Journal of Mathematical Sciences & Computational Mathematics (JMSCM)
(ISSN Number (Online) - 2644-3368)
(ISSN Number (Print) - 2688-8300)

Volume2 Issue4:


Badri Prasad Pangeni1 & Tanka Nath Dhamala2

1Tribhuvan University, Prithvi Narayan Campus, Pokhara, Nepal
Email: [email protected]
2Tribhuvan University, Central Department of Mathematics, Kathmandu, Nepal
Email: [email protected]
Page Number: 467-477

In dynamic network flows, when some commodities move from one place to another, time taken by them to traverse the path are taken into account, unlike the static flows. Time being continuous entity, network flow problems are modeled in its continuous setting to get more realistic solution to the optimization problems. Rather, it can also be discretized to get more computational results. In this paper, insight is given to the models formulated by the researchers in dynamic network flows along with some practical applications regarding the triple optimization problem in continuous time setting mainly focusing on cost minimization problems, since the quickest path problem and the maximum flow problem are considered as two important special cases of the minimum cost flow problem. Different solution strategies and their efficiencies carried out by them are also observed. Further possible modification in the existing formulations and algorithms for better solution of problems are suggested as research endeavor.
Keywords:Network optimization, dynamic flows, continuous-time model, discretization


Post Covid-19 Bio-Imaging: Cancer Detection & Secured Procurement through Dual Neurons Genetic Key (DNGK) in Advanced Medical Sciences

Joydeep Dey1, Soumi Mukherjee2, Arindam Sarkar3, Sunil Karforma4

1State Aided College Teacher & Head, Department of Computer Science, M.U.C. Women’s College, Burdwan, India.
2Former Student, Department of Microbiology, M.U.C. Women’s College, Burdwan, India.
3Assistant Professor, Department of Computer Science & Electronics, Ramakrishna Mission Vidyamandira, Belur Math, Howrah, India
4Head and Professor, Department of Computer Science, The University of Burdwan, India
Corresponding Author Email:[email protected]
Page Number: 478-492

Cancer is one of the highly-rated causes that lead to human mortality. Nowadays with the greater affect of the COVID-19 pandemic, co-morbid patients are at the dual risk of death. Therefore, the main aim of this paper is the specific detection of the cancer cells using nanoparticles further, report analysis using Artificial intelligence, and then the transmission of the medical report is to be done in a neural secured procurement. A simple mechanism to detect cancerous cells through Artificial Neural Networks (ANN) has been proposed here. Moreover, secure attainment of the patients’ medical data has been shown here with the help of Dual Neurons Genetic Key (DNGK). Structural and functionally equivalent ANNs have been iterated to generate the DNGK. In addition, genetic operations were included to make the session key more secured from the opponents. Nanoparticles are frequently used for specific cancer detection on the human body. A revolution in the form of telemedicine in the advanced medical sciences has emerged with the cameo of novel coronavirus things (IoT). It has helped to curtail the coronavirus chain through remote treatments. An Artificial Neural Network will be trained to detect the cancerous cells of the human body. The decision generated by ANN would be encrypted through the AES algorithm and DHNK before procured to the network. The Artificial Neural Network had been trained on different bio-images so that it generates an automated decision. Thus, prompt, safe, and automated cancer detection may be done using this proposed technique. Results derived from different tests on the proposed technique were evaluated and thus, validating the entire proposed technique. Thus, loads of societal development would happen in the fields of Medical Sciences, especially during these post- COVID-19 crisis hours
Keywords: COVID-19, Cancer, Artificial Neural Network, Dual Neurons Genetic Key (DNGK).



Aayushi Jain1, Viquar Husain Badshah1 & Vandana Gupta2

1School of Studies in Mathematics Vikram University Ujjain-456010, Madhya Pradesh, INDIA
Email: [email protected], [email protected]
2Department of Mathematics Govt. Kalidas Girls’ P.G. College Ankpat Marg, Ujjain-456001, Madhya Pradesh, India
Email: [email protected]
Page Number: 493-499
The present paper addresses a diffusion-reaction equation describing the dynamics of dissolved oxygen in a polluted stream of a river. The diffusion-reaction equation is a mass-balanced partial differential equation which relates the concentration of dissolved oxygen with the effect of other natural processes, viz. diffusion, natural aeration and reaction with pollutants. The well-known method of lines is used to solve the one-dimensional non-steady state case with Dirichlet boundary conditions. The study is motivated by the miserable condition of most of the rivers in India. Water pollution has now become a global concern and this study furnishes a better apprehension of complex phenomenon of maintaining desired level of oxygen and will aid water resource management.
Keywords: Advection, Diffusion, Diffusion-Reaction equation, method of lines, river-pollution, aeration.



