Two sparse preconditioned iterative methods are presented to solve dense linear systems arising in the solution of two dimensional boundary integral equations. In the rst method, the sparse preconditioner is constructedsimply by choosing a small block of elements in the coeecient matrix of a dense linear system. The two-grid method falls into this category when the dense linear system arises fr...

Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...

This paper deals with robust exponential stability of Markovian jumping stochastic Cohen–Grossberg neural networks (MJSCGNNs) with mode-dependent probabilistic time-varying delays, continuously distributed delays and impulsive perturbations. By construction of novel Lyapunov–Krasovskii functional having the triple integral terms, the double integral terms having the positive definite matrices d...

We review the matrix model approach to the anomalous dimension matrix in N = 4 SYM. We construct the path integral representation for the anomalous dimension density matrix and analyze the resulting action. In particular, we consider the large N limit with different scalings of the coupling constant and find three essentially different regimes: string, noncommutative and membrane.

A closed-loop balanced truncation technique has been applied to an integral-type optimal servomechanism (IOS) expressed in graph-operator form of normalized right coprime factorization to produce a reduced-size state-feedback gain matrix, which is then converted into proportional-derivative (PD) gain matrices. On the other hand, the states of the integral of control error in the IOS are not tru...

We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. The latter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization...

Let A be a 0 − 1 matrix with precisely two 1’s in each column and let 1 be the all-one vector. We show that the problems of deciding whether the linear system Ax ≥ 1, x ≥ 0 (1) defines an integral polyhedron, (2) is totally dual integral (TDI), and (3) is box-totally dual integral (box-TDI) are all co-NP-complete, thereby confirming the conjecture on NP-hardness of recognizing TDI systems made ...

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...