i-manager Publications

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
Some Types of Generalized Closed and Generalized Star Closed Sets in Topological Ordered Spaces
Optimizing Capsule Endoscopy Detection: A Deep Learning Approach with L-Softmax and Laplacian-SGD
Kernel Ideals in Semigroups
Modeling the Dynamics of Covid-19 with the Inclusion of Treatment, Vaccination and Natural Cure
Calculation of Combined Vibrational Frequencies in Cl₂O using Lie Algebraic Method

Most Cited

Volume 11 Issue 2 July - December 2022

Research Paper

On Kolmogorov Complexity of Unitary Transformations in Quantum Computing

Alexei Kaltchenko*

Wilfrid Laurier University, Waterloo, Ontario, Canada.

Kaltchenko, A. (2022). On Kolmogorov Complexity of Unitary Transformations in Quantum Computing. i-manager’s Journal on Mathematics, 11(2), 1-7. https://doi.org/10.26634/jmat.11.2.19190

Abstract

We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the context of quantum computing, it corresponds to the least possible amount of data to define and describe a quantum circuit or quantum computer program. Our Kolmogorov complexity of unitary transformation is built upon Kolmogorov "qubit complexity" of Berthiaume, W. Van Dam and S. Laplante via mapping from unitary transformations to unnormalized density operators, which are subsequently "purified" into unnormalized vectors in Hilbert space. We discuss the optimality of our notion of Kolmogorov complexity in a broad sense.

References

[1]. Adleman, L. M., Demarrais, J., & Huang, M. D. A. (1997). Quantum computability. SIAM Journal on Computing, 26(5), 1524-1540. https://doi.org/10.1137/S0097539795293639

[2]. Benatti, F., Krüger, T., Müller, M., Siegmund-Schultze, R., & Szkoła, A. (2006). Entropy and quantum Kolmogorov complexity: A quantum Brudno's theorem. Communications in Mathematical Physics, 265(2), 437-461. https://doi.org/10.1007/s00220-006-0027-z

[3]. Berthiaume, A., Van Dam, W., & Laplante, S. (2001). Quantum kolmogorov complexity. Journal of Computer and System Sciences, 63(2), 201-221. https://doi.org/10.1006/jcss.2001.1765

[4]. Cover, T. & Thomas, J. (2006). Elements of Information Theory. John Wiley & Sons.

[5]. Deutsch, D. (1985). Quantum theory, the church–turing principle and the universal quantum computer. Proceedings of the Royal Society of London. A Mathematical and Physical Sciences, 400(1818), 97-117. https://doi.org/10.1098/rspa.1985.0070

[6]. Gács, P. (2001). Quantum algorithmic entropy. Journal of Physics A: Mathematical and General, 34(35). https://doi.org/10.1088/0305-4470/34/35/312

[7]. Li, M., & Vitányi, P. (1993). An Introduction to Kolmogorov Complexity and its Applications. Springer, New York.

[8]. Mora, C. E., & Briegel, H. J. (2005). Algorithmic complexity and entanglement of quantum states. Physical Review Letters, 95(20), 200503. https://doi.org/10.1103/PhysRevLett.95.200503

[9]. Mora, C. E., Briegel, H. J., & Kraus, B. (2007). Quantum Kolmogorov complexity and its applications. International Journal of Quantum Information, 5(05), 729-750. https://doi.org/10.1142/S0219749907003171

[10]. Muller, J. (2006). Elementary Functions: Algorithms and Implementation. Birkhuser.

[11]. Nielsen, M. & Chuang, I. (2000). Quantum Computation and Quantum Information. Cambridge University Press.

[12]. Vitányi, P. M. (2001). Quantum Kolmogorov complexity based on classical descriptions. IEEE Transactions on Information Theory, 47(6), 2464-2479. https://doi.org/10.1109/18.945258

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Research Paper

A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations

Kaze Atsi* , Lydia Adiku, Namuma Yarima*, G. M. Kumleng****

* Department of Mathematics, Federal University Gashua, Yobe State, Nigeria.

-* Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

**** Department of Mathematics, University of Jos, Plateau State, Nigeria.

Atsi, K., Adiku, L., Yarima, N., and Kumleng, G. M. (2022). A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations. i-manager’s Journal on Mathematics, 11(2), 8-12. https://doi.org/10.26634/jmat.11.2.19206

Abstract

In this work, a second derivative block method derived from a family of modified backward differentiation formula (bdf) type for solving stiff ordinary differential equations has been constructed. Choosing a step number, k = 4, four discrete methods with uniform order 7 are obtained using the multistep collocation approach. The stability properties of the new method have been established. The solutions of two problems have been computed and compared with the corresponding exact and other existing solutions. Solutions are presented on graphs and the associated absolute errors are compared in tables.

References

[1]. Ajie, I. J., Ikhile, M. N. O., & Onumanyi, P. (2014). A family of block methods derived from TOM and BDF pairs for stiff ordinary differential equations. American Journal of Mathematics and Statistics, 4(2), 121-130. https://doi.org/10.5923/j.ajms.20140402.08

[2]. Akinfenwa, O. A., Jator, S. N., & Yao, N. M. (2012). On the stability of continuous block backward differentiation formula for solving stiff ordinary differential equations. Journal of Modern Methods in Numerical Mathematics, 3(2), 50-58. https://doi.org/10.20454/jmmnm.2012.321

[3]. Atsi, K., & Kumleng, G. M. (2020). A family of modified backward differentiation formula (BDF) type block methods for the solution of stiff ordinary differential equations. International Journal of Statistics and Applied Mathematics, 5(2), 09-16.

[4]. Atsi, K., & Kumleng, G. M. (2021). Block extended trapezoidal rule of the second kind (Etr2) for the direct soltion of second order initial value problems of ordinary differential equations. IOSR Journal of Mathematics (IOSR-JM), 17(2), 10-14. https://doi.org/10.9790/5728-1702041014

[5]. Atsi, K., Hambagda, B., Ogunwuyi, F. E., & Kumleng, G. M. (2021). A block integrator for the solution of first order ordinary differential equations using legendre polynomial. Asian Journal of Pure and Applied Mathematics, 3(2) 1-7.

[6]. Chollom, J. P., Ndam, J. N., & Kumleng, G. M. (2007). On some properties of the block linear multi-step methods. Science World Journal, 2(3), 11-17. https://doi.org/10.4314/swj.v2i3.51747

[7]. Kumleng, G. M., Chollom, J. P., & Longwap, S. (2013). A modified block adam moulton (MOBAM) method for the solution of stiff initial value problems of ordinary differential equations. Research Journal of Mathematics and Statistics, 5(4), 32-42.

[8]. Kumleng, G. M., Chollom, J. P., & Omagwu, S. (2015). A class of new block generalized adams implicit runge-kutta collocation methods. International Journal of Scientific & Engineering Research, 6(12), 10-19.

[9]. Kumleng, G. M., Longwap, S., & Adee, S. O. (2013). A class of a-stable order four and six linear multistep methods for stiff initial value problems. Mathematical Theory and Modeling, 3(11), 1-9.

[10]. Skwame, Y., Sunday, J., & Ibijola, E. A. (2012). L-stable block hybrid simpson's methods for numerical solution of initial value problems in stiff ordinary differential equations. International Journal of Pure and Applied Sciences and Technology, 11(2), 45-54.

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Research Paper

Equiprime Ideals and Equiprime Semimodules in Boolean Like Semirings

Bhagavathula Venkata Narayana Murthy*

Department of Mathematics, Maharaj Vijayaram Gajapathi Raj College of Engineering Chintalavalsa, Vizianagaram, Andhra Pradesh, India.

