Monotonicity Results For Discrete Caputo-Fabrizio Fractional Operators

Nearly every theory in mathematics has a discrete equivalent that simplifies it theoretically and practically so that it may be used in modeling real-world issues. With discrete calculus, for instance, it is possible to find the "difference" of any function from the first order up to the n-th order. On the other hand, it is also feasible to expand this theory using discrete fractional calculus and make n any real number such that the 1⁄2-order difference is properly defined. This article is divided into five chapters, each of which develops the most straightforward discrete fractional variational theory while illustrating some fundamental concepts and features of discrete fractional calculus. It is also investigated how the idea may be applied to the development of tumors. The first section provides a succinct introduction to the discrete fractional calculus and several key mathematical concepts that are utilized often in the subject. We demonstrate in section 2 that if the Caputo-Fabrizio nabla fractional difference operator  of order  and commencing at is positive for   then  is -increasing. On the other hand, if  is rising and , then . Additionally, a result of monotonicity for the Caputo-type fractional difference operator is established. We show a fractional difference version of the mean-value theorem as an application and contrast it to the traditional discrete fractional instance

Convexity and Monotonicity Analyses for Discrete Fractional Operators with Discrete Exponential Kernes

For discrete fractional operators with exponential kernels, positivity, monotonicity, and convexity findings are taken into consideration in this paper. Our findings cover both sequential and non-sequential scenarios and show how fractional differences with other kinds of kernels and the exponential kernel example are comparable and different. This demonstrates that the qualitative information gathered in the exponential kernel case does not match other situations perfectly

Generalized Pierre Numbers

In this paper, we introduce and investigate the generalized Pierre sequences for the first time and we deal with, in detail, two special cases, namely, Pierre and Pierre-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between Pierre, Pierre-Lucas and Tribonacci, Tribonacci-Lucas numbers

Video gaming among youth during covid-19 lockdowns in Chennai, Tamilnadu, India

Video gaming is the new social currency among youth. Youths have begun to exhibit addictive characteristics of videogaming affecting different facet of life during Covid-19 Pandemic lockdown. Mixed methodology and purposive sampling, snowball sampling technique was used for comprehensive interpretation. The Videogame addiction was assessed using the (7-item criterion)  Gaming Addiction Scale (GAS). Major findings include changes in daily habits, motives, experience lifestyle and career choices, changes in communication and socializing pattern, performance in education, work, Mental and physical health and understanding primary caretakers concern on youth. The suggestions, implications will be based on  social work practice for Individuals, parents and other stakeholders based on the findings

Modelling The Impact of Screening, Treatment and Underlying Health Conditions on Dynamics of Covid-19

This study formulated a SIRS classical mathematical model which is modified to incorporate the exposed and the treated individuals where COVID-19 is modelled. The model stratifies the population into two categories depending whether they have underlying health conditions or not, and describes disease transmission within or between the groups. Five compartments are considered in the model for each group that is; Susceptible individuals, exposed population, Infected individuals, treated population and the Recovered population. The objectives were to; Formulate a mathematical deterministic model based on classical SIRS model incorporating screening, treatment and underlying health conditions on covid-19 dynamics. Determine the Reproduction number and use it to analyze the model. Determining sensitivity analysis and Bifurcation. Simulating the model using data from the ministry of health. The Next generation matrix method was used to determine the basic reproduction number denoted  of the proposed model. The results of the simulation indicated that the Disease Free Equilibrium is locally asymptotically stable whenever  and globally asymptotically stable if  . On the other hand, Endemic Equilibrium was globally asymptotically stable if .The results obtained showed that increasing the rate of screening and treatment on the exposed population and weakening the disease transmission route between the susceptible, exposed and infected population are crucial to curb the spread of COVID-19 virus. The Government of Kenya should advocate treatment and screening of the exposed and infected individuals

