Archive

Abstract:

The methods to obtain a solution of non-homogeneous linear ordinary differential equations with constant coefficients vary from type of output function. The present paper addresses the undetermined coefficients, variations of parameters methods and discussed the rewards and drawbacks of these methods with examples. The method of undetermined coefficients is derived from the variation of parameters when the out function is an exponential function.

Keywords:

Non-homogeneous linear,Constant coefficients,exponential function,

Refference:

I. B. S. Grewal, Higher Engineering, 42nd Edition, Khanna Publications, New Delhi, 2012

II. Coddington, E.A and N. Levinson: theory of ordinary differential equation, New York,

III. Erwin Kreyszig: Advanced Engineering Mathematics, Wiley – India, 2006.

IV. G. F. Simmons., Differential Equations with applications and historical notes, 3rd Edition,

V. Ince, E. L., Ordinary Differential Equations, New York: Dover, (1956).

VI. Md. Alamin Khan, Abu Hashan Md. Mashud, M. A. Halim, NUMEROUS EXACT SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS BY TAN–COT METHOD, J.Mech.Cont.& Math. Sci., Vol.-11, No.-2, January (2017) Pages 37-48

VII. Mohammad Asif Arefin, Biswajit Gain, Rezaul Karim, Saddam Hossain, : A COMPARATIVE EXPLORATION ON DIFFERENT NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-12, December (2020) pp 1-11.

COMPOUND PROPOSITIONAL LAW FOR LOGICAL EQUIVALENCE, TAUTOLOGY AND CONTRADICTION

Authors:

Umair Khalid Qureshi, Parivish Sami Lander, Shahzad Ali Khaskheli, Manzar Bashir Arain, Zubair Ahmed Kalhoro, Syed Hasnain Ali Shah, Amir Khan Mari, Saifullah Bhatti

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00002

Abstract:

This paper presents a Compound Propositional Law for Logical Equivalence, Tautology and Contradiction. The proposed Law is developed with the help of negation, disjunction, conjunction, exclusive or, conditional statement and bi-conditional statement. The idea of research is taken from de-Morgan law. This proposed law is important and useful for Logical Equivalence, Tautology and Contradiction for the research purpose because these are the rare cases in the field of research. This article aims to help readers understand the compound proposition and proposition equivalence in conducting research. This article discusses propositions that are relevant for proposition equivalence. Six main compound propositions are distinguished and an overview is given in the article. Hence, it is observed from the result and discussion that the compound proposition law is a good achievement in discrete structure for the logical Equivalence, Tautology and Contradiction purpose.

Keywords:

Proposition Equivalence,Compound Proposition,Truth Table,Result Analysis,Logical Symbols,

Refference:

I. Agassi, J., Tautology and Testability in Economics, Philosophy of the Social Sciences, Phil. Soc. Sci. vol: 1, pp. 49-63.
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III. Crisler, N., P. Fisher. Discrete mathematics through Applications. W. H. Freeman and Company, 1994.
IV. Kiran, K., Computational Thinking and Its Role in Discrete Mathematics, Biz and Bytes, Vol: 7(1), 2016.
V. Kwon, I., A Tautology is a Tautology: Specificity and Categorization in Nominal Tautological Constructions, In the Proceedings of the 35th annual meeting of berkeley linguistics society, 2009.
VI. Liu, J. and L. Wang, Computational Thinking in Discrete Mathematics, Second International Workshop on Education Technology and Computer Science, 2010.
VII. Ljnda, C. M., R. I Horvotzt and A. R. Fhnstbn, A Collection of 56 Topics with Contradictory Results in Case Control Research, International Journal of Epidemiology, vol: 17(3), 2015.
VIII. Marcela, P., L. Osorio and Á. A. Caputi, Perceptual Judgments of Logical Propositions, Asian Journal of Research and Reports in Neurology, vol: 2(1), pp 1-14, 2019.
IX. Marion, B., Final Oral Report on the SIGCSE Committee on the Implementation of a Discrete Mathematics Course. In SIGCSE Technical Symposium on Computer Science Education, vol: 2006, pp-268-279, 2006.
X. Selva, J. A. N., J. L. U. Domenech and H. Gash, A Logic-Mathematical Point of View of the Truth: Reality, Perception, and Language, 2014.

DESIGN AND DEVELOPMENT OF RESOLDEPMIRROR: A SMART MIRROR FOR RESOLVING DEPRESSION

Authors:

Muhammad Waqar Aziz, Maha Maqbool Sethi, Ali Sayyed, Kifayat Ullah

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00003

Abstract:

Health is a precious gift from God. Both physical and mental health is equally important for living a quality life. Negligence towards mental health creates a lot of serious health problems affecting both physical health and society. Mental health is associated with better performance, high efficiency, and lesser work environment mishaps. Internet of Things technologies can possibly create smart products that can react to human needs and improve the quality of life and can make traditional environments more favorable and intelligent. One such internet of things solution is the design and development of smart mirrors. The opportunity to apply smart technology to healthcare to foresee and to monitor aspects of mental health is a natural but mostly underdeveloped idea. Although several smart mirror solutions have been proposed for different purposes, it has not been developed for the treatment of depression. We believe that smart mirrors involving a combination of hardware and software could identify depression as well as offer feedback for corrective measures and remedial activities. This paper examines the potential use of a smart mirror in healthcare and examines how this technology might benefit users in resolving depression. We present the design and development of a smart mirror that can diagnose and provide digitized treatment to resolve depression. The developed mirror is tested on humans, and from the obtained results, it is concluded that the developed mirror is more accurate and inexpensive as compared to existing smart mirrors.

