(ISSN Number (Online) - 2644-3368)

(ISSN Number (Print) - 2688-8300)

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.

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.

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.

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.

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 obtained.

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 brain injury.

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 [1]. 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.

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 [1]. 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 [2]. 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.

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.

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.