Quantum Conversation

This article is a sequel to the paper published earlier entitled (A new approach to gauge theory and variational principal). It is assumed that atoms are engaged in a perpetual conversation called Quantum Conversation,and the behavior of an atom varies based on the syntax, and the tonality, derived from the spectral terms. Accepting this premise, it is then explored how to identify Quantum Conversation, (QC). QuantumConversation could be identied through looking at atom from a fresh point of view. Mainly this includes re-interpreting spin, and split identied by the spectral terms which is the other behavioral characteristic of quantum particles. Split is dened both as the change in the orbit level, and the division of an atom into smaller elements. Spin, and split change as a result of Q.C. Q.C. has two major elements, 1) syntax, and 2) tonality.Given the dynamics and the diverse nature of syntax combined with tonality, it makes it possible to imagine and analyze a great number of scenarios for the behavior of the elements of an atom that would not bepossible to observe through laboratory experiments. This would open the door to a deeper understanding of the life of an atom

On the computation of zeros of Bessel functions

The zeros of some chosen Bessel functions of different orders is revised using the well-known bisection method , McMahon formula is also reviewed and the calculation of some zeros are carried out implementing a recent version of MATLAB software. The obtained results are analyzed and discussed on the lights of previous calculations

Multidimensional Poverty Analysis: assessing poverty patterns among different demographic groups of India

The concept of Multidimensional Poverty Index (MPI), which is relied upon the idea that many intertwined aspects of poverty might not be always possible to be measured in terms of fixed prices, has gained considerable familiarity over the last decades and there have been various experimentations to determine the aspects which should be most imperative to review in order to determine who are poor and who are not. In almost all studies, education, health and standard of living have been singled out as the three obligatory aspects that cannot be avoided if we are rightly trying to estimate poverty and the Alkire-Foster counting approach is the most widely acknowledged and implemented method for constructing Multidimensional Poverty Index. In this paper we have extended the idea, by using the latest 2021 Alkire and Kanagaratnam proposition, for 2015 Indian National Family Health Survey Data and we have observed significant changes (compared to the previous case studies for 2015 NFHS survey data where any older MPI computing methods were used) in the counts and ratios across India’s different states, caste groups, religious groups. The paper also looks for a method to extend the MPI counting from household level to individual level. The exploratory analysis wrt almost all possible diverse indicators of deprivation across different religions, caste groups, states and other demographic groups, is another key research aspect of this paper with the motivation to make the results easily interpretable and reusable even outside the scope of MPI construction.  It’s certain that the poverty level in India is not same for different demographic groups. This paper implements statistical tools such as Multiple Regression and Principal Component Analysis to assess the significance of the findings from the exploratory studies. &nbsp

Investigating the Effects of Working Capital Management on Firm’s Profitability: An Empirical Evidence from Egyptian Firms.

To run the company successfully, the fixed and the current assets play a commendable role. Managing the working capital is mandatory because it has a major significance on profitability and liquidity of the business concern. Usually, it is observed that, if a firm wants to take a bigger risk for bumper profits and losses, it minimizes the dimension of its working capital in relation to the revenues it generates. If it is willing to improve its liquidity, that in turn raises the level of its working capital. This research has analysed the impact of working capital on the profitability of a sample of 25 Egyptian companies listed in the Egyptian stock exchange for a period of 10 years from 2012-2021. The various components for measuring working capital management include the Receivable days, Current ratio, and Quick ratio on the Net operating profitability of Egyptian companies. The controlled variables like; Fixed assets on total assets, the Debt ratio, and the size of the firm (measured in terms of the natural logarithm of assets) have also been used for measuring working capital management. Descriptive Statistics, Pearson’s Correlation, and Regression Analysis are used for analysing this research. All these tests are used to correlate the theories contributed by the literature by several authors with the statistical results. The results depict that, there is a positive relationship between the components of the working capital management and the profitability ratios of the Egyptian firms which indicate that, as the receivable days increase it would tend to reduce the profitability of the company. It is also observed that the negative relationship between the liquidity and the profitability of Egyptian firms.  There is a positive relationship between the size and the profitability of the firm. This indicates that, as the size of the firm increases the profitability of the firm also increases. Finally, a negative relationship is observed between the debt and profitability of the Egyptian firms. The results derived from this research signify that the managers might be able to raise their profits by reducing the time for the debtors and inventories so that, time for payables would increase

The Galerkin Approximation to Forward-Backward Stochastic Partial Differential Equations

In this paper, the authors utilized the Galerkin approximation scheme approach to solve a class of fully coupled forward-backward stochastic partial differential equations in an infinite dimensional functional setup