Keywords:

Smart Mirror,Depression,Cognitive Behavior Therapy,Convolution Neural Network,Internet of Things ,

Refference:

I. A. A. E. Hippocrate, E. T. Luhanga, T. Masashi, K. Watanabe, K. Yasumoto, Smart gyms need smart mirrors: design of a smart gym concept through contextual inquiry, in: Proceedings of the 2017 ACM International Joint Conference Pervasive and Ubiquitous Computing and Proceedings of the 2017 ACM International Symposium on Wearable Computers, 2017, pp. 658-661.
II. A. Jhala, “emotions” (psychology) (01 2015).
III. A. Olowolayemo, S. Alenazi, F. A. S. Seri, Mirror that talks: A self-motivating personal vision assistant, in: Proceedings of the 2018 International Conference on Image and Graphics Processing, 2018, pp. 157-161.
IV. A. S. A. Mohamed, M. A. Wahab, S. Suhaily, D. B. L. Arasu, Smart mirror design powered by raspberry pi, in: Proceedings of the 2018 Artificial Intelligence and Cloud Computing Conference, 2018, pp. 161-171
V. A. Salgian, D. Vickerman, D. Vassallo, A smart mirror for music conducting exercises, in: Proceedings of the on Thematic Workshops of ACM Multimedia 2017, 2017, pp. 544-549.
VI. B. G. Shapero, J. Greenberg, P. Pedrelli, G. Desbordes, S. W. Lazar, Mindfulness-based cognitive therapy, in: The Massachusetts General Hospital Guide to Depression, Springer, 2019, pp. 167-177.
VII. C. Gold, Signal and noise in music therapy outcome studies (2014).
VIII. C. Sethukkarasi, V. S. Harikrishnan, R. Pitchiah, Design and development of in-teractive mirror for aware home, 2012.
IX. D. Besserer, J. Baurle, A. Nikic, F. Honold, F. Schussel, M. Weber, Fitmirror: a smart mirror for positive affect in everyday user morning routines, in: Proceedings of the Workshop on Multimodal Analyses enabling Arti cial Agents in Human-Machine Interaction, 2016, pp. 48-55.
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XIII. J. LeMoult, I. H. Gotlib, Depression: A cognitive perspective, Clinical Psychology Review 69 (2019) 51-66.
XIV. K. Fujinami, F. Kawsar, T. Nakajima, Awaremirror: a personalized display using a mirror, in: International Conference on Pervasive Computing, Springer, 2005, pp. 315-332.
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XVII. M. H. Jasim, M. M. Salih, Z. T. Abdulwahhab, M. L. Shouwandy, M. A. Ahmed, A. ALsalem, A. K. Hamzah, Emotion detection among Muslims and non-Muslims while listening to Quran recitation using EEG (2019).
XVIII. M. M. Khan, et al., Economic burden of mental illnesses in Pakistan., Journal of Mental Health Policy and Economics 19 (3) (2016) 155.
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XXII. P. Deepan, L.R. Sudha, : Fusion of Deep Learning Models for Improving Classification Accuracy of Remote Sensing Images, J. Mech. Cont.& Math. Sci., Vol.-14, No.-5, September-October (2019) pp 189-201.
XXIII. P. Henriquez, B. J. Matuszewski, Y. Andreu-Cabedo, L. Bastiani, S. Colantonio, Coppini, M. D’Acunto, R. Favilla, D. Germanese, D. Giorgi, et al., Mirror mirror on the wall… an unobtrusive intelligent multisensory mirror for well-being status self-assessment and visualization, IEEE transactions on multimedia 19 (7) (2017) 1467-1481.
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XXVI. R. Santhoshkumar, M. Kalaiselvi Geetha, : Deep Learning Approach: Emotion Recognition from Human Body Movements, J. Mech. Cont.& Math. Sci., Vol.-14, No.-3, May-June (2019) pp 182-195.
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XXXIII. Y. B. Moon, S. W. Oh, H. J. Kang, H. S. Lee, S. J. Kim, H. C. Bang, Smart mirror health management services based on IoT platform, in: Proceedings of the 14th International Conference on Applications of Computer Engineering (ACE’15), 2015, pp. 87-89.
XXXIV. Y.-C. Yu, S. D. You, D.-R. Tsai, Magic mirror table for social-emotion alleviation in the smart home, IEEE Transactions on Consumer Electronics 58 (1) (2012) 126-131.

