Archive

Abstract:

Binary polynomials representation of Aunu permutation patterns has been used to perform arithmetic operations on words and sub-words of the polynomials using addition, multiplication, and division modulo two. The polynomials were also found to form some mathematical structures such as group, ring, and field. This paper presents the extension of our earlier work as it reports the Aunu binary polynomials of cardinality eleven and how to find their greatest common divisor (gcd) using the extended Euclidean algorithm. The polynomials are pairly permuted and the results found showed that one polynomial is a factor of the other polynomial or one polynomial is relatively prime to the other and some gave different results. This important feature is of combinatorial significance and can be investigated further to formulate some theoretic axioms for this class of Aunu permutation pattern. Binary polynomials have important applications in coding theory, circuit design, and the construction of cryptographic primitives.

Keywords:

Algorithm,Aunu,Cryptography,Euclidean,Extended,Galois field,Greatest common divisor,Permutation,Patterns,Polynomials,Binary,

Refference:

I. A. A Ibrahim (2007). An Enumeration Scheme and Algebraic properties of a Special (132)-avoiding Class of permutation Pattern. Trends in Applied sciences Research Academic Journals Inc. USA. 2(4) 334-340.
II. Aminu Alhaji Ibrahim and Sa’idu Isah Abubakar (2016). Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties. Advances in Pure Mathematics, (6), 409-419 http://www.scirp.org/journal/apm http://dx.doi.org/10.4236/apm.2016.66028
III. Aminu Alhaji Ibrahim, Saidu Isah Abubakar (2016). Non-Associative Property of 123-Avoiding Class of Aunu Permutation Patterns Advances in Pure Mathematics, 2016, 6, 51-57 http://www.scirp.org/journal/apm http://dx.doi.org/10.4236/apm.2016.62006.
IV. Abubakar S.I, Shehu S., Ibrahim Z. Ibrahim A.A (2014). Some polynomials representation using the 123-avoiding class of the Aunu permutation patterns of cardinality five using binary codes. International Journal of Scientific and Engineering Research 5(8), 1-4.
V. Abubakar S.I, Ibrahim Z. Ibrahim A.A (2014). Binary polynomials representation using the 123-avoiding class of the Aunu permutation patterns of cardinality seven. A paper presented at the 1st National Conference organized by Faculty of Science, Sokoto State University in conjunction with The Algebra Group Usmanu Danfodiyo University, Sokoto held at Sokoto State University from 17th-20th March, 2014.
VI. Benvenuto, C. J. (2012). Galois field in cryptography. University of Washington, 1(1), 1-11.
VII. Daniel Panario (June 2006). A Minicourse in Finite Fields and Applications, School of Mathematics and Statistics, Carleton University.
VIII. De Piccoli, A., Visconti, A., & Rizzo, O. G. (2018). Polynomial multiplication over binary finite fields: new upper bounds. Journal of Cryptographic Engineering, 1-14.
IX. Homma, N., Saito, K., Aoki, T. (2014). Toward formal design of practical cryptographic hardware based on Galois field arithmetic. IEEE Transactions on Computers 63(10), 2604-2613.
XI. Paul Pollack (2008). Prime Polynomials over Finite Fields; A PhD Thesis, Darmouth College.
XII. Sheueling Chang Shantz (2001). From Eculid’s GCD to Montgomery Multiplication to the Great Divide” sun Microsystems laboratories MSLI TR-2001-95.
XIII. Shparlinski, I. (2013). Finite Fields: Theory and Computation: The meeting point of number theory, computer science, coding theory and cryptography 477.
XIV. Stein J. (1961). Computational problems associated with Racah algebra. Journal Computational Physics, 1.

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Abstract:

Interconnectivity necessitates the use of transportation facilities and infrastructure. All highway design agencies seek acceptable, long-lasting, and cost-effective strategies while designing these facilities. The traffic demands on roads are much higher than they have been in the past. Increased traffic loads, larger traffic volumes, and insufficient maintenance have all contributed to serious road surface distress (e.g., rutting and cracking) due to rapid development. As conventional asphalt combinations are unable to withstand high axle loads and tire pressures, interest in polymer-modified asphalt has grown. Polymer modification of asphalt is one of the most effective ways to improve asphalt qualities. The practical temperature range of binders is greatly expanded by polymers. The inclusion of the polymer can considerably improve the binder qualities by increasing the stiffness of the bitumen and enhancing its temperature susceptibility, enabling the building of safer roads and lower maintenance costs. This research presents a laboratory investigation of the Ethylene Vinyl Acetate (EVA) polymer-modified bitumen. NHA-B gradation, PARCO 60/70 grade bitumen, and EVA polymer of TPI Polene Public Company Limited were used. Penetration, softening point, ductility, and viscosity tests were used to evaluate the conventional properties of the asphalt binders. Three different percentages of polymers were used i.e., 2%, 4%, and 6%. The impact of the EVA polymer on permanent deformation and moisture susceptibility was investigated. A double wheel tracker (DWT) was used to quantify permanent deformation (rutting), and a Universal Testing Machine (UTM) was used to examine moisture susceptibility using an Indirect Tensile Strength (ITS) test. For different percentages of bitumen volumetric properties according to Marshall Mix Design procedure were measured, and then Optimum Bitumen Content (OBC) was evaluated.  Performance tests were performed using above mentioned percentages of EVA. The rutting potential of mixes was improved by the addition of EVA as compared to control asphalt mixes. The same effect of the polymer was on the moisture susceptibility of the prepared samples. This showed that EVA polymer can be used in flexible pavements to reduce permanent deformation and high-temperature problems.

Keywords:

Ethylene Vinyl Acetate,Polymer modified bitumen,performance evaluation,Optimum Bitumen Content (OBC),Indirect Tensile Strength (ITS),

Refference:

I. Ahmed, T., & Ahmed, H. (2014). Investigating the rutting and moisture sensitivity of warm mix asphalt with varying contents of recycled asphalt pavement. University of Iowa, Iowa Research Online.

II. Aljanadi, B., Miskeen, M. Bin, & Abosalah, S. (2020). Modification of Hot Mix Asphalt Using Ethylene Vinyl Acetate ( EVA ) for Hot and Arid Regions. 195–207.

III. Ameri, M., Mansourian, A., & Sheikhmotevali, A. H. (2013). Laboratory evaluation of ethylene vinyl acetate modified bitumens and mixtures based upon performance related parameters. Construction and Building Materials, 40, 438–447. https://doi.org/10.1016/j.conbuildmat.2012.09.109
IV. Chegenizadeh, A., Tokoni, L., Nikraz, H., & Dadras, E. (2021). Effect of ethylene-vinyl acetate (EVA) on stone mastic asphalt (SMA) behaviour. Construction and Building Materials, 272, 121628. https://doi.org/10.1016/j.conbuildmat.2020.121628

V. Dekhli, S., Mokhtar, K. A., Hammoum, F., & Bachir, D. S. (2015). Rheological Behaviour of Ethylene-Vinyl-Acetate (EVA) Modified Road Bitumen. Journal of Applied Sciences, 15(3), 444–455. https://doi.org/10.3923/jas.2015.444.455

VI. Garba, R. (2002). Permanent Deformation Properties of Asphalt Mixtures. NVF Conference, 1–13.

VII. Janmohammadi, O., Safa, E., Zarei, M., & Zarei, A. (2020). Simultaneous effects of ethyl vinyl acetate (EVA) and glass fiber on the properties of the hot mix asphalt (HMA). SN Applied Sciences, 2(7), 1–14. https://doi.org/10.1007/s42452-020-2977-8

VIII. Khan, K. M., & Kamal, M. A. (2012). Rutting Based Evaluation of Asphalt Mixes. Pak. J. Engg. & Appl. Sci. Vol, 11(2006), 60–65.

IX. O’Sullivan, K., & Wall, P. a. (2009). The effects of warm mix asphalt additives on Recycled Asphalt Pavement. Dissertation, Worcester Polytechnic Institute, 84. http://www.wpi.edu/Pubs/E-project/ Available/E-project-030609-183749/unrestricted/ WMA_Aided_RAP_ MQP.pdf

X. Sengoz, B., & Isikyakar, G. (2008). Evaluation of the properties and microstructure of SBS and EVA polymer modified bitumen. Construction and Building Materials, 22(9), 1897–1905. https://doi.org/10.1016/j.conbuildmat.2007.07.013

XI. Yoder, E. J., & Witczak, M. W. (1975). Principles of Pavement Design. Principles of Pavement Design. https://doi.org/10.1002/9780470172919