Murthy, B. V. N. (2022). Equiprime Ideals and Equiprime Semimodules in Boolean Like Semirings. i-manager’s Journal on Mathematics, 11(2), 13-18. https://doi.org/10.26634/jmat.11.2.18889

Abstract

In this paper, the concepts of equiprime ideals and equiprime semi-modules in Boolean like semirings (now onwards denote ℜ_B) are introduced and illustrated with examples. It is established that if Ҏ is the equiprime ℜ_B–Ideal of the ℜ_B –module Ń then (Ҏ: Ń) is equiprime ideal of ℜ_B. Also it is approved that if Ń is an equiprime ℜ_B–module then (0: Ń) is an equiprime ideal of ℜ_B. Also, an important characterization of the equiprime ideal of ℜ_B in the semimodule structure over ℜ_B is put forward. Using this result, it can be proved that ℜ_B is equiprime if there exists a faithful equiprime ℜ_B–module Ń. Finally, it is proved that if Ń is an equiprime ℜ_B–module and Ϯ is an invariant subgroup of ℜ_B such that Ϯ is not contained in (0: Ń), then Ń is an equiprime Ϯ–module.

Mathematics Subject Classification: 16Y30, 16Y80.

References

[1]. Booth, G. L., & Groenewald, N. J. (1992). Special radicals of near-ring modules. Quaestiones Mathematicae, 15(2), 127-137. https://doi.org/10.1080/16073606.1992.9631679

[2]. Booth, G. L., Groenewald, N. J., & Veldsman, S. (1990). A Kurosh-Amitsur prime radical for near-rings. Communications in Algebra, 18(9), 3111-3122. https://doi.org/10.1080/00927879008824063

[3]. Booth, G. L., Groenewald, N. J., & Veldsman, S. (1991). Strongly equiprime near-rings. Quaestiones Mathematicae, 14(4), 483-489. https://doi.org/10.1080/16073606.1991.9631665

[4]. Grainger, G. R. (1988). Left Modules for Left Nearrings (Doctoral Dissertation, the University of Arizona).

[5]. Murthy, B. V. N. (2012). A structure of semi modules over Boolean like semi rings. International Journal of Mathematical Archive, 3(8).

[6]. Pliz, G. (1983). Near Rings, the Theory and Its Applications. North-Holland, Amsterdam.

[7]. Veldsman, S. (1992). On equiprime near-rings. Communications in Algebra, 20(9), 2569-2587. https://doi.org/10.1080/00927879208824479

[8]. Venkateswarlu, K., Murthy, B. V. N., & Amarnath, N. (2011). Boolean like semirings. International Journal of Contemporary Mathematical Sciences, 6(13), 619-635.

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Research Paper

Numerical Solution of Temperature Profile in Annulus

Reshu Gupta*

Applied Science Cluster, University of Petroleum and Energy Studies, Dehradun, India.

Gupta, R. (2022). Numerical Solution of Temperature Profile in Annulus. i-manager’s Journal on Mathematics, 11(2), 19-25. https://doi.org/10.26634/jmat.11.2.19035

Abstract

The model of temperature profile in the flow of non-Newtonian second-order fluid, flowing in an annulus, is investigated. The boundary of annulus is considered porous. Appropriate similarity transformation is used to convert non-linear PDEs into non-linear ODEs. The obtained differential equations are solved numerically. The nature of the temperature profile is presented graphically for the various physical parameters.

References

[1]. Agarwal, R. (2020). Analytical study of micropolar fluid flow between two porous disks. PalArch's Journal of Archaeology of Egypt/Egyptology, 17(12), 903-924.

[2]. Agarwal, R. (2021). Heat and mass transfer in electrically conducting micropolar fluid flow between two stretchable disks. Materials Today: Proceedings, 46, 10227-10238. https://doi.org/10.1016/j.matpr.2020.11.614

[3]. Agarwal, R. (2022). An analytical study of non-newtonian visco-inelastic fluid flowbetween two stretchable rotating disks. Palestine Journal of Mathematics, 11(1), 184-201.

