JAEM 2025, Vol 15, No 4

On a class of constacyclic codes over the ring Z4[u]/< u² − 3 >

2025-04-09T10:47:56Z

On a class of constacyclic codes over the ring Z4[u]/< u² − 3 > Thoudam, Dolly; Ratnabala Devi, Okram In this paper, λ-constacyclic codes and skew-λ-constacyclic codes over the ring R = Z4[u]/< u² − 3 > are studied for λ = 3 and 2 + 3u. Introducing new Gray maps from R to the copies of Z4, we observed that Gray images of λ-constacyclic codes over R are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. λconstacyclic codes of odd length over R and generating polynomial of the Gray images are studied. Further, it is observed that the images of skew-λ- constacyclic codes over R are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4.

The extended Legendre wavelets operational matrix of integration and its applications

2025-04-09T10:25:22Z

The extended Legendre wavelets operational matrix of integration and its applications Sharma, Vivek Kumar; Singh, Sonoo; Srivastava, Hari Mohan In this paper, the general operational matrix of integration P based on the extended Legendre wavelets has been developed which generalizes the idea of the operational matrix of integration for µ = 2 given in [30]. A brief procedure for forming this matrix has been discussed. Also, we have solved Bessel differential equation of order zero by using extended Legendre wavelets method for different values of µ, M and k. The results show the better accuracy of the proposed method, which is justified through the illustrative examples.

Distinguishing number in some aspects of dendrimers

2025-04-09T07:49:53Z

Distinguishing number in some aspects of dendrimers Salat, Arti; Sharma, Amit The main purpose of the present study is to determine the distinguishing number of some dendrimers. The most known dendrimers such as Polyamidoamine (PAMAM), polylysine (PLL), Poly propyl ether imine (PETIM) and zinc porphyrin (DPZn) have a great impact in drug delivery systems, biomedical, etc. Based on structure of these dendrimers, some new graphs have been defined which resemble with the structure of dendrimers.The n-generation of hexa-cyclic dendrimer HCn,d and hexa-star dendrimer HSn,d have been introduced. Further, the distinguishing number of n−generations of graphs; C d6 , hexa-cyclic dendrimer HCn,d and hexa-star dendrimer HSn,d have been determined successfully.

Solving a nonlinear inverse problem of the Camassa-Holm equation

2025-04-09T07:06:23Z

Solving a nonlinear inverse problem of the Camassa-Holm equation Zeidabadi, Hamed; Pourgholi, Reza; Basiri, Abdolali; Boroujeni, Ahmad Aliyari In order to solve the nonlinear inverse Camassa-Holm equations, a numerical method is developed by applying finite difference formula to time discrimination and collocation of polynomial scaling functions for spatial variable. Using operational matrix of derivative, the problem is reduced to a set of algebraic equation. An estimation of error bound is investigated for presented method. Also, to show the accuracy of the proposed method, it is applied on two test problems. One of the most important advantages of this work, compared to previous works, is the implementation simplicity.