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Abstract:

In this study, a comparative analysis is to be conducted between different mathematical techniques to find out the best one which can be more suitable from all perspectives to balance equations of chemical reactions and to provide case-to-case recommendations for the practitioners. The linear algebra approach, linear programming approach, and integer linear programming approach have been successfully utilized for chemical equation balancing.  Some chemical equations have been taken from the literature to see the performance of the above approaches. After highlighting the advantages and disadvantages of the existing approaches, some proposals for modification are presented. The proposed modifications have been worked out on all problems, and the integer solution is attained for all problems; even in cases where existing methods failed. The final recommendations on easier and better techniques have been provided. The two modified methods achieved top ratings among the existing and proposed methods.

Keywords:

Mathematical methods,Chemical equations,Linear Algebra,Linear Programming,Integer Linear Programming,FLOPs, Mathematical Chemistry,

Refference:

I. Abdelrahim M. Zabadi and RamizAssaf, (2017), “Balancing a Chemical Reaction Equation Using Algebra Approach”, International Journal of Advanced Biotechnology and Research(IJBR), vol 8, Issue 1, pp: 24-33.
II. Arcesio Garcia, (1987), “A new method to balance chemical equations”, Journal of chemical equation, vol 64, pp: 247-248.
III. Charnock, N. L, (2016), “Teaching Method for Balancing Chemical Equations: An Inspection versus an Algebraic Approach”. American Journal of Educational Research, vol 4, pp: 507-511
IV. Dr. Kakde Rameshkumar Vishwambharrao, Sant Gadage Maharaj Mahavidyalaya, Loha (Maharashtra), (September 2013), “Balancing Chemical Equations by Using Mathematical Model”, International Journal of Mathematical Research & Science (IJMRS), vol. 1, Issue 4, pp: 129-132.
V. E.V. Krishnamurthy, (1978), “Generalized matrix inverse approach to automatic balancing of chemical equation”, International Journal of Mathematical Education in Science and Technology, vol 9, no 3,
pp: 323–328.
VI. Ice B Risteski, (2012), “New very Hard Problems of Balancing Chemical Reactions”, Bulgarian Journal of Science Education, vol 21, No 4, pp: 574
VII. Ice.B Ristaki, (2014), “A new generalized algebra for the balancing of chemical reactions”, Materiali technologije/materials and technology, vol 48, Issue 2, pp: 215-219.
VIII. Lochte, H.L, (1997), “Pole reaction method (ion electron/half reaction)”, Journalof chemical education, vol 74, Issue 11, pp: 146-157.
IX. Mansoor Niaz and Anton E Lawson, (1985), “Balancing Chemical Equations: The Role of Developmental level and Mental Capacity”, Journal of Research in Science Teaching, vol 22, No 1, pp: 41-51.
X. Mumtaz Yousaf, Muhammad Mujtaba Shaikh, Abdul Wasim Shaikh (2020). Efficient Mathematical Programming Techninques For Balancing Equations of Complex Chemical Reactions. Journal of Maecahnics of Continua and Mathemtical Sciences. 15 (10): 53-66.
XI. Paul M. Treichel John C. Kotz, at https://www.britannica.com/science/chemical-reaction/Photolysis-reactions
XII. R. David Jones, A. Paul Schwab, (1989), “Balancer: A computer program for balancing chemical equations”, Journal of agronomic education, vol 18, Issue 1, pp: 29-32.
XIII. R.O Akinola, S.Y. Kutchin, I.A Nyam, (2016), “using row reduced echelon form in balancing chemical equations”, Advance in linear algebra and Matrix Theorey, vol 6, Issue 4, pp: 429-445.
XIV. Risteki I.B, (2016b), “A new generalzed matrix inverse method for balancing chemical equations and their stability”, Journal of Chinese chemical Soc, vol 56, Issue 4, pp: 65-79.
XV. S K Sen, Hans Agarwal, Sagar Sen, (Feburary 2006), “Chemical Equation Balancing: An integer programming appoach”, Mathematical and Computer Modelling, vol 44, pp: 678–691
XVI. William C. Herndon, (November 1997), “On Balancing Chemical Equations: Past and Present”, Journal of Chemical Education, vol 74, No 11, pp: 1359-1362.