[4]. Agarwal, R., & Mishra, P. K. (2021). Analytical solution of the MHD forced flow and heat transfer of a non-newtonian viscoinelastic fluid between two infinite rotating disks. Materials Today: Proceedings, 46, 10153-10163. https://doi.org/10.1016/j.matpr.2020.10.632

[5]. Agrawal, D., & Agrawal, R. (2016). Flow of a non-Newtonian second-order fluid over an enclosed torsionally oscillating disc in the presence of the magnetic field. International Journal of Engineering Research & Technology (IJERT), 5(9), 469-480.

[6]. Coleman, B. D., & Noll, W. (1974). An approximation theorem for functionals, with applications in continuum mechanics. In The Foundations of Mechanics and Thermodynamics (pp. 97-112). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65817-4_5

[7]. Miles, A., & Bessaïh, R. (2021). Heat transfer and entropy generation analysis of three-dimensional nanofluids flow in a cylindrical annulus filled with porous media. International Communications in Heat and Mass Transfer, 124, 105240. https://doi.org/10.1016/j.icheatmasstransfer.2021.105240

[8]. Mohyuddin, M. R., Hayat, T., Mahomed, F. M., Asghar, S., & Siddiqui, A. M. (2004). On solutions of some non-linear differential equations arising in Newtonian and non-Newtonian fluids. Nonlinear Dynamics, 35(3), 229-248. https://doi.org/10.1023/B:NODY.0000027920.92871.99

[9]. Nikitin, N., Wang, H., & Chernyshenko, S. (2009). Turbulent flow and heat transfer in eccentric annulus. Journal of Fluid Mechanics, 638, 95-116. https://doi.org/10.1017/S002211200900812X

[10]. Sheikholeslami, M., & Abelman, S. (2015). Two-phase simulation of nanofluid flow and heat transfer in an annulus in the presence of an axial magnetic field. IEEE Transactions on Nanotechnology, 14(3), 561-569. https://doi.org/10.1109/TNANO.2015.2416318

[11]. Vajravelu, K., Radhakrishnamacharya, G., & Radhakrishnamurty, V. (2007). Peristaltic flow and heat transfer in a vertical porous annulus, with long wave approximation. International Journal of Non-Linear Mechanics, 42(5), 754-759. https://doi.org/10.1016/j.ijnonlinmec.2007.02.014

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Review Paper

Mathematical Modelling of EOR Methods

Tirumala Rao Kotini* , Aman Singh**

*-** Energy Cluster, School of Engineering, UPES, Bidholi, Dehradun, Uttarakhand, India.

Kotni, T. R., and Singh, A. (2022). Mathematical Modelling of EOR Methods. i-manager’s Journal on Mathematics, 11(2), 26-34. https://doi.org/10.26634/jmat.11.2.19034

Abstract

The choice of appropriate and affordable procedures to boost oil recovery is usually recognized as one of the main challenges in reservoir development due to the huge demand for crude oil. Reservoir flow simulators are valuable tools for understanding and forecasting fluid flow in complex systems. The goal of this study is to run a mathematical model to evaluate the performance of various oil recovery methods, as well as to validate the model's accuracy with simulated field data. Thereby, the results of this developed model indicate that the model is approximately matched with the simulated field data. Enhanced oil recovery typically refers to chemical, miscible, thermal, and microbial processes. A system of nonlinear partial differential equations composed of Darcy's and mass conservation equations governs the model. The system is then numerically solved using the IMPEC (Implicit Pressure and Explicit Concentration) scheme by a finite difference method. We chose this approach because the experimental approaches are not only time consuming, but also costly. As a result, mathematical models could aid in the understanding of a reservoir and how such processes can be optimized to maximize oil recovery while lowering production costs. This paper provides a brief overview of mathematical modelling of various enhanced oil recovery methods, focusing on developing a generalized framework and describing some of the key challenges and opportunities.

References

[1]. Abramowitz, M., & Stegun, I. A. (1972). Handbook of Mathematical Functions. Dover Publishing, New York.