Sonal Dixit1, Kirti Verma2

1Associate Professor, Department of Mathematics, SJHS Gujarati Innovative College of Commerce and Science,Indore (M. P.) India.
2Associate Professor, Department of Engineering Mathematics, Lakshmi Narain College of Technology, Bhopal (M.P.), India.
Corresponding Author Email: [email protected]
Page Number: 500-510

Fuzzy mathematics is considered to be an important aspect in the field of mathematics that interprets the uncertainties and deals with the unreliable information and vagueness of data. In this chapter we shall discuss the concept of fuzzy mathematics as fuzzy set and fuzzy logics and the beginning of fuzzy set theory and the fuzzy logics with their applications in the real life. As fuzzy mathematics and fuzzy logics are becoming increasingly significant as it is applied in almost every field of developments, engineering design and models and in new technologies also. We also discuss some recent models of fuzzy logics given by T. Patro[8] and C.K. Muthumaniraj [2] Fuzzy logics are playing very important role in many areas. I tried to make this chapter as a strong base for researchers and students so that it can prove strong base for further researches for comparative study of fuzzy set theory and fuzzy logics.
Keywords: Fuzzy metric space, Fuzzy set theory, Fuzzy logics, Real life application of fuzzy logics.


Telecardiological COVID-19 (2nd) Wave: Metaheuristic-Key Guides Protected Encryption of Heterogeneous Cardiac Reports

Joydeep Dey

Head & SACT, Department of Computer Science, M.U.C. Women’s College, Burdwan, India
Email: [email protected]
Page Number: 511-523

The epic COVID-19 had pushed the clinical sciences for another new allied branch as telemedicine services. In the field of COVID-19 (2nd) wave telemedicine, Internet and nature propelled algorithms helped to impart private data of various cardiovascular reports to various cardiologists for better treatment, perspectives, and opinion. Such heterogeneous cardiovascular reports are to be gotten so as to re-establish the patients' protection. Metaheuristic-key has been proposed through metaheuristics calculation followed by the standard AES 128 bits encryption. Cardiovascular infections (CVDs) are heart sickness identified with blockage of arteries and veins. Heart co-morbid patients are at the most elevated danger of COVID-19. Such patients are to be analyzed and treated appropriately within the restrictions of lockdown. This paper presents a got protected directing of the heterogeneous cardiovascular reports of the patients. Such were to be applied on the proposed metaheuristic-key followed by AES encryption. Making the heterogeneous reports into non-meaningful organization for the gatecrashers is the vital target of the proposed method. A few numerical tests were carried on the proposed strategy, and getting worthy outcomes. To translate the proposed metaheuristic-key through quickest figuring computing framework, the measure of time required has been calculated as 8.5× 1052 years. Along with these fine lines, pushing the COVID-19 telecardiology framework with more got and remarkable credits on the society.
Keywords:COVID-19 (2nd) Wave Telecardiology, Cardiac Reports, Metaheuristic-key, Harmony Search Algorithm.



George Albert Toma1 and Shaza Alturky1

1Department of Mathematics, Aleppo University, Aleppo, Syria
Email: [email protected], [email protected]
Page Number: 524-531

This paper suggests a new hybrid strategy for partial integro-differential equations arising in engineering applications. The new proposed method is based on hybridization the Kharrat-Toma integral transform with the homotopy perturbation method. This hybrid scheme aims to obtain exact solutions to several partial integro- differential equations subject to boundary or initial conditions in an effective and elegant compared to the numerical and analytical methods. In addition, that it reduces the integrals and computational steps. The obtained results display the applicability of the new suggested technique.
Keywords: hybrid approach, Kharrat-Toma integral transform method, homotopy perturbation method, partial integro-differential equations, initial and boundary value problems, exact solution.