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Abstract:

In this paper, the framework of polyp image segmentation is developed using a Deep neural network (DNN). Here Unet Mobile NetV2 is considered to evaluate the performance of the image from the CVC-612 dataset for the segmentation method. The proposed model outperformed earlier results. To compare our results two parameters, normally Dice co-efficient and Intersection over Union (IoU) are considered. The proposed model may be used for accurate computer-aided polyp detection and segmentation during colonoscopy examinations to find out abnormal tissue and thereby decrease the chances of polyps growing into cancer. MobileNetV2 significantly outperforms U-Net and MobileNetV2, two key state-of-the-art deep learning architectures, by achieving high evaluation scores with a dice coefficient of 89.71%, and an IoU of 81.64%.

Keywords:

Deep Neural network,Semantic segmentation,UNet MobileNetV2,

Refference:

I. A. Arezzo, A. Koulaouzidis, A. Menciassi, D. Stoyanov, E. B. Mazomenos, F. Bianchi, G. Ciuti, P. Brandao, P. Dario, R. Caliò, Fully convolutional neural networks for polyp segmentation in colonoscopy. In: International Society for Optics and Photonics. Medical Imaging 2017: Computer-Aided Diagnosis, v. 10134, p. 101340F, 2017.
II. A. Howard, M. Zhu, A. Zhmoginov, L-C. Chen, M. Sandler, MobileNetV2: Inverted Residuals and Linear Bottlenecks. 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, p. 4510-4520, 2018.
III. A. Howard, M. Zhu, A. Zhmoginov, L-C. Chen, M. Sandler, MobileNetV2: Inverted Residuals and Linear Bottlenecks. 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, p. 4510-4520, 2018.
IV. A. V. Mamonov, I. N. Figueiredo, P. N. Figueiredo Y-H. R. Tsai, Automated polyp detection in colon capsule endoscopy. IEEE transactions on medical imaging, v. 33, n. 7, p. 1488–1502, 2014.
V. B. Paul, S. A. Fattah, T. Mahmud, Polypsegnet: A modified encoderdecoder architecture for automated polyp segmentation from colonoscopy images. Computers in Biology and Medicine, p. 104119, 2020.
VI. D-P. Fan, G. Chen, G-P. Ji, H. Fu, J. Shen, L. Pranet Shao, T. Zhou, : Parallel reverse attention network for polyp segmentation. In: SPRINGER.International Conference on Medical Image Computing and ComputerAssisted Intervention, p. 263–273, 2020.
VII. D. Jha, D. Johansen, H. D. CVC-612, Johansen, M. A. Riegler, P. Halvorsen, P. H. Smedsrud, T. Lange : A Segmented Polyp Dataset. In Proc. of International Conference on Multimedia Modeling (MMM), p. 451-462, 2019.
VIII. D. Jha, H. D. Johansen, M. A. Riegler, P. Halvorsen, P. H. Smedsrud, T. Lange, ResUNet++: An Advanced Architecture for Medical Image Segmentation. 2019 IEEE International Symposium on Multimedia (ISM),2019.
IX. E. Dekker, J. C. V. Rijn, J. B. Reitsma, J. Stoker, P. M. Bossuyt, S. J. V. Deventer, Polyp miss rate determined by tandem colonoscopy: a systematic review. The American journal of gastroenterology, v. 101, p. 343, 2006.
X. E. Nasr-Esfahani, K. Najarian, M. Akbari, M. Mohrekesh, N. Karimi, S. M. R. Soroushmehr, S. Samavi, Polyp segmentation in colonoscopy images using fully convolutional network. In: IEEE. 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), p. 69–72, 2018.