[2]. Babalyan, G. A., Levy, B. I., Tumasyan, A. B., & Khalimov, E. M. (1983). Oilfield Development using Surfactants. Nedra, Moscow.

[3]. Lake, L. W. (1989). Enhanced Oil Recovery. Prentice-Hall, Inc.

[4]. Sorbie, K. S. (1991). Introduction to polymer flooding. In Polymer-Improved Oil Recovery (pp. 1-5). Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3044-8_1

[5]. Latil, M. (1980). Enhanced Oil Recovery. Éditions Technip.

[6]. Armstrong, R. T., & Wildenschild, D. (2012). Investigating the pore-scale mechanisms of microbial enhanced oil recovery. Journal of Petroleum Science and Engineering, 94, 155-164. https://doi.org/10.1016/j.petrol.2012.06.031

[7]. Akhmed-Zaki, D., Danaev, N., Mukhambetzhanov, S., & Imankulov, T. (2012, September). Analysis and evaluation of heat and mass transfer processes in porous media based on Darcy-Stefan's model. In ECMOR XIII-13th European Conference on the Mathematics of Oil Recovery (pp. cp-307). European Association of Geoscientists & Engineers. https://doi.org/10.3997/2214-4609.20143274

[8]. Flory, P. J. (1953). Principles of Polymer Chemistry. Cornell university press.

[9]. Wegner, J., & Ganzer, L. (2012, October). Numerical simulation of oil recovery by polymer injection using COMSOL. In Excerpt from the Proceedings of the 2012 COMSOL Conference Milan.

[10]. Alexander, J. D., Martin, W. L., & Dew, J. N. (1962). Factors affecting fuel availability and composition during in situ combustion. Journal of Petroleum Technology, 14(10), 1154-1164. https://doi.org/10.2118/296-PA

[11]. Collins, R. E. (1961). Flow of Fluids through Porous Materials. Reinhold Publishing, New York.

[12]. Glasstone, S. (1946). Textbook of Physical Chemistry. D.Van Nostrand Company, New York.

[13]. Mcadams, W. H. (1954). Heat Transmission, McGraw-Hill, New York.

[14]. Treybal, R. E. (1955). Mass Transfer Operations. McGraw-Hill, New York.

[15]. Reddy, D. S., & Kumar, G. S. (2014a). A numerical investigation on the role of oil saturations on performance of in-situ combustion in porous media. International Journal of Scientific & Engineering Research, 5(5), 531-538

[16]. Reddy, D. S., & Kumar, G. S. (2014b). A comprehensive analysis on thermal and kinetic aspects of in situ combustion: Numerical approach. In Applied Mechanics and Materials, 592, 1393-1397. Trans Tech Publications Ltd. https://doi.org/10.4028/www.scientific.net/AMM.592-594.1393

[17]. Reddy, D. S., & Kumar, G. S. (2015a). Numerical simulation of heavy crude oil combustion in porous combustion tube. Combustion Science and Technology, 187(12), 1905-1921. https://doi.org/10.1080/00102202.2015.1065822

[18]. Reddy, D. S, & Kumar, G. S. (2015b). A numerical study on phase behavior effects in enhanced oil recovery by in situ combustion. Petroleum Science and Technology, 33(3), 353-362. https://doi.org/10.1080/10916466.2014.979999

[19]. Kudapa, V. K., Sharma, P., Kunal, V., & Gupta, D. K. (2017). Modeling and simulation of gas flow behavior in shale reservoirs. Journal of Petroleum Exploration and Production Technology, 7(4), 1095-1112. https://doi.org/10.1007/s13202-017-0324-4

[20]. Kudapa, V. K., Gupta, D. K., & Sharma, P. (2018). Modeling of gas flow within the shale fracture network. In Advances in Fire and Process Safety (pp. 21-43). Springer, Singapore. https://doi.org/10.1007/978-981-10-7281-9_3

