we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

Abstract: New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of singular fractional linear systems is d...

in this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl‎. ‎308 (2000) 203-211] and [linear algebra appl‎. ‎428 (2008) 2177-2191]‎.

Using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of Monge-Amp`{e}re equations are established‎.‎

The stability and stabilization of linear continuous time singular Markov switched systems with time delay are investigated. Based on the linear matrix inequality method (LMIs), the robust stability of uncertain linear stochastic delay system is guaranteed irrespective of the value of the time delay. Then the proposed theory can be extended to discuss the robust stabilization of uncertain stoch...

‎Artificial neural networks have the advantages such as learning, ‎adaptation‎, ‎fault-tolerance‎, ‎parallelism and generalization‎. ‎This ‎paper is a scrutiny on the application of diverse learning methods‎ ‎in speed of convergence in neural networks‎. ‎For this aim‎, ‎first we ‎introduce a perceptron method based on artificial neural networks‎ ‎which has been applied for solving a non-singula...

In Part I, under the bit operation cost model we achieved nearly optimal randomized solution of nonsingular Toeplitz/Hankel linear system of equations based on Hensel's lifting. In Part II, we extend these results to the singular Toeplitz/Hankel-like case based on the MBA divide-and conquer algorithm and its combination with Hensel's lifting. We specify randomization and estimate the error/fail...