangladesh (2017), pp. 860-863.
VIII. Maudling, J.S., Harris R.H.,”Effect of ionic environment and temperature on the coagulation of color-causing organic compounds with ferric sulphate”, J. Am. Water Works Assoc., 60: 460, 1968.
IX. Minnesota river basin data center, 2008, http://mrbdc.mnsu.edu/basin/wq/turbidity.html
Protocol for turbidity TMDL development March 2008, www.pca.state.mn.us/publications/wq-iwl-07.pdf
X. N. Vijayakumar, R. Ramya, “The Real Time Monitoring of Water Quality in IoT Environment”, International Conference on Circuit, Power and Computing Technologies [ICCPCT], 2015.
XI. Tripathi, S. (2017). Typhoid and its health effects-A Review. Biochem Mol Biol Lett, 3(2), 129.
XII. The Environmental and Protection Agency. 2001. Parameters of water quality.
Environmental Protection (2001), 133. https://doi.org/10.1017/CBO9781107415324.
XIII. Theofanis P. Lambrou, Christos C. Anastasiou, Christos G. Panayiotou, Marios M. Polycarpou A low-cost sensor network for real-time monitoring and contamination detection in drinking water distribution systems IEEE Sensor. J., 8 (2014), pp. 2765-2772.
XIV. UNICEF/WHO (2008) UNICEF and WHO Joint Monitoring Programme for Water Supply and Sanitation. Progress on Drinking Water and Sanitation: Special Focus on Sanitation. UNICEF, New York and WHO, Geneva.
XV. V. V. Nikesh, Hitesh K B, K Rakesh, Joel J Antony, Mohammed Nabeel Khan, : A REVIEW ON WATER LEVEL MEASUREMENT AND CONTROL, J. Mech. Cont.& Math. Sci., Vol.-15, No.-2, February (2020) pp 349-358.
XVI. WHO1972-73 Technical Report Series No.505, 532. World Health Organization, Geneva.

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Abstract:

Numerical integration is one of the fundamental tools of numerical analysis to cope with the complex integrals which cannot be evaluated analytically, and for the cases where the integrand is not mathematically known in closed form. The quadrature rules are used for approximating single integrals, whereas cubature rules are used to evaluate integrals in higher dimensions. In this work, we consider the closed Newton-Cotes cubature schemes for double integrals and discuss consequent error analysis of these schemes in terms of the degree of precision, local error terms for the basic form approximations, composite forms and the global error terms. Besides, the computational cost of the implementation of these schemes is also presented. The theorems proved in this work area pioneering investigation on error analysis of such schemes in the literature.      

Keywords:

Cubature,Double integrals,closed Newton-Cotes,Precision,Order of accuracy,Local error,Computational cost,

Refference:

I. Bailey, D. H., and J. M. Borwein, “High-precision numerical integration: progress and challenges,” Journal of Symbolic Computation, vol. 46, no. 7, pp. 741–754, 2011.
II. Bhatti AA, Chandio MS, Memon RA and Shaikh MM, A Modified Algorithm for Reduction of Error in Combined Numerical Integration, Sindh University Research Journal-SURJ (Science Series) 51.4, (2019): 745-750.
III. Burden, R. L., and J. D. Faires, Numerical Analysis, Brooks/Cole,Boston, Mass, USA, 9th edition, 2011.
IV. Burg, C. O. E. Derivative-based closed Newton-cotes numerical quadrature, Applied Mathematics and Computations, 218 (2012) 7052-7065.
V. Burg, C. O. E., and E. Degny, Derivative-based midpoint quadrature rule, Applied Mathematics and Computations, 4 (2013) 228-234.
VI. Dehghan, M., M. Masjed-Jamei, and M. R. Eslahchi, “On numerical improvement of open Newton-Cotes quadrature rules,” Applied Mathematics and Computation, vol. 175, no. 1, pp.618–627, 2006.
VII. Dehghan, M., M. Masjed-Jamei, and M. R. Eslahchi, “On numerical improvement of closed Newton-Cotes quadraturerules,” Applied Mathematics and Computation, vol. 165, no. 2,pp. 251–260, 2005.
VIII. Jain, M. K., S.R.K.Iyengar and R.K.Jain, Numerical Methods for Scientific and Computation, New Age International (P) Limited, Fifth Edition, 2007.
IX. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Some new and efficient derivative-based schemes for numerical cubature. Journal of Mechanics of Continua and Mechanical Sciences, 15 (10): 67-78, 2020.
X. Memon K, Shaikh MM, Chandio MS and Shaikh AW, A Modified Derivative-Based Scheme for the Riemann-Stieltjes Integral, Sindh University Research Journal-SURJ (Science Series) 52.1, (2020): 37-40.
XI. Memon K, Shaikh MM, Chandio MS and Shaikh AW, A new and efficient Simpson’s 1/3-type quadrature rule for Riemann-Stieltjes integral, Journal of Mechanics of Continua and Mechanical Sciences, 15 (11):, 2020.
XII. Memon, A. A., Shaikh, M. M., Bukhari, S. S. H., & Ro, J. S. (2020). Look-up Data Tables-Based Modeling of Switched Reluctance Machine and Experimental Validation of the Static Torque with Statistical Analysis. Journal of Magnetics, 25(2), 233-244.
XIII. Pal, M., Numerical Analysis for Scientists and Engineers: theory and C programs, Alpha Science, Oxford, UK, 2007.
XIV. Shaikh, M. M. “Analysis of Polynomial Collocation and Uniformly Spaced Quadrature Methods for Second Kind Linear Fredholm Integral Equations – A Comparison”, Turkish Journal of Analysis and Number Theory. 2019, 7(4), 91-97.
XV. Shaikh, M. M., Chandio, M. S., Soomro, A. S. A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration, Sindh Univ. Res. Jour. (Sci. Ser.) Vol. 48 (2) 389-392 2016.
XVI. Walter Guatschi, Numerical analysis second edition, Springer Science business, Media LLC 1997, 2012.
XVII. Weijing Zhao and Hongxing, “Midpoint Derivative-Based Closed Newton-Cotes Quadrature”, Abstract and Applied Analysis, vol.2013, Article ID 492507, 10 pages, 2013.
XVIII. Zafar, F., Saira Saleem and Clarence O.E.Burg, New derivative based open Newton-Cotes quadrature rules, Abstract and Applied Analysis, Volume 2014, Article ID 109138, 16 pages, 2014.

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Abstract:

Light metals and alloys are highly fascinated by aircraft industries due to their good strength-to-weight ratio, which is the prime requirement for aviation’s designers. Assembling of aircrafts components is often carried out using tungsten inert gas (TIG) welding, which is more acceptable for heat treatable aluminum alloys. We focus on the viable use of TIG welded assemblies of 6061 aluminum alloys to homogenize its hardness properties by heat treatment. Investigation proceeds by perceiving the effect of different precipitation hardening conditions on Aluminum alloy through their micro and macro-structural behavior and microhardness analysis. The statistical examination was conducted to evaluate the integrity of heat treated samples.  A new and efficient measure – the coefficient of reliability – is introduced to outline the best hardness preserving samples. The statistical analysis shows the effectiveness of the coefficient of reliability to outline the best samples. The experimental results show that the samples aged at 175^oC for 12 hours preserve the hardness profile of the welded alloy. The result is also verified from the mean hardness, coefficient of reliability and standard deviation values and in agreement with literature.