XII. Ullah Irfan, Dr. Rawid Khan, Manzoor Elahi, Ajab Khurshid.: ‘CHARACTERIZATION OF THE NONLINEAR BEHAVIOR OF FLEXIBLE ROAD PAVEMENTS’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-12, December (2020) pp 111-126. DOI : https://doi.org/10.26782/ jmcms.2020.12.00010

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Abstract:

The role of numbers is very important not only in mathematics but also in any branch of science and technology. The author developed a new concept of the theory of dynamics of numbers. According to the new concept, 0 (zero) is the starting point of any number. There are infinite number of directions through which the numbers can move from starting point 0 (zero) and can return in the vertically opposite direction towards the starting point 0 (zero). The motion of any number (object) is positive whether it is forward motion or backward motion. Similarly, countup and countdown motions of numbers are also positive. Therefore, there is no existence of negative numbers.             The author framed the law of the theory of dynamics of numbers. The author solved the quadratic equation in one countable unknown object or quantity (say x) in the form, ax² + bx + c = 0, even if the numerical value of the discriminant, b² – 4ac <0. The author applied the theory of dynamics of numbers to solve the problems of plane co-ordinate geometry and also to solve the problems of the quadratic equation in the present paper.

Keywords:

Cartesian Co-ordinate System,Dynamics of Numbers,Quadratic Equation,Rectangular Bhattacharyya’s Co-ordinate System,Theory of Numbers,

Refference:

I. Prabir Chandra Bhattacharyya. : ‘AN INTRODUCTION TO RECTANGULAR BHATTACHARYYA’S CO-ORDINATES: A NEW CONCEPT’ J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, November (2021) pp 76-86. DOI : https://doi.org/10.26782/jmcms.2021.11.00008
II. http//en-wikipedia.org/wiki/Number
III. http://en. wikipedia.org/wiki/Shridhara
IV. http://en.wikipedia.org

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Abstract:

The numerous applications in medical fields as well as in industrial areas have drawn substantial attention of the researchers to study the fluid flow and heat transfer (HT) through a bent duct. The present paper demonstrates a spectral-based numerical study of 2D flow in a bent square geometry for various curvature ratios. The numerical calculation has been conducted over Dn, and the curvature ranges from 0.001 to 0.5. The horizontal walls are thermally different where the bottom wall is heated while the ceiling wall cooled, the vertical walls being thermally insulated. After an extensive investigation, we found two branching structures of the solution, each consisting of two branches with 2- to 8-vortex solutions for small and medium curvatures while three branches of solution structure for large curvature. The instability of the flow is then calculated by performing time-evolution (TEv) analysis and by sketching the phase-space (PS) of the solutions. This study also demonstrates that the HT is significantly boosted with the effect of secondary flows (SF) and the increasing secondary vortices boost heat transfer more effectively than other physically realizable solutions.

Keywords:

Heat transfer,2D flow,Time-Evolution (TEv),Phase-Space (PS),

Refference:

I. Chanda, R. K., Hasan, M. S., Alam, M. M. and Mondal, R. N. (2020), Hydrothermal Behavior of Transient Fluid Flow and Heat Transfer through a Rotating Curved Rectangular Duct with Natural and Forced Convection, Mathematical Modelling of Engineering Problems, 7(4), 501-514.
II. H. Ito, Flow in curved pipes, JSME International Journal. 30, 1987, pp.543-52.
III. K. Nandakumar and J. H. Masliyah, Swirling Flow and Heat Transfer in Coiled and Twisted Pipes, Adv. Transport Process. 4, 1986, pp.49-112.
IV. K. Yamamato, W. Xiaoyum, N. Kazou, and H. Yasutuka, Visualization of Taylor-Dean flow in a curved duct of square cross section, J. Fluid Dyn. Res. 38, 2006, pp. 1-18.
V. M. Norouzi, M. H. Kayhani M. R. H. Nobari and M. K. Demneh, Convective Heat Transfer of Viscoelastic Flow in a Curved Duct, World Academy of Science. Engineering and Technology. 32, 2009, pp.327-333.
VI. M. Z. Islam, R. N. Mondal, M. M. Rashidi, Dean-Taylor flow with convective heat transfer through a coiled duct, Computers and Fluids. 149, 2017, pp.41-55.

