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
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).
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.
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.
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.
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.
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.
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.
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.