Keywords:

6061-Al-alloy,Tungsten inert gas welding (TIG),Precipitation hardening,Micro and macro structures,Microhardness,Statistical analysis,

Refference:

I. Alipooramirabad H., A. Paradowska, R. Ghomashchi, and M. Reid, “Investigating the effects of welding process on residual stresses, microstructure and mechanical properties in HSLA steel welds,” J. Manuf. Process., vol. 28, pp. 70–81, Aug. 2017.
II. Boonchouytan W., J. Chatthong, S. Rawangwong, and R. Burapa, “Effect of Heat Treatment T6 on the Friction Stir Welded SSM 6061 Aluminum Alloys,” presented at the 11th Eco-Energy and Materials Science and Engineering (11th EMSES), 2014, vol. 56, pp. 172 – 180.
III. Chunli Y., L. Xiangchun, R. Yanbin, Z. Yiliang, and Z. Feifei, “Statistical Analysis and Countermeasures of Gas Explosion Accident in Coal Mines,” Procedia Eng., vol. 84, pp. 166–171, Jan. 2014.
IV. Davis J. R., “Aluminum and Aluminum Alloys,” in Alloying: Understanding the Basics, ASM International, 2001, pp. 351–416.
V. De Salazar J. M. G., A. Ureña, E. Villauriz, S. Manzanedo, and I. Barrena, “TIG and MIG welding of 6061 and 7020 aluminium alloys. Microstructural studies and mechanical properties,” Weld. Int., vol. 13, no. 4, pp. 293–295, Jan. 1999
VI. DeCoursey W., Statistics and Probability for Engineering Applications. Elsevier, 2003.
VII. Demir H. and S. Gündüz, “The effects of aging on machinability of 6061 aluminium alloy,” Mater. Des., vol. 30, pp. 1480–1483, 2009.
VIII. Kim J.-Y., H. . Jeong, S. I. Hong, Y. Kim, and W. J. Kim, “Effect of aging treatment on heavily deformed microstructure of a 6061 aluminum alloy after equal channel angular pressing,” Scr. Mater., vol. 45, pp. 901–907, 2001.
IX. Kou S., Welding Metallurgy. John Wiley & Sons, 2003.
X. Malekan A., M. Emamy, J. Rassizadehghani, and A. R. Emami, “The effect of solution temperature on the microstructure and tensile properties of Al–15%Mg2Si composite,” Mater. Des., vol. 32, no. 5, pp. 2701–2709, May 2011.
XI. Menzemer C. C., E. Hilty, S. Morrison, R. Minor, and T. S. Srivatsan, “Influence of Post Weld Heat Treatment on Strength of Three Aluminum Alloys Used in Light Poles,” Metals, vol. 6, no. 3, p. 52, Mar. 2016.
XII. Milkereit B., O. Kessler, and C. Schick, “Precipitation and Dissolution Kinetics in Metallic Alloys with Focus on Aluminium Alloys by Calorimetry in a Wide Scanning Rate Range,” in Fast Scanning Calorimetry, Springer, Cham, 2016, pp. 723–773.
XIII. Montgomery D. C., Design and Analysis of Experiments. John Wiley & Sons, 2017.
XIV. Musfirah A. H. and A. G. Jaharah, “Magnesium and Aluminum Alloys in Automotive Industry,” J. Appl. Sci. Res., vol. 8, no. 9, pp. 4865–4875, 2012.
XV. Pasqualini O., F. Schoefs, M. Chevreuil, and M. Cazuguel, “Measurements and statistical analysis of fillet weld geometrical parameters for probabilistic modelling of the fatigue capacity,” Mar. Struct., vol. 34, pp. 226–248, Dec. 2013.
XVI. Polmear I., D. StJohn, J.-F. Nie, and M. Qian, “2 – Physical Metallurgy of Aluminium Alloys,” in Light Alloys (Fifth Edition), Boston: Butterworth-Heinemann, 2017, pp. 31–107.
XVII. Rajan R., P. Kah, B. Mvola, and J. Martikainen, “Trends in Aluminum Alloy Development and thier Joining Methods,” Rev. Adv. Mater. Sci., vol. 44, no. 4, pp. 383–397, 2016.