VII. Md. Hasanuzzaman, Md. Mosharrof Hossain, M.M. Ayub Hossain. : ‘SIMILARITY SOLUTION OF HEAT AND MASS TRANSFER FOR LIQUID EVAPORATION ALONG A VERTICAL PLATE COVERED WITH A THIN POROUS LAYER’. J. Mech. Cont. & Math. Sci., Vol.-16, No.-4, April (2021) pp 47-60. DOI : https://doi.org/10.26782/jmcms.2021.04.00004

VIII. Rafiuddin, Noushima Humera. G. : ‘ NUMERICAL SOLUTION OF UNSTEADY TWO – DIMENSIONAL HYDROMAGNETICS FLOW WITH HEAT AND MASS TRANSFER OF CASSON FLUID’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-9, September (2020) pp 17-30. DOI : https://doi.org/10.26782/jmcms.2020.09.00002
IX. R. N. Mondal, T. Watanabe, M. A. Hossain and S. Yanase, Vortex-Structure and Unsteady Solutions with Convective Heat Transfer through a Curved Duct, Journal of Thermophysics and Heat Transfer. 31(1), 2017, pp.243-254.
X. R. N. Mondal, Y. Kaga, T. Hyakutake and S. Yanase, Effects of curvature and convective heat transfer in curved square duct flows, Trans. ASME, Journal of Fluids Engineering. 128(9), 2006, pp.1013-1022.
XI. S. A. Berger, L. Talbot, L. S. Yao, Flow in Curved Pipes, Annual. Rev. Fluid. Mech. 35, 1983, pp.461-512.
XII. S. N. Dolon, M. S. Hasan, S. C. Ray, and R. N. Mondal, Vortex-structure of secondary flows with effects of strong curvature on unsteady solutions through a curved rectangular duct of large aspect ratio, AIP Conference Proceedings. 2121, 050004, 2019.
XIII. S. Yanase, Y. Kaga, R. Daikai, Laminar Flows through a curved rectangular duct over a wide range of the aspect ratio, Fluid Dynamics Research. 31, 2002, pp.151–183.
XIV. W. R. Dean, Note on the motion of fluid in a curved pipe, Philos Mag. 4, 1927, pp.208-223.

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Abstract:

A gas turbine is a device that converts the energy of fuel into mechanical energy and is used to derive several types of rotating equipment. One of the major drawbacks of a gas turbine is that the performance (power output and thermal efficiency) of a gas turbine decreases instantly with the rise of ambient temperature. At Daur SSGCL Gas Compression Station, gas turbines are used to derive centrifugal type gas compressors to raise the pressure of natural gas where ambient temperature varies between 7⁰ to 50⁰C which decreases the performance of gas turbines. Inlet air cooling is a method through which the effect of ambient temperature on the performance of gas turbines can be decreased. This technique of cooling intake air increases the performance of gas turbines by increasing air density. There are various types of inlet air cooling but, in this study, two types of inlet air cooling techniques are discussed, one of which is wetted media evaporative type and the other one is vapour absorption type. The Evaporative type inlet air cooling technique is suitable for sites with high ambient temperature and low relative humidity and vapour absorption type is used for a wide range of ambient air temperature. In this study, thermodynamic models of the gas turbine have been developed without inlet air cooling (base case/cycle) with inlet air cooling for analyzing the effects of ambient conditions (temperature and relative humidity) on the performance of the gas turbine. The simulated results obtained from Engineering Equation Solver with inlet air cooling systems (vapour absorption and wetted media evaporator cooler) are compared without inlet air cooling (base cycle) gas turbine. On comparison of results of a gas turbine with inlet air cooling systems to without inlet air cooling at ambient conditions, T_0=298.15K (25⁰C) and ∅=60% it is found that gas turbine with evaporator cooler produces 289kW more power than base case/cycle and 390kW more output power with vapour absorption inlet air cooling.

