1Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria
Page Number: 119-165
This paper presents a seven-dimensional ordinary differential equation of mathematical model of zika virus
between humans and mosquitoes population with non-linear forces of infection in form of saturated
incidence rate. Vertical transmission is introduced into the model. These incidence rates produce antibodies
in response to the presence of parasite-causing zika virus in both human and mosquito populations. The
existence of region where the model is epidemiologically feasible is established (invariant set) and the
positivity of the models is also established. The basic properties of the model are determined including the
reproduction number of both cases,R 0 and R 0 | p q 0 respectively .Stability analysis of the disease-free
equilibrium is investigated via the threshold parameter (reproduction number R 0 | p q 0 ) obtained using the
next generation matrix technique. The special case model results shown that the disease-free equilibrium is
locally asymptotical stable at threshold parameter less than unity and unstable at threshold parameter greater
than unity. Under specific conditions on the model parameters, the global dynamics of the special case
model around the equilibra are explored using Lyapunov functions. For a threshold parameter less than
unity, the disease-free equilibrium is globally asymptotically stable. While the endemic equilibrium is
shows to be globally asymptotically stable at threshold parameter greater than unity. Numerical simulations
are carried out to confirm the analytic results and explore the possible behavior of the formulated model.
The result shows that, horizontal and vertical transmission contributes a higher percentage of infected
individuals in the population than only horizontal transmission.
1Department of Mathematics,
Federal University of Technology, Owerri, P. M. B. 1556, Owerri Imo State.
Page Number: 166-178
In this investigation, regular perturbation procedures in asymptotic expansions of the relevant variables are
employed to discuss the static buckling analysis of a finite deterministically imperfect but viscously damped
column resting on some quadratic–cubic nonlinear elastic foundations, but struck by a step load. The
governing equation for the system under discussion is fully nonlinear, so that a closed form and easy
solution to the problem is not possible. An approximate analytical solution to the problem is obtained using
asymptotic and perturbation techniques and numerical results obtained show that increase in imperfection
factors lower the static buckling loads of the column.
Keywords: Static Buckling, Asymptotic and perturbation methods, Light and Viscous damping, Step Load.
1Department of Mathematics, Springdale high school, Kalyani, India
2Department of Mathematics, Regent Education and Research Foundation, Kolkata
Page Number: 179-192
In fuzzy mathematics fuzzy system reliability can be analysed by fuzzy sets. We can use various types
of fuzzy sets for that analyzing the fuzzy system reliability but here we specially used intuitionistic
fuzzy set theory. At first, TrIFNs and their arithmetic operations are introduced. Expressions for
computing the fuzzy reliability of a series system, parallel system, series-parallel and parallel-series
system following TrIFNs have been described. Here an imprecise failure to start of a truck is taken. To
compute the imprecise failure of the above said system, failure of each component of the systems is
represented by Trapezoidal Intuitionistic Fuzzy Number. This process can be utilise to measure the
failure is various aspects like portfolio in stock market etc. The numerical expression also calculated
and presented in this paper for the failure to start of a truck using TrIFN.
Keywords: fuzzy set, IFN, intuitionistic fuzzy number, system reliability, TrIFN, trapezoidal
intuitionistic fuzzy number.
Project Associate International Institute of Information Technology, Bangalore
Page Number: 193-200
In this note we have studied some properties of decimal digits obtained by dividing 1 by primes which have
maximum period property, namely, inverses of primes, p, whose decimal representation repeats after p-1.
For such primes up to 1000, we have given a method for finding decimal digits of their inverses without
using division. This works for many non-primes also. We have also given a construction method for
obtaining magic squares for primes, 17, 29, 61 and 97 for which such magic squares are not known.
1Department of Mathematics, Federal University Of Technology, Owerri Imo State. P.M.B 1526
2Department of Mathematics, University Of Ilorin, Ilorin Nigeria.
Page Number: 201-217
We study a new subclass T ∗ (g, φ, α, λ, μ, β, t) of univalent functions with negative
coefficients defined by Hadamard product using a generalized differential operator.
Coefficient estimates, distortion theorems are established. Further, extremal properties and
radii of close-to-convexity, starlikeness and convexity of the class T ∗ (g, φ, α, λ, μ, β, t) are
1Department of ECE, Institute of Engineering & Management, Salt Lake Electronics Complex, Kolkata-700091.
2 Department of Basic Science & Humanities, Institute of Engineering & Management, Salt Lake Electronics Complex, Kolkata-700091.
3Department of CSE, Institute of Engineering & Management, Salt Lake Electronics Complex, Kolkata-700091.
4Department of IT, Institute of Engineering & Management, Salt Lake Electronics Complex, Kolkata-700091.
5 Department of EE, Institute of Engineering & Management, Salt Lake Electronics Complex, Kolkata-700091.
Page Number: 218-224
The cause, effect and remedial measures of head injury is presented in a capsule form. The position of Brain
is in the central location of the cranium and is well protected by nature with some layers surrounding it.
