In this paper, we aim to study the solutions of superlinear hyperbolic problems with boundary condition Dirichlet type where show existence and uniqueness strong for by method energy inequality.

Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for minimax problems, which call J-symmetric method. The is obtained by exploiting structure of second-order derivative objective function in problem. We show that Hessian estimation (as well as its inverse) can be updated rank...

Inspired by Alves and Souto [2], we investigate the existence of nontrivial solutions to a class fractional Schrödinger equations with potentials well. Taking superlinear nonlinearities into consideration, obtain loosing monotonicity. Furthermore, ground state solution is established.

We propose and analyze a perturbed version of the classical Josephy– Newton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly constrained Lagrangian me...

The solution to the biharmonic equation in a simply connected region in the plane is computed in terms of the Goursat functions. The boundary conditions are conformally transplanted to the disk with a numerical conformal map. A linear system is obtained for the Taylor coeecients of the Goursat functions. The coeecient matrix of the linear system can be put in the form I + K where K is the discr...

In this paper, a fast and practical GPU-based implementation of Fuzzy C-Means (FCM) clustering algorithm for image segmentation is proposed. First, an extensive analysis is conducted to study the dependency among the image pixels in the algorithm for parallelization. The proposed GPU-based FCM has been tested on digital brain simulated dataset to segment white matter(WM), gray matter(GM) and ce...

We consider the class of quadratically-constrained quadratic-programming methods in the framework extended from optimization to more general variational problems. Previously, in the optimization case, Anitescu (SIAM J. Optim. 12, 949–978, 2002) showed superlinear convergence of the primal sequence under the Mangasarian-Fromovitz constraint qualification and the quadratic growth condition. Quadr...

In this paper we consider the question of whether NC circuits can generate pseudorandom distributions. While we leave the general question unanswered, we show • Generators computed by NC circuits where each output bit depends on at most 3 input bits (i.e, NC03 circuits) and with stretch factor greater than 4 are not pseudorandom. • A large class of “non-problematic” NC generators with superline...