Keywords:

Gas turbine,Ambient conditions,Daur Sindh Pakistan,Inlet air cooling,Evaporator cooler,Vapour absorption cooler,

Refference:

I. Alhazmy, M. M., & Najjar, Y. S. (2004). Augmentation of gas turbine performance using air coolers. Applied thermal engineering, 24(2-3), 415-429.
II . Ameri, M. O. H. A. M. M. A. D., & Hejazi, S. H. (2004). The study of capacity enhancement of the Chabahar gas turbine installation using an absorption chiller. Applied thermal engineering, 24(1), 59-68.
III. Arabi, S. M., Ghadamian, H., Aminy, M., Ozgoli, H. A., Ahmadi, B., & Khodsiani, M. (2019). The energy analysis of GE-F5 gas turbines inlet air–cooling systems by the off-design method. Measurement and Control, 52(9-10), 1489-1498.
IV. Baakeem, S. S., Orfi, J., & AlAnsary, H. (2015). Performance of a typical simple gas turbine unit under saudi weather conditions. Int. J. Fluid Mech. Therm. Sci, 1, 59-71.
V. Boonnasa, S., Namprakai, P., & Muangnapoh, T. (2006). Performance improvement of the combined cycle power plant by intake air cooling using an absorption chiller. Energy, 31(12), 2036-2046.
VI. De Lucia, M., Bronconi, R., & Carnevale, E. (1994). Performance and economic enhancement of cogeneration gas turbines through compressor inlet air cooling.
VII. Jaber, Q. M., Jaber, J. O., & Khawaldah, M. A. (2007). Assessment of power augmentation from gas turbine power plants using different inlet air cooling systems. Jjmie, 1(1), 7-15.
VIII. Khaliq, A., & Dincer, I. (2011). Energetic and exergetic performance analyses of a combined heat and power plant with absorption inlet cooling and evaporative aftercooling. Energy, 36(5), 2662-2670.
IX. Meherwan P.Boyce (2012), Gas turbine engineering hand book (fourth ed.)
X. Mohapatra, A. K. (2014). Thermodynamic assessment of impact of inlet air cooling techniques on gas turbine and combined cycle performance. Energy, 68, 191-203.
XI. Onoroh, F., Ogbonnaya, M., & Onochie, U. P. (2020). Modeling and simulation of the effect of moisture content and ambient temperature on gas turbine power plant performance in Ughelli, Nigeria. Nigerian Journal of Technology, 39(1), 182-188.
XII. Popli, S., Rodgers, P., & Eveloy, V. (2013). Gas turbine efficiency enhancement using waste heat powered absorption chillers in the oil and gas industry. Applied Thermal Engineering, 50(1), 918-931.
XIII. Santos, A. P., & Andrade, C. R. (2012). Analysis of gas turbine performance with inlet air cooling techniques applied to Brazilian sites. Journal of Aerospace sTechnology and Management, 4(3), 341-353.
XIV. Solar Turbines (2019), Introduction to Gas Turbine Theory (Third ed.)
XV. Yazdi, M. R. M., Ommi, F., Ehyaei, M. A., & Rosen, M. A. (2020). Comparison of gas turbine inlet air cooling systems for several climates in Iran using energy, exergy, economic, and environmental (4E) analyses. Energy Conversion and Management, 216, 112944.

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Abstract:

Most of the functional responses which have been incorporated to formulate mathematical biology consider individual contact or predator cooperation. In this study, we have introduced a different functional response that describes the prey-predator system when predators form a line and cooperatively attack a group of predators. We have also described the effect of prey on this system. Additionally, we find all the equilibrium points and their local stability behaviour.

Keywords:

Predator cooperation,Prey predator system,Equilibrium points,Local stability behaviour,

Refference:

I. C. Cosner, D. L. DeAngelis, J. S. Ault, D. B. Olson, Effects of spatial grouping on the functional response of predators, Theoretical population biology 56 (1) (1999) 65–75.
II. C. S. Holling, Some characteristics of simple types of predation and parasitism1, The Canadian Entomologist 91 (7) (1959) 385–398.
III. C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, The Memoirs of the Entomological Society of Canada 97 (S45) (1965) 5–60.
IV. D. L. DeAngelis, R. Goldstein, R. V. O’Neill, A model for tropic interaction, Ecology 56 (4) (1975) 881–892.
V. D. Xiao, S. Ruan, Codimension two bifurcations in a predator–prey system with group defense, International Journal of Bifurcation and Chaos 11 (08) (2001) 2123–2131.
VI. H. I. Freedman, G. S. Wolkowicz, Predator-prey systems with group defence: the paradox of enrichment revisited, Bulletin of Mathematical Biology 48 (5-6) (1986) 493–508.
VII. J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, The Journal of Animal Ecology (1975) 331–340.
VIII. K.-S. Cheng, S.-B. Hsu, S.-S. Lin, Some results on global stability of a predator-prey system, Journal of Mathematical Biology 12 (1) (1982) 115–126.
IX. R. Arditi, L. R. Ginzburg, H. R. Akcakaya, Variation in plankton densities among lakes: a case for ratio-dependent predation models, The American Naturalist 138 (5) (1991) 1287–1296.