Brain is the controlling organ of the human body, so its damage or even injury has gained attention among
the scientists and physicians. As nobody will allow his/her head for investigation so modelling is a must
for study of brain injury problems. The analytical study may give some idea on the location and degree of
Keywords: Skull, Scalp, Diploë, Cranium, CSF, Brain Injury
1Department of Basic Science and Humanities, Institute of Engineering & Management, Kolkata-700091,
Page Number: 225-228
The word cryptography was coined from two Greek words ‘Krypto’, meaning hidden and ‘graphein’
meaning writing. Thus, cryptography means hidden writing. Cryptography is the method of protecting
important data and information from third parties called adversaries or the public. It is also known as
encryption. Modern cryptography is basically based on Mathematics and Computer science. The roots of
cryptography are found in Roman and Egyptian civilizations. Hieroglyph is the oldest cryptographic
technique. Based on security needs and threats, various cryptographic methods such as symmetric key
cryptography, public key, private key, microdots, etc are adopted . It is a two step process; encryption
and decryption. The encryption process uses a cipher (code) in order to encrypt plaintext and convert it into
ciphertext. Decryption is the opposite of encryption that is to decode the encrypted message or information.
Cryptography was used extensively in the American Revolutionary War, the First World War and the
Second World War. For example if the code was ‘CVVCEM’ then it would mean ‘ATTACK’. The initials
of each letter is shifted by two places. This paper is basically a survey paper and we have studied the
importance, features, advantages, and disadvantages and authenticated on the topic cryptography. Note:
This paper is a REVIEW PAPER.
Keywords: hieroglyph, cipher, cryptanalysis, cryptosystem, key, cryptology, encryption, decryption,
alice, bob, confidential, authentication, data integrity, repudiation.
1Institute of Engineering & Management, EP Block, Sector V, Salt Lake, Kolkata, India
Page Number: 229-238
Machine learning is a way to study the algorithm and statistical model that is used by computer to
perform a specific task through pattern and deduction . It builds a mathematical model from a sample
data which may come under either supervised or unsupervised learning. It is closely related to
computational statistics which is an interface between statistics and computer science. Also, linear
algebra and probability theory are two tools of mathematics which form the basis of machine learning.
In general, statistics is a science concerned with collecting, analysing, interpreting the data. Data are
the facts and figure that can be classified as either quantitative or qualitative. From the given set of data,
we can predict the expected observation, difference between the outcome of two observations and how
data look like which can help in better decision making process . Descriptive and inferential statistics
are the two methods of data analysis. Descriptive statistics summarize the raw data into information
through which common expectation and variation of data can be taken. It also provides graphical
methods that can be used to visualize the sample of data and qualitative understanding of observation
whereas inferential statistics refers to drawing conclusions from data. Inferences are made under the
framework of probability theory. So, understanding of data and interpretation of result are two important
aspects of machine learning. In this paper, we have reviewed the different methods of ML, mathematics
behind ML, its application in day to day life and future aspects.
Keywords: Algorithm, Statistical model, Computational statistics, Descriptive statistics, Inferential statistics
1Department of Electronics and Communication Engineering Institute of Engineering & Management D1 Management House, Salt Lake, Sector V, Kolkata-700091, West Bengal, India. 2Department of Electrical Engineering Institute of Engineering & Management D1 Management House, Salt Lake, Sector V, Kolkata-700091, West Bengal, India.
3Department of Basic Science and Humanities Institute of Engineering & Management D1 Management House, Salt Lake, Sector V, Kolkata-700091, West Bengal, India.
Page Number: 239-250
We have stepped into a world of undeniable data breach fatigues. Thus to ensure data security, encryption
schemes come into action, one such highly talked about encryption nowadays is “Homomorphic
Encryption” which is mainly used to compress data for their easy storage involving secure transmission and
processing on cloud without compromising on privacy since special keys are needed for primary encryption
and final decryption. Homomorphic encryption allows operation on two ciphertexts to give an encrypted
(coded) result which when decrypted (decoded) maps to result of the operation, if it would have been on
plaintext. It can be either multiplicative like the RSA or additive like the Pallier cryptosystem. Here we also
focused on ideal lattice based public key encryption scheme which is almost bootstrappable. Multihop
homomorphic encryption also has vital roles to play here. A strong homomorphic encryption is one which
is resistant to all attacks using various algorithms. Thus our main objective is to allow encrypted computing
on data, minimize memory usage and to save energy and time. Our presentation will try to focus on the
researches done so far and also on the success rates of the scheme which is affecting the real world.
Keywords:Homomorphic, Public Key Encryption, Decryption, RSA, Pallier Cryptosystem, Cloud, Ideal Lattice, Bootstrappable
1Department of Mechanical Engineering Institute of Engineering & Management Salt Lake Electronics Complex, Kolkata-700091.
2Department of Information Technology Institute of Engineering and Management Salt Lake Electronics Complex, Kolkata-700091
3Department of Computer Science and Engineering Institute of Engineering and Management
Page Number: 251-256
The paper deals with the topic of improvising human perception using Artificial Intelligence to make human
beings more efficient and productive. Understanding human perception takes a lot of non-verbal cues such
as facial expressions, gesture, body language and tone of voice. Recent research has been made through
facial coding and neurofeedback training. To analyse the probable response of a human being at certain
expression of emotion, collection of data based on facial expression, vocal utterances, brainwave frequency
under challenging condition ssuch as anger, contempt, disgust, fear, sadness and surprise is required. If we
can formulate a nalgorithm based on the data collected ,then not only it would be possible to calculate
certain human action , it can also be possible to change or reduce the chances of success of a certain action.
Modern advancements has introduced faster problem solving capability but it has some restrictions, which
can be coped by the utilisation of human brain which has far better capabilities.The main concern of this
paper is why to use AI and how it will revolutionize the mankind.
Keywords: AI driven machines, emotion AI, subliminal effect, robots
Journal of Mathematical Sciences & Computational Mathematics (JMSCM)
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