Rohan Bhattacharjee1, Debjyoti Ghosh2 & Abhirup Mazumder3

1,2,3Department of Basic Science and Humanities, Institute of Engineering & Management, Salt Lake Electronics Complex, Kolkata-700091. India
3Corresponding Author Email: [email protected]
Page Number: 532-541

It has been found that during the runtime of a deep learning experiment, the intermediate resultant values get removed while the processes carry forward. This removal of data forces the interim experiment to roll back to a certain initial point after which the hyper-parameters or results become difficult to obtain (mostly for a vast set of experimental data). Hyper-parameters are the various constraints/measures that a learning model requires to generalise distinct data patterns and control the learning process. A proper choice and optimization of these hyper-parameters must be made so that the learning model is capable of resolving the given machine learning problem and during training, a specific performance objective for an algorithm on a dataset is optimised. This review paper aims at presenting a Parameter Optimisation for Learning (POL) model highlighting the all-round features of a deep learning experiment via an application-based programming interface (API). This provides the means of stocking, recovering and examining parameters settings and intermediate values. To ease the process of optimisation of hyper-parameters further, the model involves the application of optimisation functions, analysis and data management. Moreover, the prescribed model boasts of a higher interactive aspect and is circulating across a number of machine learning experts, aiding further utility in data management.
Keywords: Hyper-Parameters, Parameter Optimization for Learning (POL), Algorithm, Optimisation functions, Application-based programming interface (API), Learning model.



Kaushef Salamat1 , Nousheen Ilyas2

1Mathematics Department, Lahore Garrison University
2Mathematics Department, Assistant Professor, Lahore Garrison University
Email: [email protected]
Page Number: 542-563

The most useful technique of the mathematics which are used to finding the solutions of a lot of problems just like bending of beam, electrical network, heat related problems, which occurs in many disciplines of engineering and sciences are the techniques of integral transforms. In our research I discussed the duality between Fourier Sine transforms and some others effective integral transforms (namely Laplace transform, Mahgoub transform, Aboodh transform and Mohand transform). To justify the scope of dualities relation between Fourier Sine transform and other integral transforms (that are mentioned above, I presented the tabular representation of integral transform (namely Laplace transform, Aboodh transform, Mohand transform and Mahgoub transform) of various used functions by using Fourier Sine and other integral transforms dualities relation to signify fruitfulness of such connections. Results showed that these integral transform are strongly related with Fourier Sine transform.
Keywords: Laplace transform, Aboodh transform, Mahgoub transform, Mohand transform, Fourier sine transform.


Secured Telepsychiatry for Geriatric Patients (TGP) in the Face of COVID-19 2 nd Wave

Joydeep Dey1, Dr Bappaditya Chowdhury2, Arindam Sarkar3, Sunil Karforma4

1Head of the Department, Department of Computer Science, M.U.C. Women’s College, Burdwan
2Neuropsychiatrist, Department of Psychiatry, AMRI, Salt Lake, Kolkata
3Assitant Professor, Department of Computer Science & Electronics, R.K.M. Vidyamandira, Belur Math
4Head of the Department, Department of Computer Science, The University of Burdwan, Burdwan
Corresponding author Email: [email protected]
Page Number: 564-571

A second wave of COVID-19 has immensely affected the entire community. In the face of COVID-19 second wave scenario, geriatric patients with allied morbidities are most vulnerable under the COVID-19 threats. They suffer a lot from different mental complications. In this manuscript, secured telepsychiatry for geriatric patients (TGP) services are being highlighted with patients’ data security. In most of the telepsychiatry systems, patients’ data are under intruders’ attacks that lead to different malpractices. The secret key that is used in telepsychiatry system should be robust and non-deciphered by the intruders during the public network transmission. More importantly, secured telepsychiatry services are the best option to serve the geriatric patients with patients’ confidentiality. Thus, the COVID-19 attacks on such geriatric patients can be curtailed with efficacy.
Keywords:COVID-19 2nd wave, Telepsychiatry, Geriatric patients, Secured data transmission.