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Abstract:

A modified extended iteration procedure is applied to compute the analytical periodic solutions of the nonlinear oscillator having fractional terms. A nonlinear oscillator with force is given to demonstrate the effectiveness and expediency of the iteration scheme. Mickens’ extended iteration method is a well-established method for studying random oscillations. The method is also simple and straightforward to accomplish approximate frequency and the corresponding periodic solution of the strongly nonlinear oscillator. The method gives high validity for both small and large initial amplitudes of oscillations. We have used an appropriate truncation of the obtained Fourier cosine series in each step of iterations to determine the approximate analytic solution of the oscillators. The second, third, and fourth approximate frequencies of the truly nonlinear oscillator with force show a good agreement with their exact values. Also, we have compared the calculated results with some of the existing results. We have shown that the method performs reasonably better.

Keywords:

Mickens’ Extended iteration procedure,Nonlinear oscillator with the fractional term,Nonlinearity,Fourier series,

Refference:

I. Ayub Hossain M.M. and Haque, B.M.I., 2019,” A solitary convergent periodic solution of the inverse truly nonlinear oscillator by modified Mickens’ extended iteration procedure”, J. Mech. Con t. & Math. Sci., Vol. – 16, No. – 8, pp 1 – 9.
II. Azami R, Ganji D D, Babazadeh H, Dvavodi A G, Ganji S S, 2009, “ He’s Max-min method for the relativistic oscillator and high order Duffing equation”, International journal of modern physics B, Vol. 23 (32), pp. 5915-5927.
III. Beléndez A, 2009, “Homotopy perturbation method for a conservative force nonlinear oscillator”, Computers and Mathematics with Applications, Vol. 58, pp. 2267–2273.
IV. Beléndez A, Hernamdez A, Beléndez T, Fernandez E, Alvarez M L and Neipp C, 2007, “Application of He’s homotopy perturbation method to Duffing-harmonic Oscillator”, Int. J. Nonlinear Sci. and Numer. Simul., Vol. 8(1), pp.79-88.
V. Beléndez, A., Pascual, C., Ortuno, M., Beléndez, T. and Gallego, S., 2009 “Application of a modified He’s homotopy perturbation method to obtain higher order approximations to a nonlinear oscillator with discontinuities” Nonlinear Anal. Real World Appl, Vol.10 (2), pp. 601-610.
VI. Chowdhury M S H, Alal Md Hosen, Kartini Ahmed, Ali M Y, Ismail A F, 2017, “ High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method”, Results in physics, Vol. 7, pp. 3962-3967.
VII. Daeichin, M., Ahmadpoor, M.A., Askari, H., Yildirim, A., 2013, “Rational energy balance method to nonlinear oscillators with cubic term”, Asian European Journal of Mathematics, Vol. 6 (02), pp. 13500-19.