[21]. Kumar, G. S., & Reddy, D. S. (2017). Numerical modelling of forward in-situ combustion process in heavy oil reservoirs. International Journal of Oil, Gas and Coal Technology, 16(1), 43-58. https://doi.org/10.1504/IJOGCT.2017.085981

[22]. Prince, M. J. A., Avula, V. R., & Kudapa, V. K. (2022). Investigation of anionic in place of cationic surfactants onto oil wet carbonate surfaces for improving recovery. Materials Today: Proceedings, 52, 825-828 https://doi.org/10.1016/j.matpr.2021.10.213

[23]. Sharma, P., & Kudapa, V. K. (2022). Assessment of hydrocarbon generation potential of coal seams from Raniganj basin, India. Materials Today: Proceedings, 52, 842-846. https://doi.org/10.1016/j.matpr.2021.10.226

[24]. Kudapa, V. K., Iqbal, M. I., Memon, S., Azharuddin, S., & Rajawy, I. A. (2022). Production enhancement using prosper software with reference to well test matching and modeling for good financial management. Materials Proceedings, 10(1), 7. https://doi.org/10.3390/materproc2022010007

[25]. Pavan, T. N. V., Devarapu, S. R., & Govindarajan, S. K. (2022). Comparative analysis on impact of water saturation on the performance of in-situ combustion. Rudarsko-Geološko-Naftni Zbornik, 37(4), 167-175. https://doi.org/10.17794/rgn.2022.4.14

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Most Read

Most Cited

Volume 11 Issue 2 July - December 2022

On Kolmogorov Complexity of Unitary Transformations in Quantum Computing

Alexei Kaltchenko*

Wilfrid Laurier University, Waterloo, Ontario, Canada.

Kaltchenko, A. (2022). On Kolmogorov Complexity of Unitary Transformations in Quantum Computing. i-manager’s Journal on Mathematics, 11(2), 1-7. https://doi.org/10.26634/jmat.11.2.19190

Abstract

References

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A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations

Kaze Atsi* , Lydia Adiku**, Namuma Yarima***, G. M. Kumleng****

* Department of Mathematics, Federal University Gashua, Yobe State, Nigeria. **-*** Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria. **** Department of Mathematics, University of Jos, Plateau State, Nigeria.

Abstract

References

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Equiprime Ideals and Equiprime Semimodules in Boolean Like Semirings

Bhagavathula Venkata Narayana Murthy*

Department of Mathematics, Maharaj Vijayaram Gajapathi Raj College of Engineering Chintalavalsa, Vizianagaram, Andhra Pradesh, India.

Murthy, B. V. N. (2022). Equiprime Ideals and Equiprime Semimodules in Boolean Like Semirings. i-manager’s Journal on Mathematics, 11(2), 13-18. https://doi.org/10.26634/jmat.11.2.18889

Abstract

References

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Numerical Solution of Temperature Profile in Annulus

Reshu Gupta*

Applied Science Cluster, University of Petroleum and Energy Studies, Dehradun, India.

Gupta, R. (2022). Numerical Solution of Temperature Profile in Annulus. i-manager’s Journal on Mathematics, 11(2), 19-25. https://doi.org/10.26634/jmat.11.2.19035

Abstract

References

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Mathematical Modelling of EOR Methods

Tirumala Rao Kotini* , Aman Singh**

*-** Energy Cluster, School of Engineering, UPES, Bidholi, Dehradun, Uttarakhand, India.

Kotni, T. R., and Singh, A. (2022). Mathematical Modelling of EOR Methods. i-manager’s Journal on Mathematics, 11(2), 26-34. https://doi.org/10.26634/jmat.11.2.19034

Abstract

References

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Kaze Atsi* , Lydia Adiku, Namuma Yarima*, G. M. Kumleng****

* Department of Mathematics, Federal University Gashua, Yobe State, Nigeria.

-* Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

**** Department of Mathematics, University of Jos, Plateau State, Nigeria.