XI. F. Chollet, Keras. https://github.com/fchollet/keras, 2015.
XII. J. Deng, K. Li, L. Fei-Fei, L-J. Li, R. Socher, W. Dong, Imagenet: A large-scale hierarchical image database. In: IEEE conference on computer vision and pattern recognition, p. 248–255, 2009.
XIII. J. Liang, N. Tajbakhsh, S. R. Gurudu, Automated polyp detection in colonoscopy videos using shape and context information. IEEE transactions on medical imaging, v. 35, n. 2, p. 630–644, 2015.
XIV. O. Ronneberger, P. Fischer, T. Brox, U-net: Convolutional networks forbiomedical image segmentation. In: SPRINGER. International Conference on Medical image computing and computer-assisted intervention, p. 234–241, 2015.
XV. N. K. Tomar, Automatic Polyp Segmentation using Fully Convolutional Neural Network, 2021.

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Abstract:

The existing article examines the mathematical model (MM) representing electrical engineering (EE). We implement the unified technique (UT) to discover new wave solutions (WS) and to erect numerous kinds of solitary wave phenomena (SWP) for the studied model (SM). The SM is one of the models that have vital applications in the area of EE. The taken features provide a firm mathematical framework and may be necessary to the WSs. As an outcome, we get new kinds of WSs from. With 3-d, density, contour, and 2-d for different values of time parameters, mathematical effects explicitly manifest the suggested algorithm's full reliability and large display. We implement a few figures in 3-d, density, contour, and 2-d for diverse values of time parameters to express that these answers have the properties of soliton waves.

Keywords:

The UT method,MM,the modified Zakharov-Kuznetsov equation,EE,WSs,

Refference:

I. Abdul Majeed, Muhammad Naveed Rafiq, Mohsin Kamran, Muhammad Abbas and Mustafa Inc, Analytical solutions of the fifth-order time fractional nonlinear evolution equations by the unified method, Modern Physics Letters BVol. 36, No. 02, 2150546 (2022)
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III. A.B.T. Motcheyo, C. Tchawoua and J.D.T. Tchameu, Supra transmission induced by waves collisions in a discrete electrical lattice, Phys. Rev. E, 88 (4), 040901 (2013).
IV. A. Das, Explicit weierstrass traveling wave solutions and bifurcation analysis for dissipative Zakharov-Kuznetsov modified equal width equation, Comput. Appl. Math., 37(3), 3208-3225 (2018).
V. A. Korkmaz, O.E. Hepson, K. Hosseini, H. Rezazadeh, M. Eslami, Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class, J. King Saud University-Science, 32 (1) (2020), pp. 567-574
VI. A.S. Fokas and I.M. Gelfand, A Unified Method for Solving Linear and Nonlinear Evolution Equations and an Application to Integrable Surfaces. In: Gelfand, I.M., Lepowsky, J., Smirnov, M.M. (eds) The Gelfand Mathematical Seminars, 1993–1995. (1996). Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4082-2_5