VIII. Durmaz, S., Kaya, M.O., 2012, “High-order energy balance method to nonlinear oscillators”, Journal of Applied Mathematics.
IX. Elias-Zuniga A, Oscar Martinez-Romero, and Rene K, Cordoba-Diaz, 2012, “Approximate solution for the Duffing-harmonic oscillator by the Enhanced Cubication Method”, Mathematical problems in Engineering, Vol. 2012(10), pp 1155-66.
X. Ganji S. S., Ganji D. D. and Karimpour S., 2008, “Determination of the frequency-amplitude relation for nonlinear oscillators with fractional potential using He’s energy balance method” Progress in Electromagnetics Research C, Vol. 5, pp. 21–33.
XI. Haque B M I, Alam M S and Majedur Rahmam M, 2013, “Modified solutions of some oscillators by iteration procedure”, J. Egyptian Math. Soci., Vol.21, pp.68-73.
XII. Haque B M I, 2013, “A new approach of Mickens’ iteration method for solving some nonlinear jerk equations”, Global Journal of Sciences Frontier Research Mathematics And Decision Science, Vol.13 (11), pp. 87-98.
XIII. Haque B M I, Alam M S, Majedur Rahman M and Yeasmin I A, 2014, “Iterative technique of periodic solutions to a class of non-linear conservative systems”, Int. J. Conceptions on Computation and Information technology, Vol.2(1), pp.92-97.
XIV. Haque B M I, 2014, “A new approach of Mickens’ extended iteration method for solving some nonlinear jerk equations”, British journal of Mathematics & Computer Science, Vol.4(22), pp.3146-3162.
XV. Haque, B.M.I., Bayezid Bostami M., Ayub Hossain M.M., Hossain M.R. and Rahman M.M., 2015 “Mickens Iteration Like Method for Approximate Solution of the Inverse Cubic Nonlinear Oscillator” British journal of Mathematics & Computer Science, Vol. 13, pp.1-9.
XVI. Haque, B.M.I., Ayub Hossain M.M., Bayezid Bostami M. and Hossain M.R., 2016 “Analytical Approximate Solutions to the Nonlinear Singular Oscillator: An Iteration Procedure” British journal of Mathematics & Computer Science, Vol. 14, pp.1-7.
XVII. Haque, B.M.I., Asifuzzaman M. and Kamrul Hasam M., 2017 “Improvement of analytical solution to the inverse truly nonlinear oscillator by extended iterative method” Communications in Computer and Information Science, Vol. 655, pp. 412-421.

XVIII. Haque, B.M.I., Selim Reza A.K.M. and Mominur Rahman M., 2019 “On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method” Journal of Advances in Mathematics and Computer Science, Vol. 33, pp. 1-9.
XIX. Haque, B.M.I. and Ayub Hossain M.M., 2019 “A Modified Solution of the Nonlinear Singular Oscillator by Extended Iteration Procedure” Journal of Advances in Mathematics and Computer Science, Vol. 34, pp.1-9.
XX. Haque B M I and Afrin Flora S, 2020 “On the analytical approximation of the quadratic nonlinear oscillator by modified extended iteration Method”, Applied Mathematics and Nonlinear Sciences, June 15th, pp. 1-10.
XXI. Haque B M I, Zaidur Rahman M and Iqbal Hossain M, 2020 “Periodic solution of the nonlinear jerk oscillator containing velocity times acceleration-squared: an iteration approach”, journal of Mechanics of Continua and Mathematical Sciences, Vol. 15(6), pp. 419-433.
XXII. Haque B M I and Iqbal Hossain M, 2021 “An Analytical Approach for Solving the Nonlinear Jerk Oscillator Containing Velocity Times Acceleration-Squared by An Extended Iteration Method”, journal of Mechanics of Continua and Mathematical Sciences, Vol. 16(2), pp. 35-47.
XXIII. Hosen MA, Chowdhury MSH, Ali MY, Ismail AF, 2016, “A new analytic approximation technique for highly nonlinear oscillations based on energy balanced method”, Results Phys., Vol. 6, pp. 496-504.
XIV. Hosen MA, Chowdhury MSH, 2015, “A new reliable analytic solution for strongly nonlinear oscillator with cubic and harmonic restoring force”, Results Phys., Vol. 5, pp. 111-4.
XXV. Lai SK, Lim CW, Wu BS, Wang C, Zeng QC, He XF, 2008, “Newton-harmonic balanced approach for accurate solutions to nonlinear cubic-quintic Duffing oscillator”, Appl Math Model, Vol. 33(2), pp. 852-66.
XXVI. Mickens R E, 1984, “Comments on the method of harmonic balance”, J. Sound Vib., Vol. 94, pp.456- 460.
XXVII. Mickens R E, 1987, “Iteration Procedure for determining approximate solutions to nonlinear oscillator equation”, J. Sound Vib., Vol. 116, pp.185-188.

XXVIII. Mickens R E, 2005, “A general procedure for calculating approximation to periodic solutions of truly nonlinear oscillators”, J. Sound Vib., Vol. 287, pp.1045-1051.
XXIX. Mickens R E, 2010, “Truly Nonlinear Oscillations, World Scientific, Singapore”.
XXX. Nayfeh A H, 1973, “Perturbation Method”, John Wiley & sons, New York.
XXXI. Nayfeh A H Mook D T, 1979, “Nonlinear Oscillations”, John Wiley & sons, New York.

