‎in this paper‎, ‎we construct a new iterative method for solving nonlinear volterra integral equation of second kind‎, ‎by approximating the legendre polynomial basis‎. ‎error analysis is worked using banach fixed point theorem‎. ‎we compute the approximate solution without using numerical method‎. ‎finally‎, ‎some examples are given to compare the results with some of the existing methods‎.

The reduced density matrix of a given subsystem, denoted by $\rho_A$, contains the information on subregion duality in holographic theory. We may extract using spectrum (eigenvalue) matrix, called entanglement this paper. evaluate eigenstates, one-point and two-point correlation functions microcanonical ensemble state $\rho_{A,m}$ associated with an eigenvalue $\lambda$ for some examples, inclu...

Recently there has been great interest in geometricallymotivated approaches to data analysis and pattern recognition. Low-dimensional structure in higher-dimensional data can be exploited by manifold-based data reduction and learning algorithms to improve performance. The existence of such a structure in speech has not been formally documented. Toward this end, I present a derivation of the app...

In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.