Volume-10 , Issue-2 , Apr 2023, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.

  Toyesh Prakash Sharma, Etisha Sharma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.2 , pp.1-8, Apr-2023

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  Abstract
  The central aim of this paper is to introduce another generalization to the well-known integral from the class of exponential integrals. For a better understanding of the main result presented here. the knowledge of elementary integrations of continuous functions, definite and indefinite integration, the Concept of Mathematical Induction, and Basic Algebraic Manipulation are pre-requesting. Further on the basis of providing generalization, authors also give some applications that can show the generalization’s versatility, such as alternative proofs of the properties of Laplace Transform, Integration of e^ax sinbx and e^ax cosbx etc.

  Key-Words / Index Term
  Elementary Integration, Definite Integral, Indefinite Integration, Exponential class of Integration, Upper and Lower Bounds, Laplace Transform, Integration by Parts etc.

  References
  [1]. Toyesh Prakash Sharma, "A Generalization to? e x (ƒ (x) + ƒ1(x))dx", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.6, pp.46-50, 2020.
  [2]. Toyesh Prakash Sharma, "A Generalization to Integral e^-x. (f(x)-f’(x))dx", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.1, pp.72-75, 2021.
  [3]. NCERT- Mathematics Textbook for class XII Ch-7 integrals Ex-7.6. P.326. ISBN-81-7450-653-5.
  [4]. Toyesh Prakash Sharma, "A Generalization to? e x (ƒ (x) + ƒ1(x))dx" section VI “Open Problem, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.6, pp.49, 2020.
  [5]. Toyesh Prakash Sharma, "A Generalization to Integral e^-x. (f(x)-f’(x))dx" section IV “Open Problem”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.1, pp.75, 2021.
  [6]. Toyesh Prakash Sharma, "Solution to an Open Problem", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.44-46, 2021.
  [7]. Hj. Kim, “The intrinsic structure and properties of Laplace-typed integral transforms”, Mathematical Problem in Engineering, pp. 1-8, 2017.

  Citation
  Toyesh Prakash Sharma, Etisha Sharma, "Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.1-8, 2023

• Open Access   Article

  Methods for solving ordinary differential equations of second order with coefficients that is constant

  Shohal Hossain, Samme Akter Mithy

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.2 , pp.9-16, Apr-2023

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  Abstract
  This article provides a detailed overview of the techniques and methods used to solve second-order ordinary differential equations having coefficients that remain constant. The article begins by introducing the general form of 2nd-order differential equations and explaining the concept of constant coefficients. Next, the article presents the characteristic of equation and its roots, which are used to determine the nature of the solutions. The article then goes on to discuss the three possible cases: distinct and real roots, complex conjugate roots, and repeated roots, and present the general solution for each case, including examples to illustrate the application of the method. The article concludes with a brief discussion of applications of second-order differential equations in engineering and physics. The aim of this article is to provide a clear and concise guide for students and researchers interested in this important topic.

  Key-Words / Index Term
  Second-order differential equations, Constant coefficients, Homogeneous linear equations Real and distinct roots, Complex conjugate roots, Repeated roots

  References
  [1]. S. M. Yahya, "Solution of Second-Order Ordinary Differential Equations with Constant Coefficients," International Journal of Mathematics and Mathematical Sciences, vol. 2014, Article ID 121950, 12 pages, 2014. https://doi.org/10.1155/2014/121950
  [2]. J. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 11th ed. Hoboken, NJ: Wiley, 2017.
  [3]. Euler, L. (1748). Institutiones calculi differentialis. St. Petersburg.
  [4]. Gauss, C. F. (1815). Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Perthes et Besser
  [5]. Churchill, R. V., & Brown, J. W. (1990). Complex variables and applications (4th ed.). New York: McGraw-Hill.
  [6]. S.A. Mithy, S. Hossain, S. Akter, U. Honey, S.B. Sogir, "Classification of Iris Flower Dataset using Different Algorithms," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.1-10, 2022
  [7]. Hossain S, Aktar S, and Mithy SA. (2021). Solution of large-scale linear programming problem by using computer technique, Int. J. Mat. Math. Sci., 4(1), 15-34.

  Citation
  Shohal Hossain, Samme Akter Mithy, "Methods for solving ordinary differential equations of second order with coefficients that is constant," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.9-16, 2023

• Open Access   Article

  Approximating Non-Elementary Integrals Appling Elementary Techniques Of Integration And Inequalities.