AN EFFICIENT FOUR-POINT QUADRATURE SCHEME FOR RIEMANN-STIELTJES INTEGRAL

Authors:

Kashif Memon , Muhammad Mujtaba Shaikh, Muhammad Saleem Chandio, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00004

Abstract:

In this work, a new four-point quadrature scheme is proposed for efficient approximation of the Riemann-Stieltjes integral (RS-integral). The composite form of the proposed scheme is also derived for the RS-integral from the concept of precision. Theoretically, the theorems related to the basic form, composite form, local and global errors of the new scheme are proved on the RS-integral. The correctness of the new proposed scheme is checked by g(t) = t, which reduces the proposed scheme into the original form of Simpson’s 3/8 rule for Riemann integral. The efficiency of the new proposed scheme is demonstrated by experimental work using programming in MATLAB against existing schemes. The order of accuracy and computational cost of the new proposed scheme is computed. The average CPU time is also measured in seconds. The obtained results demonstrate the efficiency of the proposed scheme over the existing schemes.

Keywords:

Quadrature rule,Riemann-Stieltjes,Simpson’s 3/8 rule,Composite form, Local error,Global error,Cost-effectiveness,Time-efficiency,

Refference:

I. Bartle, R.G. and Bartle, R.G., The elements of real analysis, (Vol. 2). John Wiley & Sons, 1964.
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., Faires, J.D., Numerical Analysis, Brooks/Cole, Boston, Mass, USA, 9th edition, 2011.
IV. Dragomir, S.S., and Abelman S., Approximating the Riemann-Stieltjes integral of smooth integrands and of bounded variation integrators, Journal of Inequalities and Applications 2013.1 (2013), 154.
V. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Error analysis of closed Newton-Cotes cubature schemes for double integrals, : J. Mech. Cont. & Math. Sci., Vol. 15, No.11, pp. 95-107, 2020.
VI. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Some new and efficient derivative-based schemes for numerical cubature J. Mech. Cont. & Math. Sci., Vol. 15, No.10, pp. 67-78, 2020.
VII. Mastoi, Adnan Ali, Muhammad Mujtaba Shaikh, and Abdul Wasim Shaikh. A new third-order derivative-based iterative method for nonlinear equations., J. Mech. Cont. & Math. Sci., Vol. 15, No.10, pp. 110-123, 2020.
VIII. 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.
IX. Memon K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. A new and efficient Simpson’s 1/3-type quadrature rule for Riemann-Stieltjes integral., : J. Mech. Cont. & Math. Sci., Vol. 15, No.11, pp. 132-148, 2020.
X. Memon, A. A., Shaikh, M. M., Bukhari, S. S. H., & Ro, J. S. 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, 2020.
XI. Mercer, P.R., Hadamard’s inequality and Trapezoid rules for the Riemann-Stieltjes integral, Journal of Mathematica Analysis and Applications, 344 (2008), 921-926.
XII. Mercer, P.R., Relative convexity and quadrature rules for the Riemann-Stieltjes integral, Journal of Mathematica inequality, 6 (2012), 65-68.
XIII. Protter, M.H. and Morrey, C.B., A First Course in Real Analysis . Springer, New York, NY, 1977.
XIV. Shaikh, MM., MS Chandio and AS Soomro, A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration, Sindh University Research Journal- SURJ (Science Series)
48.2 (2016).
XV. Shaikh, Muhammad Mujtaba, Shafiq-ur-Rehman Massan, and Asim Imdad Wagan. “A new explicit approximation to Colebrook’s friction factor in rough pipes under highly turbulent cases.” International Journal of Heat and Mass Transfer 88 (2015): 538-543.

XVI. Shaikh, Muhammad Mujtaba, Shafiq-ur-Rehman Massan, and Asim Imdad Wagan. “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 (2019): 104733.
XVII. Shaikh, Muhammad Mujtaba. “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 7.4 (2019): 91-97
XVIII. Umar, Sehrish, Muhammad Mujtaba Shaikh, and Abdul Wasim Shaikh. A new quadrature-based iterative method for scalar nonlinear equations. J. Mech. Cont. & Math. Sci., : Vol. 15, No.10, pp 79-93, 2020.
XIX. Zhao, W., and H. Li, Midpoint Derivative-Based Closed Newton-Cotes Quadrature, Abstract And Applied Analysis, Article ID 492507, (2013).
XX. Zhao, W., Z. Zhang, and Z. Ye, Composite Trapezoid rule for the Riemann-Stieltjes Integral and its Richardson Extrapolation Formula, Italian Journal of Pure and Applied Mathematics, 35 (2015), 311-318.
XXI. Zhao, W., Z. Zhang, and Z. Ye, Midpoint Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral, Italian Journal of Pure and Applied Mathematics, 33, (2014), 369-376.