XVIII. Rambabu P., N. E. Prasad, V. V. Kutumbarao, and R. J. H. Wanhill, “Aluminium Alloys for Aerospace Applications,” in Aerospace Materials and Material Technologies, Springer, Singapore, 2017, pp. 29–52.
XIX. Radhika chada1, N. Shyam Kumar, : INVESTIGATION OF MICRO STRUCTURE AND MECHANICAL PROPERTIES OF FRICTION STIR WELDED AA6061 ALLOY WITH DIFFERENT PARTICULATE REINFORCEMENTS ADDITION, J. Mech. Cont.& Math. Sci., Vol.-15, No.-4, April (2020) pp 264-278
XX. Shah L. H., N. A. Abdul Razak, A. Juliawati, and M. Ishak, “Investigation on the Mechanical Properties of TIG Welded AA6061 Alloy Weldments Using Different Aluminium Fillers,” GSTF J. Eng. Technol., vol. 2, no. 2, Aug. 2013.
XXI. Shaikh M. M., S.-R. Massan, and A. I. Wagan, “A new explicit approximation to Colebrook’s friction factor in rough pipes under highly turbulent cases,” Int. J. Heat Mass Transf., vol. 88, no. Supplement C, pp. 538–543, Sep. 2015.
XXII. Shaikh, M. M. , Massan, S-u-R. and Wagan, A. I. (2019). A sixteen decimal places’ accurate Darcy friction factor database using non-linear Colebrook’s equation with a million nodes: a way forward to the soft computing techniques. Data in brief, 27 (Decemebr 2019), 104733.
XXIII. Shan D. and L. Zhen, “10 – Aging behavior and microstructure evolution in the processing of aluminum alloys,” in Microstructure Evolution in Metal Forming Processes, Woodhead Publishing, 2012, pp. 267–297.
XXIV. Sivaraj P., D. Kanagarajan, and V. Balasubramanian, “Effect of post weld heat treatment on tensile properties and microstructure characteristics of friction stir welded armour grade AA7075-T651 aluminium alloy,” Def. Technol., vol. 10, no. 1, pp. 1–8, Mar. 2014.
XXV. Smallman R. E. and A. H. W. Ngan, “Chapter 13 – Precipitation Hardening,” in Modern Physical Metallurgy (Eighth Edition), Oxford: Butterworth-Heinemann, 2014, pp. 499–527.
XXVI. Srbislav G., A. Ivan, K. Petar, J. Marko, B. Nikola, and G. Vojislav, “A review of explicit approximations of Colebrook’s equation,” FME Trans., vol. 39, no. 2, pp. 67–71, 2011.
XXVII. Tiruveedula Prakash N. B., T.CH. Anil Kumar, Pagidi Madhukar, Balasubramanian Ravisankar4 , S.Kumaran5, Effect of back pressure and temperature on the densification behaviour of Al-Mg alloy, J. Mech. Cont.& Math. Sci., Vol.-15, No.-7, July (2020) pp 684-695.
XXVIII. Walpole R. E., Introduction to statistics. Macmillan, 1982.
XXIX. Wang S., Y. Huang, and L. Zhao, “Effects of different a ging treatments on microstructures and mechanical properties of Al-Cu-Li alloy joints welded by electron beam welding,” Chin. J. Aeronaut., Jul. 2017.
XXX. Wilcox R. R., Basic Statistics: Understanding Conventional Methods and Modern Insights. Oxford University Press, 2009.

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Abstract:

In this work, we explore some unknown properties of the Boubaker polynomials. The orthogonalization of the Boubaker polynomials has not been discussed in the literature. Since most of the application areas of such polynomial sequences demand orthogonal polynomials, the orthogonality of the Boubaker polynomials will help extend its theareas of application. We investigate orthogonality of classical Boubaker polynomials using Sturm-Liouville form and then apply the Gram-Schmidt orthogonalization process to develop modified Boubaker polynomials which are also orthogonal. Some classical properties, like orthogonality and orthonormality relation and zeros, of the modified Boubaker polynomials, have been proved. The contributions from this study have an impact on the further application of modified Boubaker polynomials to not only the cases where classical polynomials could be used but also in cases where the classical ones could not be used due to orthogonality issue.

Keywords:

Orthogonalization,Boubaker polynomials,zeros,Recurrence relation,Gram-Schmidt process,Sturm-Liouville form,

Refference:

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