  Toyesh Prakash Sharma, Ankush Kumar Parcha

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.2 , pp.17-26, Apr-2023

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  Abstract
  The central aim of this paper is to put forward an aspect of functional inequality for finding nearby numerical values of non-elementary integrals without using advanced calculus and advanced functions like the Gamma function Incomplete gamma function, Beta function, Error function etc.. Still, for matching the values of those non-elementary integrals for some fixed lower and upper bounds of it there we use Wolfram Alpha and Desmos. For a better understanding, readers should be aware of Cauchy-Bunyakovsky-Schwarz Integral Inequality, Hermite-Hadamard Inequality for Convex functions, Hermite-Hadamard Inequality for Concave functions etc.

  Key-Words / Index Term
  Elementary Integrals, non-elementary Integrals, Closed Form, Upper Bound and Lower Bound, Error Functions, Convex Functions, Concave Function, Strictly Increasing Function, Cauchy-Bunyakovsky-Schwarz Integral Inequality, Hermite-Hadamard Inequality for Convex and Concave functions, Hermite-Hadamard Inequality for Concave functions etc.

  References
  [1] Toyesh Prakash Sharma, "Application of Inequalities for Finding Range of Non-elementary Integrals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.7-20, 2022
  [2] S.L. Mewada, “Exploration of Efficient Symmetric AES Algorithm,” Journal of Physics and Chemistry of Matierials, Vol.4, Issue.11, pp.111-117, 2015.
  [3] A. Mardin, T. Anwar, B. Anwer, “Image Compression: Combination of Discrete Transformation and Matrix Reduction,” International Journal of Scientific Research Chemical Sciences, Vol.5. No.1, pp.1-6, 2017.
  [4] H.R. Singh, “Randomly Generated Algorithms and Dynamic Connections,” Journal of Mathematics, Vol.2, Issue.1, pp.231-238, 2014.
  [5] Thomas L., “A Scheme to Eliminate Redundant Rebroadcast and Reduce Transmission Delay Using Binary Exponential Algorithm in Ad-Hoc Wireless Networks,” International Journal of Scientific in Multidisciplinary Studies, Vol.3, Issue.8, pp.1-6, 2017.
  
  [6] G.H. Hardy, Littlewood, G. Pólya,” Inequalities.” Cambridge University Press, Cambridge pp.324, 1952.
  [7] Toyesh Prakash Sharma, "Application of Inequalities for Finding Range of Non-elementary Integrals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.8, 2022.
  
  [8] Toyesh Prakash Sharma, "Application of Inequalities for Finding Range of Non-elementary Integrals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.13, 2022.
  [9] Toyesh Prakash Sharma, "Application of Inequalities for Finding Range of Non-elementary Integrals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.15, 2022.

  Citation
  Toyesh Prakash Sharma, Ankush Kumar Parcha, "Approximating Non-Elementary Integrals Appling Elementary Techniques Of Integration And Inequalities.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.17-26, 2023

• Open Access   Article

  Queue Modeling Simulation for Vessel Traffic in Nigeria Sea Ports

  T.C. Nwachukwu, C.U. Akpudo, C.A. Enyinda, M.S. Stephens

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.2 , pp.27-32, Apr-2023

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  Abstract
  Seaport operation, especially at the container terminal, has been a major concern to port users all over the world. Long waiting times to be served at the quay apron are always the main problem faced by seaports, especially Nigerian ports. This situation has been a common complaint by the port users. Therefore, the objectives of this study are to investigate the waiting arrival time of a ship, ship service time, and turnaround time of ships calling at the Apapa Port Complex (APC) and Tincan Island Port (TCIP) by using simulation techniques. To do this, the study employed only primary data collection. Ship traffic for vessels calling at the ports during the study period was recorded from the ship traffic data report, the quay record book, and the ship’s record folder. At the end of the assessment period, a total of six-two (62) vessels were observed in TinCan Island Port (TCIP), while eight-four (84) vessels were recorded in the Apapa Port Complex (APC). The collection of waiting times for this study is based on the arrival rate and service rate of vessels at the port. The data was calculated and analyzed using Microsoft Excel and queuing theory, respectively. Based on the analyzed data, the queuing system of the ports` current situation was modelled and simulated using the ARENA software. The result obtained from the simulation model shows that the waiting arrival time of the ship calling at APC and TCIP is on average 6 hours, 46 minutes, and 8 hours, 28 minutes, respectively. The study further revealed that ship service time at berth is on average 1.02 and 1.41 vessels. On the turnaround time, the study established that the ship turnaround times are 1.49 and 2 days, respectively. The study recommends that port equipment and infrastructure be adjusted in line with current traffic flows, which invariably increases port performance and reduces the amount of time vessels spend at port.