CLOSED NEWTON-COTES CUBATURE SCHEMES FOR TRIPLE INTEGRALS WITH ERROR ANALYSIS

Authors:

Kamran Malik , Muhammad Mujtaba Shaikh, Muhammad Saleem Chandio, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00005

Abstract:

Most of the problems in applied sciences in engineering contain integrals, not only in one dimension but also in higher dimensions. The complexity of integrands of functions in one variable or higher variables motivates the quadrature and cubature approximations. Much of the work is focused on the literature on single integral quadrature approximations and double integral cubature schemes. On the other hand, the work on triple integral schemes has been quite rarely focused. In this work, we propose the closed Newton-Cotes-type cubature schemes for triple integrals and discuss consequent error analysis of these schemes in terms of the degree of precision and local error terms for the basic form approximations. The results obtained for the proposed triple integral schemes are in line with the patterns observed in single and double integral schemes. The theorems proved in this work on the local error analysis will be a great aid in extending the work towards global error analysis of the schemes in the future.

Keywords:

Cubature,Triple integrals,closed Newton-Cotes,Precision,Order of accuracy,Local error,Global error,

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., :J. Mech. Cont. & Math. Sci., Vol. 15, No.11, pp. 67-78, 2020.
X. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Error analysis of closed Newton-Cotes cubature schemes for double integrals., : J. Mech. Cont. & Math. Sci.,Vol. 15, No.11, pp. 95-107, 2020.
XI. 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.
XII. Memon K, Shaikh MM, Chandio MS and Shaikh AW, A new and efficient Simpson’s 1/3-type quadrature rule for Riemann-Stieltjes integral, : J. Mech. Cont. & Math. Sci.,Vol. 15, No.11, pp. 132-148, 2020.
XIII. 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.
XIV. Pal, M., Numerical Analysis for Scientists and Engineers: theory and C programs, Alpha Science, Oxford, UK, 2007.
XV. 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.
XVI. 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.
XVII. Walter Guatschi, Numerical analysis second edition, Springer Science business, Media LLC 1997, 2012.
XVIII. Weijing Zhao and Hongxing, “Midpoint Derivative-Based Closed Newton-Cotes Quadrature”, Abstract and Applied Analysis, vol.2013, Article ID 492507, 10 pages, 2013.
XIX. 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.

THE MAXIMUM RANGE COLUMN METHOD – GOING BEYOND THE TRADITIONAL INITIAL BASIC FEASIBLE SOLUTION METHODS FOR THE TRANSPORTATION PROBLEMS

Authors:

Huzoor Bux Kalhoro , , Hafeezullah Abdulrehman, Muhammad Mujtaba Shaikh, Abdul Sattar Soomro

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00006

Abstract:

The transportation problems (TPs) are a fundamental case-study topic in operations research, particularly in the field of linear programming (LP). The TPs are solved in full resolution by using two types of methods: initial basic feasible solution (IBFS) and optimal methods. In this paper, we suggest a novel IBFS method for enhanced reduction in the transportation cost associated with the TPs. The new method searches for the range in columns of the transportation table only, and selects the maximum range to carry out allocations, and is therefore referred to as the maximum range column method (MRCM). The performance of the proposed MRCM has been compared against three traditional methods: North-West-Corner (NWCM), Least cost (LCM) and Vogel’s approximation (VAM) on a comprehensive database of 140 transportation problems from the literature. The optimal solutions of the 140 problems obtained by using the TORA software with the modified distribution (MODI) method have been taken as reference from a previous benchmark study. The IBFSs obtained by the proposed method against NWCM, LCM and VAM are mostly optimal, and in some cases closer to the optimal solutions as compared to the other methods. Exhaustive performance has been discussed based on absolute and relative error distributions, and percentage optimality and nonoptimality for the benchmark problems. It is demonstrated that the proposed MRCM is a far better IBFS method for efficiently solving the TPs as compared to the other discussed methods, and can be promoted in place of the traditional methods based on its performance.

Keywords:

Transportation problem,optimal solution,MODI method,TORA software,Minimum cost,Initial basic feasible solution,Maximum range,

Refference:

I. Adlakha, Veena, and Krzysztof Kowalski. “Alternate solutions analysis for transportation problems.” Journal of Business & Economics Research 7.11 (2009): 41-49.
II. Bhan, Veer, Ashfaque Ahmed Hashmani, and Muhammad Mujtaba Shaikh. “A new computing perturb-and-observe-type algorithm for MPPT in solar photovoltaic systems and evaluation of its performance against other variants by experimental validation.” Scientia Iranica 26, no. Special Issue on machine learning, data analytics, and advanced optimization techniques in modern power systems [Transactions on Computer Science & Engineering and Electrical Engineering (D)] (2019): 3656-3671.
III. Chungath Linesh, “Comparison of Transportation Problems Solved by Vogel’s Approximation Method (VAM-1958), Revised Distribution Method (RDI -2013) & The New Method”, available online, 2004 @ https://www.academia.edu/1137498
IV. Das, Utpal Kanti, et al. “Logical development of vogel’s approximation method (LD-VAM): an approach to find basic feasible solution of transportation problem.” International Journal of Scientific & Technology Research 3.2 (2014): 42-48.
V. Deshmukh, N. M. “An innovative method for solving transportation problem.” International Journal of Physics and Mathematical Sciences 2.3 (2012): 86-91.
VI. Goyal, S. K. “Improving VAM for unbalanced transportation problems.” Journal of the Operational Research Society 35.12 (1984): 1113-1114.
VII. Hakim, M. A. “An alternative method to find initial basic feasible solution of a transportation problem.” Annals of pure and applied mathematics 1.2 (2012): 203-209.
VIII. Islam Md Amirul, Aminur Rehman Khan, Sharif Uddin M and Abdul Malek M Islam. “Determination of basic feasible solution of transportation problem: a new approach.” Jahangirnagar University Journal of Science 35.1 (2012): 101-108.
IX. Jamali, S., Shaikh, M. M., & Soomro, A. S. (2019). Overview of Optimality of New Direct Optimal Methods for the Transportation Problems. Asian Research Journal of Mathematics, 15(4), 1-10.
X. Jamali S., Soomro, A. S., & Shaikh, M. M. (2020). The Minimum Demand Method – A New and Efficient Initial Basic Feasible Solution Method for Transportation Problems., : J. Mech. Cont.& Math. Sci., Vol. 15, No.10, pp. 94-105.
XI. Kalhoro H. B., Abdulrehman H., Shaikh, M. M., Soomro, A. S. (2020). A pioneering and comprehensive database of balanced and unbalanced transportation problems for ready performance evaluation of existing and new methods. J. Mech. Cont.& Math. Sci., Vol. 15, No.11, pp. 149-159.
XII. Korukoğlu, Serdar, and Serkan Ballı. “A Improved Vogel’s Approximation Method for the Transportation Problem.” Mathematical and Computational Applications 16.2 (2011): 370-381.
XIII. Mamidi, Pushpa Latha. “Ones method for finding an optimal solution for transportation problem.” In Proceedings International Conference On Advances In Engineering And Technology, International Association of Engineering & Technology for Skill Development, 41-45, ISBN NO: 978 – 1503304048,
XIV. Massan, S.-u-R., Wagan, A. I., & Shaikh, M. M.. “A new metaheuristic optimization algorithm inspired by human dynasties with an application to the wind turbine micrositing problem.” Applied Soft Computing 90 (2020): 106176.
XV. Pandian, P., and G. Natarajan. “A new method for finding an optimal solution for transportation problems.” International J. of Math. Sci. and Engg. Appls 4 (2010): 59-65.
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STRUM-LIOUVILLE FORM AND OTHER IMPORTANT PROPERTIES OF MODIFIED ORTHOGONAL BOUBAKER POLYNOMIALS

Authors:

Nazeer Ahmed Khoso, Muhammad Mujtaba Shaikh, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00007

Abstract:

In this paper, some classical properties of modified orthogonal Boubaker polynomials (MOBPs) are considered, which are: the three-term recurrence relation, Rodriguez formula, characteristic differential equation and the Strum-Liouville form. The only properties of the MOBPs known so far are orthogonality evidence, weight function, orthonormality evidence and zeros. The new properties established in this work will to the applicability of the MOBPs in different areas of science and engineering where the classical non-orthogonal Boubaker polynomials could be applied, and even in cases where these cannot be applied.

Keywords:

Recurrence relation, Rodriguez’s formula, Orthogonality, Strum-Liouville form.,Rodriguez’s formula,Orthogonality,Strum-Liouville form,

Refference:

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ENHANCING STRUCTURAL RESPONSE USING INERTER DAMPERS

Authors:

Shahad Nazar Jabbar, Waleed K. Al-Ashtari

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00008

Abstract:

This paper deals with one kind of dampers which is inerter damper, Inerter is a new mechanical element proposed by Professor Malcolm C. Smith from Cambridge University, which is defined as a mechanical two-terminal, one-port device with the property that the equal and opposite force applied at the terminals is proportional to the relative acceleration between the terminals the principle work of inerter damper is how to convert the linear motion into rotational motion to mitigation the external excitation. Theoretical analysis was presented first part is the analytical study which made modeling for the damping structure proposed and get the equation of motion for the inerter behavior, secondly numerical analysis where the program (ANSYS WORK-Bench 18.2) was adopted, and study the parameters which effected on the damping behavior of inerter structure proposed that is (stiffness, coefficient of friction and mass of flywheel). Where it was found that when the stiffness of the springs increased gradually from (0.2, 0.3, 0.4, 0.6 and 0.8) Kn/mm the amplitude reduced from (25.791, 17.194, 12.896, 8.5974 to 6.4482) mm respectively for each stiffness reading, also the mass of inerter when increased gradually (200,400,600,800 and 1000) g with a constant coefficient of friction and constant stiffness 0.4, 0.6 Kn/mm respectively, the amplitude decrease from 6.3525 to 4.036290. Finally, to study the effect inerter mass on the structures, the mass of inerter increased from (200,400,600,800 to 1000) g gradually to the constant cantilever mass structure equal to 130g. The ratio of the inerter mass to the threshold mass is approximately 1.5 to 7.5 As results obtained from the previous study, the amplitude obtained for each mass (1.0778, 1.069, 1.0509, 0.9514 to 0.872) respectively

Keywords:

Inerter damper,enhancing response,ball-screw inerter,

Refference:

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VI. Michael Z. Q. Chen • Yinlong Hu, Inerter and Its Application in Vibration Control Systems Nanjing University of Science and Technology Nanjing, Jiangsu, China
VII. Rami Faraj?, Lukasz Jankowski, Cezary Graczykowski, Jan Holnicki-Szulc , Can the inerter be a successful shock-absorber? The case of a ball-screw inerter with a variable thread lead, Polish Academy of Sciences, Warsaw, Poland.
VIII. Y. G. Wu a, L. Li a,b, Y. Fana,b,∗, H.Y.Maa, W.J.Wanga, J.-L. Christenc, M.
Ichchou, Design of semi-active dry friction dampers for steady-state vibration: sensitivity analysis and experimental studies School of Energy and Power Engineering, Beihang University, Beijing, 100191, China

EXPERIMENTAL INVESTIGATION OF MECHANICAL PROPERTIES OF SOLID CONCRETE BLOCK MASONRY EMPLOYING DIFFERENT MORTAR RATIOS

Authors:

Muhammad Rizwan, Hanif Ullah, Ezaz Ali Khan, Nayab Khan, Talha Rasheed

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00009

Abstract:

This research work aims to investigate experimentally the mechanical properties of solid concrete blocks as an individual unit and assembly (block masonry) employing different mortar mix ratios. The material properties of the concrete block unit, such as compressive strength and unit weight were explored by taking three samples from the four local factories. The block masonry assemblages were subjected to various load patterns for the evaluation of compressive strength, diagonal tensile strength and shear strength. For the bond, four types of mortars i.e., cement - sand (1:4), cement - sand (1:8), cement – sand - khaka (1:2:2) and cement - sand - khaka (1:4:4) were used in the joints of concrete block masonry assemblages. (Khaka is a by-product formed in the stone crushing process). For each type of mortar, three samples of block masonry were fabricated for compressive strength, shear strength and diagonal tensile strength, and tested in the laboratory. It is observed that the replacement of sand by khaka enhanced the mechanical properties of masonry.

Keywords:

block masonry,mortar,khaka,compressive strength,diagonal tensile strength,shear strength,

Refference:

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XII. G. Mohamad, F. S. Fonseca, A. T. Vermeltfoort, D. R. Martens, and P. B. Lourenço, “Strength, behavior, and failure mode of hollow concrete masonry constructed with mortars of different strengths,” Construction and Building Materials, vol. 134, pp. 489-496, 2017.
XIII. G. Mohamad, F. S. Fonseca, A. T. Vermeltfoort, D. R. Martens, and P. B. Lourenço, “Strength, behavior, and failure mode of hollow concrete masonry constructed with mortars of different strengths,” Construction and Building Materials, vol. 134, pp. 489-496, 2017.
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MODIFIED SIRD MODEL OF EPIDEMIC DISEASE DYNAMICS: A CASE STUDY OF THE COVID-19 CORONAVIRUS

Authors:

Asish Mitra

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00001

Abstract:

The present study shows that a simple epidemiological model can reproduce the real data accurately. It demonstrates indisputably that the dynamics of the COVID-19 outbreak can be explained by the modified version of the compartmental epidemiological framework Susceptible-Infected-Recovered-Dead (SIRD) model. The parameters of this model can be standardized using prior knowledge. However, out of several time-series data available on several websites, only the number of dead individuals (D(t)) can be regarded as a more reliable representation of the course of the epidemic. Therefore it is wise to convert all the equations of the SIRD Model into a single one in terms of D(t). This modified SIRD model is now able to give reliable forecasts and conveys relevant information compared to more complex models.

Keywords:

COVID-19,Epidemic Disease,Modified SIRD Model,Parameter Estimation,

Refference:

I. Anastassopoulou et al. Data-based analysis, modelling and forecasting of the covid-19 out-break. PLOS ONE, 2020. doi:10.1371/journal.pone.0230405.

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III. Castilho et al. Assessing the efficiency of different control strategies for the coronavirus (covid-19) epidemic. ArXiv e-prints, 2020, 2004.03539.

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VI. Duccio Fanelli and Francesco Piazza. Analysis and forecast of covid-19 spreading in China, Italy and France. Chaos, Solitons and Fractals, 134:109761, 2020, 2003.06031. doi:10.1016/j.chaos.2020.109761.

VII. Goncalo Oliveira. Refined compartmental models, asymptomatic carriers and covid-19. ArXiv e-prints, 2020, 2004.14780. doi:10.1101/2020.04.14.20065128.

VIII. Herbert W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42(4):599-653, 2000.

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X. Julie Blackwood and Lauren M. Childs. An introduction to compartmental modeling for the budding infectious disease modeler. Letters in Biomathematics, 5:1:195-221, 2018. doi:10.1080/23737867.2018.1509026.

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XII. Lipsitch et al. Transmission dynamics and control of severe acute respiratory syndrome.Science, 300(5627):1966-1970, 2003. doi:10.1126/science.1086616.

