This paper addresses the generalized Euler polynomial matrix E (α) (x) and the Euler matrix E .Taking into account some properties of Euler polynomials and numbers, we deduce product formulae for E (α) (x) and define the inverse matrix of E .We establish some explicit expressions for the Euler polynomial matrix E (x), which involves the generalized Pascal, Fibonacci and Lucas matrices, respectively.From these formulae, we get some new interesting identities involving Fibonacci and Lucas numbers.Also, we provide some factorizations of the Euler polynomial matrix in terms of Stirling matrices, as well as a connection between the shifted Euler matrices and Vandermonde matrices.
The particle that moving on a circular path under a certain constraint is studied using Lagrangian mechanics (Euler Lagrange equation). The action function is obtained by integrating the Lagrangian through time interval ; from this function we can calculate the wave function , the behavior for the action function and the wave function is described through illustrative graphs.
: In this paper, we proposed an optimal control of the COVID-19 transmission dynamics. First, we investigated system features such as solution boundedness, positivity, disease-free and endemic equilibrium, and the local and global stability of equilibrium points. Besides, a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one, and an endemic equilibrium point exists otherwise. Secondly, we have shown the sensitivity analysis of the basic reproduction number. Also the model is then fitted using COVID-19 infected reported in Ethiopia from February 1,2023 to March 2,2023. The values of model parameters are then estimated from the data reported using the least square method together with the the MATLAB software. Moreover, the optimal corruption minimization strategies are determined using three controls strategies, namely prevention, vaccination and treatment. The existence of the optimal controls and characterization is established using Pontryagin’s Maximum Principle. Finally, based on analysis of optimality system, the combination of the prevention and treatment of infected is the most optimal and least cost strategy to minimize the burden of the disease.
In our previous work, we introduced a clustering algorithm based on clique formation. Cliques, the obtained clusters, are constructed by choosing the most dense complete subgraphs by using similarity values between instances. The clique algorithm successfully reduces the number of instances in a data set without substantially changing the accuracy rate. In this current work, we focused on reducing the number of features. For this purpose, the effect of the clique clustering algorithm on dimensionality reduction has been analyzed. We propose a novel algorithm for support vector machine classification by combining these two techniques and applying different strategies by differentiating the clique structures. The results obtained from well known data sets confirm the compatibility of clique clustering algorithm with dimensionality reduction.
In this paper, we propose new polynomial discrete logistic equations based on the classical logistic map, which exhibit chaotic behavior as control parameters vary. We also explore versions with fractional derivatives. Using the chaotic sequence generated by these equations, we develop an encryption scheme for text. The scheme relies on initial conditions, control parameters, and a transformation of text characters into values between 0 and 1, followed by a transformation to discrete chaotic values for transmission