  Key-Words / Index Term
  Seaport, Queue model, Waiting time, Service time, Turnaround time, Traffic intensity

  References
  [1]. R. Preeti, U. Amit, “Container retrieval and wagon assignment planning at container rail terminals,”. Computers and Industrial Engineering, Vol. 172, 2022.
  [2]. J. Bo, Y. Zhishan, Y. Mingzhu, “Inbound container remarshaling problem in an automated container terminal,” Transportation research part E: Logistics and Transportation Review, ELSEVIER, vol. 168., pp 1-15, 2022.
  [3]. J. Xu, D. Liu, “Queuing Models to Improve Port Terminal Handling Service,”. In Systems Engineering Procedia, ELSEVIER. pp. 345 – 351, 2012.
  [4]. S. Shichao, Z. Yong, D. Yao, L. Na, J. Zhihong, Y. Qing, “In Reducing external container trucks’ turnaround time in ports: A data-driven approach under truck appointment systems,” vol. 174., 2022.
  [5]. L.E. Henesey, “Multi-Agent Systems for Container Terminal Management,” A PhD thesis submitted to Blekinge Institute of Technology, School of Engineering, 2006.
  [6]. Z. Zdenka, M. Edna, “Modelling of port container terminal using the queue theory PART 3,” 2017
  [7]. A.S Shahpanah, S. Shahpanah, C. Ali, A. Gholamkhasi, M. Shahpanah, “Improvement in queuing network model to reduce waiting time at berthing area of port container terminal via discrete event simulation,”. In Applied Mechanics and Materials. 2014.
  [8]. C.U. Akpudo, C.A. Enyinda, “Assessment of port performance using queuing theory approach: The case of Apapa port complex,” Journal of logistics and Transport, vol. 7, issue 1, pp. 122-134, 2015
  [9]. E. O Oyatoye, S.O. Adebiyi, J.C. Okoye, B. B. Amole, “Application of Queuing theory to port congestion problem in Nigeria,” European Journal of Business and Management, vol.3, No. 8, pp. 24-36, 2011
  [10]. B. M. Fazeeda, S.B. Nurul, A. A. Ahmad,”Reducing Ship Queuing Time in Port Operation: A Modelling and Simulation Approach,” International Journal of Engineering & Technology, vol. 7, issue 3, pp. 114 -118, 2018.
  [11]. L. Na, H. Hercules, S. Haotian, J. Zhihong., “A new vocation queuing model to optimize truck appointments and yard handling-equipment use in dual transactions systems of container terminals,” ELSEVIER, 2022.
  [12]. A. Nao, S. B. Nur, “Application of queuing theory model and simulation to patient flow at the outpatient department,” Proceedings of the International Conference on Industrial Engineering and Operations Management Bandung, Indonesia, March 6-8, 2018.
  [13]. A.R. Rashida, M. Fadzi, S. Ibrahim, S.R. Goh, “Modeling and simulation of M/M/c queuing pharmacy system with adjustable parameters,” AIP Conference, 2016.
  [14]. N. Guerrouahane, N. Farhi, D. Aissani, L. Bouallouche-Medjkoune, “A queuing model for road traffic simulation,”AIP Conference proceeding, 1648. 2015.
  [15]. S. Malik, R. Gupta, “Analysis of Finite Capacity Queueing System with Multiple Vacations and Encouraged Customers” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 9, Issue. 2, pp. 17-22, 2022
  [16]. O. A Adedayo, O. Ojo, J. K. Obamiro, “Operations Research in Decision analysis and production Management,” Pumark Educational Publishers, 2006.
  [17]. T. L.Satty, “Elements of queuing theory with applications” Mcgraw-Hil book Co, new York, 1961.
  [18]. B. Raton, “Operations Research Calculations Handbook,” New York: Taylorand Francis Group, 2009.
  [19]. A.A Mohammed, K. Bilavari, R. Neela, “Simulation of Container Queues for Port Investment Decisions,” The Sixth International Symposium on Operations Research and Its Applications (ISORA’06) Xinjiang, pp. 155 – 167, 2006
  [20]. Y. Zhang, Q. Qian Zheng, L. Jun He, H. Wei Tian, “Ship traffic optimization method for solving the approach channel and lock co-scheduling problem of the Three Gorges Dam on the Yangzi River,” Ocean Engineering, ELSEVIER, vol. 276, 2023.