XIII. Loli et al. Preliminary analysis of covid-19 spread in Italy with an adaptive SEIRD model. ArXiv e-prints, 2020, 2003.09909.
XIV. Md. Zaidur Rahman, Md. Abul Kalam Azad, Md. Nazmul Hasan, : MATHEMATICAL MODEL FOR THE SPREAD OF EPIDEMICS, J. Mech.Cont. & Math. Sci., Vol.-6, No.-2, January (2012) Pages 843-858.

XV. Michael Y Li. An Introduction to Mathematical Modeling of Infectious Diseases. Springer International Publishing, 2018.

XVI. Natalie M Linton et all. Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data. Journal of clinical medicine, 9(2):538, 2020.

XVII. Prem et al. The effect of control strategies to reduce social mixing on outcomes of the covid-19 epidemic in Wuhan, China: a modelling study. The Lancet, 5:261-270, 2020. doi:10.1016/S2468-2667(20)30073-6.

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EXPERIMENTAL STUDY OF SPACE HEATING BY AIR HEATER SOLAR WITH PHASE CHANGE THERMAL STORAGE

Authors:

Duaa Saad Saleh, Najim Abid Jassim

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00002

Abstract:

In the current research, studied experimentally of a solar air collector was conducted using latent thermal storage (wax of paraffin), in which energy of solar is collected during the time day, and released after sunset. Experimental studies were conducted under the Climate of Iraq - Baghdad (longitude 44.4 degrees east and latitude 33.34 degrees north). At various rates of mass flow air 0.027 kg / s, 0.03255 kg / s, and 0.038 kg / s in winter 2020 and on clear days, measurements and experimental work were conducted. The experimental findings indicated that the speed of paraffin wax melting is reversely proportional to the rate of mass flow of air. In m=0.038kg/s, the maximum heat gain value occurs. An increase in the rate of air mass flow decreases heat storage time.

Keywords:

Air heater solar,Thermal storage,paraffin wax,Space heating,Phase Change Material (PCM).,

Refference:

I. A. E. Kabeel, A. Khalil, S. M. Shalaby, and M. E. Zayed, “Experimental investigation of thermal performance of flat and v-corrugated plate solar air heaters with and without PCM as thermal energy storage,” Energy Convers. Manag., vol. 113, pp. 264–272, 2016.

II. A. S. Mahmood, “Experimental Study on Double-Pass Solar Air Heater with and without using Phase Change Material,” J. Eng., vol. 25, no. 2, pp. 1–17, 2019.

III. Alaa A.Ghulam, Ihsan Y. Hussain, : PERFORMANCE ENHANCEMENTS OF PHASE CHANGE MATERIAL (PCM) CASCADE THERMAL ENERGY STORAGE SYSTEM BY USING METAL FOAM, J. Mech. Cont. & Math. Sci., Vol.-15, No.-5, May (2020) pp 159-173.

IV. Firas Ahmed Khalil, Najim Abed Jassim, : THERMAL PERFORMANCE OF A SOLAR-ASSISTED HEAT PUMP WITH A DOUBLE PASS SOLAR AIR COLLECTOR UNDER CLIMATE CONDITIONS OF IRAQ, J. Mech. Cont.& Math. Sci., Vol.-14, No.-6 November-December (2019) pp 426-449.
V. J. A. Duffie, W. A. Beckman, and N. Blair, Solar engineering of thermal processes, photovoltaics and wind. John Wiley & Sons, 2020.

VI. K. Bin Sopian, M. Sohif, and M. Alghoul, “Output air temperature prediction in a solar air heater integrated with phase change material,” Eur. J. Sci. Res., vol. 27, no. 3, pp. 334–341, 2009.

VII. K. I. Abaas, “The Effect of Using a Paraffin Wax-Aluminum Chip Compound As Thermal Storage Materials in a Solar Air Heater,” Al-Rafidain Univ. Coll. Sci., no. 34, pp. 259–284, 2014.

VIII. M. Sajawal, T. Rehman, H. M. Ali, U. Sajjad, A. Raza, and M. S. Bhatti, “Experimental thermal performance analysis of finned tube-phase change material based double pass solar air heater,” Case Stud. Therm. Eng., vol. 15, p. 100543, 2019.

IX. O. Ojike and W. I. Okonkwo, “Study of a passive solar air heater using palm oil and paraffin as storage media,” Case Stud. Therm. Eng., vol. 14, p. 100454, 2019.

X. P. Charvat, L. Klimes, and O. Pech, “Experimental and numerical study into solar air collectors with integrated latent heat thermal storage,” Cent. Eur. Towar. Sustain. Build. Low-tech high-tech Mater. Technol. Sustain. Build., pp. 1–4, 2013.

XI. S. Bouadila, S. Kooli, M. Lazaar, S. Skouri, and A. Farhat, “Performance of a new solar air heater with packed-bed latent storage energy for nocturnal use,” Appl. Energy, vol. 110, pp. 267–275, 2013.

XII. S. M. Salih, J. M. Jalil, and S. E. Najim, “Experimental and numerical analysis of double-pass solar air heater utilizing multiple capsules PCM,” Renew. Energy, vol. 143, pp. 1053–1066, 2019.