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Abstract:

In AC and DC drives, the use of switched reluctance machine (SRM) is becoming popular as it has a few preferences over AC and DC drives in a simple and robust construction without brushes, low inertia, and high torque to weight ratio, without rotor windings, simple circuit power converter, etc. SRM is widely used in variable speed and servo drives. Because of the double saliency structure and the high nonlinearity of magnetic material, it is difficult to represent the flux-linkage and static torque characteristic of the SRM. This work promotes the use of an improved numerical integration scheme for the static characteristics of SRM. The static torque function that depends on the rotor position and the phase current of the flux linkage features family (for different rotor positions) is improved in the proposed work. Firstly, we use an experimental setup for the electromagnetic characteristic of SRM. Then, we use the improved scheme to develop an efficient mathematical model for static characteristics and finally simulate the static characteristic of SRM through MATLAB code. In the last step, we compare the performance of the proposed integrator model with an existing approach for better efficiency of the static characteristic of SRM with experimental validation.

Keywords:

Numerical scheme,Switched Reluctance machine,Static Torque,Numerical Integration,Experimental Validation,

Refference:

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Abstract:

All-optical n-bit paired to 2's complement converter has been planned with the assistance of Terahertz optical unbalanced demultiplexer (TOAD) switches. The paper depicts all-optical transformation conspire to utilize a bunch of every single optical switch. PC framework ordinarily utilizes 2's complement for paired deduction and intelligent control. By embracing a definite mathematical reproduction the impact of these critical boundaries on the measurements that decide the nature of exchange is completely examined and diverse plan rules are extricated for their legitimate determination to guarantee ideal activity.  

Keywords:

Terahertz optical asymmetric demultiplexer,semiconductor optical amplifier,2’s complement operation,optical logic,

Refference:

I. A. Bhattacharyya, D. K. Gayen, and T. Chattopadhyay, “All-optical 4-bit Binary to Binary Coded Decimal Converter with the help of Semiconductor Optical Amplifier -assisted Sagnac Switch”, Optics Communications, Elsevier, 293, 31–42 (2013).
II. B. C. Wang, V. Baby, W. Tong, L. Xu, M. Friedman, R. J. Runster, I. Glesk, and P. Prucnal, “A novel fast optical switch based on two Cascaded Terahertz optical asymmetric demultiplexers (TOAD),” Opt. Express, vol.10, pp. 15-23, Jan. 2002.
III. D. K. Gayen, T. Chattopadhyay, M. K. Das, J. N. Roy, and R. K. Pal, “All-optical binary to gray code and gray to binary code conversion scheme with the help of semiconductor optical amplifier -assisted sagnac switch”, IET Circuits, Devices & Systems, 5(2), 123-131 (2011)
IV. G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE Quantum Electronics, vol. 25, pp. 2297-2306, 1989.
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VI. H. Le-Minh, Z. Ghassemlooy, and W. P. Ng, “Ultrafast all-optical self clock extraction based on two inline symmetric Mach-Zehnder Switches,” in Proc. ICTON 2006, vol. 4, pp. 64-67, Nottingham, UK, 2006.
VII. Hoa Le Minh, Zabih Ghassemlooy, Wai Pang Ng,” Characterization and Performance Analysis of a TOAD Switch Employing a Dual Control Pulse Scheme in. High-speed OTDM Demultiplexer”, IEEE Communications Letters, vol. 12, 4, APRIL 2008.
VIII. J. P. Sokoloff, I. Glesk, P. R. Prucnal, “Performance of a 50Gb/s Optical Time Domain Multiplexed System using a TOAD”, IEEE Pho. Tech. Lett., 6(1), pp. 98-100, 1994.

IX. K. E. Zoiros, J. Vardakas, T. Houbavlis, and M. Moyssidis, “Investigation of SOA-assisted Sagnac recirculating shift register switching characteristics”, International Journal for Light and Electron Optics, 116(11), 527-541 (2005).
X. M. Eiselt, W. Pieper, H. G. Weber, LALOM: Semiconductor Laser Amplifier in a Loop Mirror”, IEEE Light. Tech., 13(10), pp. 2099-2112.
XI. W. Hong, D. Huang, and G. Zhu, “Switching window of an SOA loop mirror with SOA sped-up by a CW assist light at transparency wavelength”, Optics Communications, 238(1-3), 151-156 (2004).

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