We study the motion of the Kovalevskaya top about a fixed point, construct invariant sets (in particular, images of Liouville tori and three-dimensional isoenergetic surfaces) in the movable space of angular velocities, and classifies all... more
We study the motion of the Kovalevskaya top about a fixed point, construct invariant sets (in particular, images of Liouville tori and three-dimensional isoenergetic surfaces) in the movable space of angular velocities, and classifies all possible types of those sets. A family of curves on Poisson sphere illustrates the Liouville foliation for Kovalevskaya top.
The purpose of this article is to establish weak and strong convergence results of AI iterative scheme for fixed points of generalized α-nonexpanisve mappings in uniformly convex Banach spaces. Furthermore, we carry out a numerical... more
The purpose of this article is to establish weak and strong convergence results of AI iterative scheme for fixed points of generalized α-nonexpanisve mappings in uniformly convex Banach spaces. Furthermore, we carry out a numerical experiment to compare the convergence of AI iterative scheme with several prominent iterative schemes. Finally, we use AI iteration process to find the unique solution of a functional Volterra-Fredholm integral equation with deviating argument in Banach spaces. The results of this paper are new and extend several results in the literature.
ABSTRACT This paper constitutes an effort towards the generalization of the most common classical iterative methods used for the solution of linear systems (like Gauss–Seidel, SOR, Jacobi, and others) to the solution of systems of... more
ABSTRACT This paper constitutes an effort towards the generalization of the most common classical iterative methods used for the solution of linear systems (like Gauss–Seidel, SOR, Jacobi, and others) to the solution of systems of nonlinear algebraic and/or transcendental equations, as well as to unconstrained optimization of nonlinear functions. Convergence and experimental results are presented. The proposed algorithms have also been implemented and tested on classical test problems and on real-life artificial neural network applications and the results
The search for new integrable (3+1)-dimensional partial differential systems is among the most important challenges in the modern integrability theory. It turns out that such a system can be associated to any pair of rational functions of... more
The search for new integrable (3+1)-dimensional partial differential systems is among the most important challenges in the modern integrability theory. It turns out that such a system can be associated to any pair of rational functions of one variable in general position, as established below using contact Lax pairs introduced in arXiv:1401.2122v5.
In this article, using the principles of Random Matrix Theory (RMT) with Gaussian Unitary Ensemble (GUE), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two point Out of Time... more
In this article, using the principles of Random Matrix Theory (RMT) with Gaussian Unitary Ensemble (GUE), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two point Out of Time Order Correlation function (OTOC) expressed in terms of square of the commutator bracket of quantum operators which are separated in time scale. We also provide a strict model independent bound on the measure of quantum chaos, −1/N (1 − 1/π) ≤ SFF ≤ 0 and 0 ≤ SFF ≤ 1/πN , valid for thermal systems with large and small number of degrees of freedom respectively. We have studied both the early and late behaviour of SFF to check the validity and applicability of our derived bound. Based on the appropriate physical arguments we give a precise mathematical derivation to establish this alternative strict bound of quantum chaos. Finally, we provide an example of integrability from GUE based RMT from Toda Lattice model to explicitly show the application of our derived bound on SFF to quantify chaos.
In this paper, a multi-step iterative method is introduced for contraction mappings. We prove that our new iterative method converges at a rate faster than some of the leading iterative schemes in the existing literature which have been... more
In this paper, a multi-step iterative method is introduced for contraction mappings. We prove that our new iterative method converges at a rate faster than some of the leading iterative schemes in the existing literature which have been used recently to obtain the solutions of a mixed type Volterra-Fredholm functional nonlinear integral equation and a delay differential equation. A numerical example is also used to show that our new iterative scheme converges at a rate faster than a number of existing iterative schemes for contraction mappings. As some applications, we prove that our new iterative method converges strongly to the unique solutions of a mixed type Volterra-Fredholm functional nonlinear integral equation and a delay differential equation. In addition, we give data dependence result for the solution of the nonlinear integral equation we are considering with the help of our new iterative scheme. Our results improve, generalize and unify some well known results in the existing literature.
In this article, using the principles of Random Matrix Theory (RMT) with Gaussian Unitary Ensemble (GUE), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two point Out of Time... more
In this article, using the principles of Random Matrix Theory (RMT) with Gaussian Unitary Ensemble (GUE), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two point Out of Time Order Correlation function (OTOC) expressed in terms of square of the commutator bracket of quantum operators which are separated in time scale. We also provide a strict model independent bound on the measure of quantum chaos, −1/N (1 − 1/π) ≤ SFF ≤ 0 and 0 ≤ SFF ≤ 1/πN, valid for thermal systems with large and small number of degrees of freedom respectively. We have studied both the early and late behaviour of SFF to check the validity and applicability of our derived bound. Based on the appropriate physical arguments we give a precise mathematical derivation to establish this alternative strict bound of quantum chaos. Finally, we provide an example of integrability from GUE based RMT from Toda Lattice model to explicitly show the application of o...
We present an infinite hierarchy of nonlocal conservation laws for the Przanowski equation, an integrable second-order PDE locally equivalent to anti-self-dual vacuum Einstein equations with nonzero cosmological constant. The hierarchy in... more
We present an infinite hierarchy of nonlocal conservation laws for the Przanowski equation, an integrable second-order PDE locally equivalent to anti-self-dual vacuum Einstein equations with nonzero cosmological constant. The hierarchy in question is constructed using a nonisospectral Lax pair for the equation under study. As a byproduct, we obtain an infinite-dimensional differential covering over the Przanowski equation.
In a paper [Appl. Math. Comput., 188 (2) (2007) 1587-1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a... more
In a paper [Appl. Math. Comput., 188 (2) (2007) 1587-1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.