TWO-DIMENSIONAL HYDRODYNAMIC EROSION MODEL APPLIED TO SPUR DYKES

Authors:

Fayaz A. Khan, Humna Hamid, Yasir I. Badrashi

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00003

Abstract:

With the advances in the field of computing, robust CFD models have evolved in the last two decades. Initially, one and two-dimensional models were used but these days, three-dimensional models are used frequently that produce more accurate results. However, the solution of 3D models is expensive not only in terms of computational costs but is time-consuming. In this work, a two-dimensional CFD model that is based on shallow water equations coupled with an erosion model is presented. The equations are solved using finite volume formulation and high-resolution shock capturing methods. This study is an attempt to cover accuracy issues with 2D models by incorporating high-resolution shock capturing methods as compared to 3D models, the solution of which is based on conventional schemes. The model is initially used to simulate dam-break problems over fixed and mobile beds to assess the model stability and hydraulic performance in terms of simulating the flow and bed morphology. The assessment has shown the model to be stable throughout the simulation and the produced results have shown the hydro-dynamic capability of the model. The model is then applied to simulate flow over an erodible sediment bed in a channel with spur dykes on its flood plain. The simulated results are compared with experimental results and numerical results of a 3D model. The comparison has shown a close agreement both with experimental and numerical 3D model results that show that the model could be applied to study bed morphology confidently.

Keywords:

CFD,High Resolution,Shock Capturing,Mobile Beds,

Refference:

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AN ANALYTICAL APPROACH FOR SOLVING THE NONLINEAR JERK OSCILLATOR CONTAINING VELOCITY TIMES ACCELERATION-SQUARED BY AN EXTENDED ITERATION METHOD

Authors:

B. M. Ikramul Haque, Md. Iqbal Hossain

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00004

Abstract:

The technique to evade jerk from a dynamical system is to reduce the rate of acceleration or deceleration. It is an important issue for our real life. In motion control systems the term “jerk” is the main topic. The jerk equation containing velocity times acceleration-squared describes the characteristics of chaotic behaviour in many nonlinear phenomena, cosmological analysis, kinematical physics, pendulum analysis etc. Thus, the mentioned equation is important in its own right. An extended iteration method, based on Haque’s approach has been applied to find the analytical solution of the oscillator. The recently various method has been developed for finding analytical solutions of the nonlinear equation but; modified extended iteration method based on Haque’s approach is faster and straight forward than others.

Keywords:

Jerk equation,Nonlinear oscillator,Extended iteration technique,Truncated Fourier series,

Refference:

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XIV. Haque, B.M.I., Selim Reza A.K.M. and Mominur Rahman M., “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, 2019.
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NUMERICAL SOLUTION OF TIME FRACTIONAL TIME REGULARIZED LONG WAVE EQUATION BY ADOMINAN DECOMPOSITION METHOD AND APPLICATIONS

Authors:

Bhausaheb Sontakke, Rajashri Pandit

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00005

Abstract:

In the paper, we develop the Adomian Decomposition Method for the fractional-order nonlinear Time Regularized Long Wave Equation (TRLW) equation. Caputo fractional derivatives are used to define fractional derivatives. We know that nonlinear physical phenomena can be explained with the help of nonlinear evolution equations. Therefore solving TRLW is very helpful to obtain the solution of many physical theories. In this paper, we will solve the time-fractional TRLW equation which may help researchers with their work. We solve some examples numerically, which will show the efficiency and convenience of the Adomian Decomposition Method.

Keywords:

Time Regularized Long Wave equation,Fractional derivative,Adomian Decomposition Method,Convergence,Mathematica,

Refference:

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GENERATION OF NEW OPERATIONAL MATRICES FOR DERIVATIVE, INTEGRATION AND PRODUCT BY USING SHIFTED CHEBYSHEV POLYNOMIALS OF TYPE FOUR

Authors:

Faiza Chishti, Fozia Hanif, Urooj Waheed, Yusra Khalid

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00006

Abstract:

While solving the fractional order differential equation the requirement of the higher-order derivative is obvious therefore, this paper gives a definite expression for constructing the operational matrices of derivative which is the direct method to find the derivative of higher-order according to the requirement of the total differential equation. The proposed work expands the Chebyshev polynomial of type four up to six degrees that could help get the accuracy for the numerical solution of a given differential equation. Previously Chebyshev polynomial of the third type has been used by cutting the domain from [-1, 1] to [0, 1]. This study also generates the integrational operational matrix for solving the integral equation as well as an integrodifferential equation by using the Chebyshev polynomial of type four and expand it up to six order and generate the matrix by cutting the domain from [-1, 1] to [0, 1]. This is the first attempt to generate an integrational operational matrix that has never been highlight nor generate by any researcher. Another contribution of this paper is the generation of categorical expressions for the product of two Chebyshev vectors that will help in solving the differential equation of several kinds.

Keywords:

Operational matrix of derivative,Operational matrix of integration,Operational matrix of the product of Shifted Chebyshev polynomials of type four,

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