VII. B. Augner, Well-posedness and stability of infinite dimensional linear port-Hamiltonian systems with nonlinear boundary feedback, SIAM J. Control Optim., 57 (3), 1818-1844, (2019).
VIII. B.S. Bardin and E.A. Chekina, On the constructive algorithm for stability analysis of an equilibrium point of aperiodic hamiltonian system with two degrees of freedom in the case of combinational resonance, Regul. Chaotic Dynam., 24 (2), 127-144 (2019).
IX. Deiakeh RA, Ali M, Alilquran M, Sulaiman TA, Momani S, Smadi MA. On finding closed-form solutions to some nonlinear fractional systems via the combination of multi-Laplace transform and the Adomian decomposition method. Romanian Reports in Physics. 2022; 74(2): 111.
X. F. F. Linares and G. Ponce, On special regularity properties of solutions of the Zakharov-Kuznetsov equation, Commun. Pure Appl. Anal., 17 (4), 1561-1572 (2018).
XI. F. Usta, Numerical analysis of fractional Volterra integral equations via Bernstein approximation method, J. Compu. Appl. Maths., 384 (2021), Article 113198, (2021).
XII. G.R. Deffo, S.B. Yamgoue and F.B. Pelap, Modulational instability and peak solitary wave in a discrete nonlinear electrical transmission line described by the modified extended nonlinear Schrodinger equation, Eur. Phys. J.B, 91 (10), 242 (2018).
XIII. G. R. Duan, Analysis and design of descriptor linear systems. Springer, (2010).
XIV. H. Ahmad, Md. Nur Alam, Md. Abdur Rahman, Maged F Alotaibid and M. Omri, The unified technique for the nonlinear time-fractional model with the beta-derivative, Results in Physics, 29 (2021), 104785; DOI: https://doi.org/10.1016/j.rinp.2021.104785
XV. Joseph SP. New traveling wave exact solutions to the coupled Klein–Gordon system of equations, Partial Differential Equations in Applied Mathematics. 2022; 5: 100208.
XVI. K.S. Nisar, O.A. Ilhan, S.T. Abdulazeez, J. Manafian, S.A. Mohammed, M.S. Osman, Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method Results Phys., 21 (2021), p. 103769
XVII. Ma WX, Soliton solutions by means of Hirota bilinear forms. Partial Differential Equations in Applied Mathematics. 2022; 5: 100220.
XVIII. M. Eslami and H. Rezazadeh, The first integral method for Wu–Zhang system with conformable time-fractional derivative, Calcolo, 53 (2016), pp. 475-485, (2016).
XIX. M. N. Alam, A. R. Seadawy and D. Baleanu, Closed-form solutions to the solitary wave equation in an unmagnatized dusty plasma, Alexandria Engineering Journal, 59(3): 1505-1514, (2020).
XX. M. N. Alam, A. R. Seadawy and D. Baleanu, Closed-form wave structures of the space-timefractional Hirota–Satsuma coupled KdVequation with nonlinear physical phenomena, Open Physics, 18(1): 555-565, (2020).