  Citation
  T.C. Nwachukwu, C.U. Akpudo, C.A. Enyinda, M.S. Stephens, "Queue Modeling Simulation for Vessel Traffic in Nigeria Sea Ports," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.27-32, 2023

• Open Access   Article

  Application of Jensen’s Inequality for Proving Nesbitt’s Inequality and Further Generalizing It

  Toyesh Prakash Sharma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.2 , pp.33-37, Apr-2023

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  Abstract
  With the help of this article, the author is introducing new generalizations of a very popular inequality that we call Nesbitt’s inequality. For obtaining new generalizations, there is a use of another inequality called Jensen’s Inequality for convex functions, which is directly linked with derivatives of a function. There is a need for essential calculus and a better understanding of the proofs.

  Key-Words / Index Term
  Jensen’s Inequality, Nesbitt’s Inequality Generalization, Convex function, Concave Function, Functional Inequalities, Three Variables etc.

  References
  [1]. Nesbitt, A.M., Problem 15114, Educational Times, 55, 1902.
  [2]. Jensen, J. L. W. V. "Sur les fonctions convexes et les inégalités entre les valeurs moyennes". Acta Mathematica. Vol. 30 issue 1: pp. 175–193, 1906.
  [3]. Bakula, M.K., Nikodem, K.: Converse Jensen inequality for strongly convex set-valued maps. J. Math. Inequal. Vol. 12 issue 2, pp 545–550 2018.
  [4]. Lu, G.: “New refinements of Jensen’s inequality and entropy upper bounds.” J. Math. Inequal. Vol. 12 issue 2, pp 403–421, 2018.

  Citation
  Toyesh Prakash Sharma, "Application of Jensen’s Inequality for Proving Nesbitt’s Inequality and Further Generalizing It," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.33-37, 2023

• Open Access   Article

  Time Series Analysis of Crude Oil Production in Nigeria between the Years 2010 to 2020

  N.F. Adeleye, H.O. Ilo, T.O. Gbadamosi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.2 , pp.38-45, Apr-2023

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  Abstract
  In Nigeria and other regions worldwide, crude oil is a crucial source of income and energy that necessitates careful attention and technical expertise in its production, refining, and global distribution. Throughout history, crude oil has been the cornerstone of Nigeria`s economy, playing a significant role in shaping its political, industrial, and economic future. According to reports, Nigeria`s petroleum sector is the nation`s biggest industry. This is likely a result of the widespread perception that petroleum is one of the main sources of energy all over the world. In addition to this, petroleum products make a wide range of additional contributions to national development, including the creation of jobs, revenue generation, earnings in foreign currencies, industrialization, and advancements in other economic indicators. The Nigerian National Petroleum Company Limited (NNPC Limited), formerly known as the Nigerian National Petroleum Corporation (NNPC), emerged in April 1977 out of merging the commercial and regulatory responsibilities of the Ministry of Petroleum Resources and the Nigerian National Oil Corporation (NNOC). Nigeria is Africa`s top producer of oil and gas. Using the Mann-Whitney test in our analysis section, it was discovered that there is a significant difference in crude oil production between the years 2010 and 2020. After the discovery that the time series data set was non-stationary using the Augmented Dickey-Fuller test, the Detrending method was applied to remove the trend in the dataset and transform it into a stationary dataset that would be suitable for prediction and forecasting. The Augmented Dickey-Fuller test was later used to test if the dataset is truly stationary. The Seasonal Autoregressive Integrated Moving Average (SARIMA) was used to test the model and was also used for the prediction and forecasting of the Crude Oil dataset. The result of the analysis indicates that SARIMA is a good statistical tool that can be used in the prediction of this kind of data (Crude Oil Data).