XXI. M. N. Alam and C. Tunc, The new solitary wave structures for the (2 + 1)-dimensional time-fractional Schrodinger equation and the space-time nonlinear conformable fractional Bogoyavlenskii equations, Alexandria Engineering Journal, 59(4): 2221-2232, (2020).
XXII. M.N. Alam, O.A. Ilhan, J. Manafian, M.I. Asjad, H. Rezazadeh and H.M. Baskonus, New results of some conformable models arising in dynamical systems, Advances in Mathematical Physics, Volume 2022 (2022), Article ID 7753879 DOI: https://doi.org/10.1155/2022/7753879.
XXIII. M. N. Alam, S. Aktar and C. Tunc, New solitary wave structures to time fractional biological population model, Journal of Mathematical Analysis-JMA, 11(3): 59-70, (2020).
XXIV. M. N. Alam and X. Li, New soliton solutions to the nonlinear complex fractional Schrödinger equation and the conformable time-fractional Klein–Gordon equation with quadratic and cubic nonlinearity, Physica Scripta, 95: 045224, (2020).
XXV. M.N. Alam, O.A. İlhan, M.S. Uddin and M.A. Rahim, Regarding on the results for the fractional Clannish Random Walker’s Parabolic equation and the nonlinear fractional Cahn-Allen equation, Advances in Mathematical Physics, 2022, Article ID 5635514, (2022).
XXVI. N. Raza, M.H. Rafiq, M. Kaplan, S. Kumar and Y.M. Chu, The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations, Results in Physics, 22, 103979, (2021).
XXVII. N. Raza and M.H. Rafiq, Abundant fractional solitons to the coupled nonlinear Schrödinger equations arising in shallow water waves, Internat J Modern Phys B, 34 (18) (2020), Article 2050162, (2020).
XXVIII. R. Saleh, S.M. Mabrouk and A.M. Wazwaz, Lie symmetry analysis of a stochastic gene evolution in double-chain deoxyribonucleic acid system. Waves in Random and Complex Media, https://doi.org/10.1080/17455030.2020.1871109 (2021).
XXIX. Shakeel M, Attaullah, Shah NA, Chung JD. Application of modified exp-function method for strain wave equation for finding analytical solutions. Ain Shams Engineering Journal. 2022; 2022: 101883. DOI: https://doi.org/10.1016/j.asej.2022.101883
XXX. Shakeel M, Attaullah, El-Zahar ER, Shah NA, Chung JD. Generalized exp-function method to find closed form solutions of nonlinear dispersive modified Benjamin-Bona-Mahony equation defined by seismic sea waves. Mathematics. 2022; 10(7): article no. 1026. doi.org/10.3390/math 10071026.
XXXI. S. Duran S, Travelling wave solutions and simulation of the Lonngren wave equation for tunnel diode. Optical and Quantum Electronics, 53, Article number: 458, (2021).
XXXII. S. Duran S, Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics. International Journal of Modern Physics B, 35(9): 2150130. (2021).
XXXIII. Shakeel M, Attaullah, El-Zahar ER, Shah NA, Chung JD. Generalized exp-function method to find closed form solutions of nonlinear dispersive modified Benjamin-Bona-Mahony equation defined by seismic sea waves. Mathematics. 2022; 10(7): article no. 1026. doi.org/10.3390/math 10071026.
XXXIV. Thottoli SR, Tamsir M, Dhiman N, Souadi G. Computational modeling of the Balitsky–Kovchegov equation and its numerical solution using hybrid B-spline collocation technique. Partial Differential Equations in Applied Mathematics. 2022; 5: 100348.
XXXV. Tripathy A, Sahoo S. The new optical behaviour of the LPD model with Kerr law and parabolic law of nonlinearity. Partial Differential Equations in Applied Mathematics.2022; 5: 100334.
XXXVI. T.T. Guy and J.R. Bogning, Construction of Breather soliton solutions of a modeled equation in a discrete nonlinear electrical line and the survey of modulationnal in stability, J. Phys. Commun., 2 (11), 115007 (2018).
XXXVII. Yiren Chen1 and Shaoyong Li, New Traveling Wave Solutions and Interesting Bifurcation Phenomena of Generalized KdV-mKdV-Like Equation, Advances in Mathematical PhysicsVolume 2021 |Article ID 4213939 | https://doi.org/10.1155/2021/4213939
XXXVIII. Younas U, Sulaiman TA, Ren J. Diversity of optical soliton structures in the spinor Bose-Einstein condensate modeled by three-component Gross–Pitaevskii system. International Journal of Modern Physics B. 2022; 2022: 2350004. https://doi.org/10.1142/S0217979223500042.
XXXIX. Younas U, Sulaiman TA, Ren J. On the optical soliton structures in the magneto electro elastic circular rod modeled by nonlinear dynamical longitudinal wave equation. Optical and Quantum Electronics. 2022; 54: 688.
XL. Yusuf A, Sulaiman TA, Alshomrani AS, D. Baleanu D. Optical solitons with nonlinear dispersion in parabolic law medium and threecomponent coupled nonlinear Schrödinger equation. Optical and Quantum Electronics. 2022; 54 (6): 1-13.
XLI. X. Zhou, W. Shan, Z. Niu, P. Xiao and Y. Wang, Lie symmetry analysis and some exact solutions formodified Zakharov-Kuznetsov equation, Mod. Phys. Lett. B, 32(31), 1850383 (2018).
XLII. Z. Rached, On exact solutions of Chafee–Infante differential equation using enhanced modified simple equation method, J. Interdiscip. Math., 22 (6) (2019), pp. 969-974, (2019).

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