  Key-Words / Index Term
  Augmented Dickey-Fuller Test, Mann Whitney Test, Detrending, Nigerian National Petroleum Company Limited (NNPCL), Seasonal Autoregressive Integrated Moving Average (SARIMA), Crude Oil.

  References
  [1] C. Okunroumu, “Niger’s refinery now supplies fuel to Northern states” This day Newspaper October 2004.
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  [5] A. A. Akinyemi, O. S. Enilolobo, & N. I. Theodore, “Impact of Oil Revenue and Exchange Rate Fluctuation on Economic Growth in Nigeria 1981-2015.” Journal of Management and Administration, 2: 77-104, 2017.
  [6] J. Gylych, A. A. Jibrin, B. Celik, & A. Isik, “Impact of Oil Price Fluctuation on the Economy of Nigeria, the Core Analysis for Energy Producing Countries, Global Market and Global Trade,” Intech Open, pp. 1-28, 2020.
  [7] E. Odupitan, “Effects of crashing crude oil prices on oil producing countries: Nigeria’s Perspective.” Central University of Applied Sciences, Kokkola, Finland. 2017.
  [8] A. Adedokun, “The effects of oil shocks on government expenditures and government revenues nexus in Nigeria: With erogeneity restrictions,” Future Business Journal, 4(2): pp 219-232, 2018.
  [9] O. S. Adesina, “Unemployment and Security Challenges in Nigeria: International Journal of Humanities and Social Science,” 3(7): pp 146-156, 2013.
  [10] E. G. Okoro, “Oil Price Volatility and Economic Growth in Nigeria: a Vector Auto-Regression (VAR) Approach,” ACTA UNIVERSITATIS DANUBIUSŒCONOMICA, 10(1): pp 70-82, 2014.
  [11] S. A. Aniche, “Rising price of premium motor spirit (PMS) and widening poverty gap in Nigeria,” International Journal of Management Sciences and Humanities, 1(1): pp12-25, 2015.
  [12] A. Englama, O. O. Duke, T. S. Ogunleye, & F. U. Ismail, “Oil Prices and Exchange Rate Volatility in Nigeria: An Empirical Investigation. Central Bank of Nigeria Economic and Financial Review,” 48(3), pp 31-48, 2010.
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  Citation
  N.F. Adeleye, H.O. Ilo, T.O. Gbadamosi, "Time Series Analysis of Crude Oil Production in Nigeria between the Years 2010 to 2020," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.38-45, 2023

• Open Access   Article

  Evaluation And Selection Of Supplier In A Healthcare Supply Chain Using TOPSIS

  Trupti Bhosale, Hemant Umap

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.2 , pp.46-50, Apr-2023

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  Abstract
  The objective of SS (SS) process is to minimize risk in purchasing, enhance overall profit of the customer, and build the long lasting and close relations between suppliers and buyers. SS process is one of the main key processes of the supply chain management (SCM). So, selection of a supplier has become an important issue for development of a proper supply chain (SC) system. Here, we have provided a case study for SS using Technique for Order Performance by Similarity to Ideal Solution (TOPSIS). We have explained it using crisp data. In this study, we evaluate five suppliers using crisp TOPSIS. This method can be used when one have to select one particular supplier from no. of suppliers in short period of time. It will be also helpful to the Pharmacists to select the best supplier who can fulfill all their needs. In spite of the no. of studies on SS, the evaluation and selection of suppliers using the specific measures of the healthcare sector are less investigated. In order to fill this gap, this research proposed a guide for SS of antibiotic drug.

  Key-Words / Index Term
  supplier, TOPSIS, crisp, antibiotic, pharmacist

  References
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  [9] Putri Candra Anggani, Imam Baihaqi dan Dewanti Anggrahini ,”SS Using Analytical Hierarchy Process at PT”. Indolakto Jurnal Sains Dan Seni ITS Vol.6, Issue.4, pp.D27-D31, 2017.
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  [19] R. M. Zulqarnain, S. Abdal, B. Ali, L. Ali, F. Dayan, M. I. Ahamad, Z. Zafar, “Selection of Medical Clinic for Disease Diagnosis by Using TOPSIS Method,” Int. J. Pharm. Sci. Rev. Res, Vol.61, Issue.1, pp.22-27, 2020.
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  Citation
  Trupti Bhosale, Hemant Umap, "Evaluation And Selection Of Supplier In A Healthcare Supply Chain Using TOPSIS," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.46-50, 2023