The study of parameter estimation under additive and multiplicative noise terms constitutes an interesting signal processing research topic with important consequences in the development of high-performance digital communication receivers. In this sense, the paper addresses the analysis of non-assisted digital synchronizers based on up to fourthorder moments and it shows how this alternative ou...

A coordinate-splitting economic diierence scheme is proposed for generalized parabolic equations (GPE) containing fourth-order diiusion operators and the algorithm for its implementation is developed. The performance of the scheme is demonstrated for diierent cases, e.g. for treating bifurcation phenomena. The technique is applied to the numerical solution of Swift-Hohenberg equation describing...

Fourth-order Schrödinger equations have been introduced by Karpman and Shagalov to take into account the role of small fourth-order dispersion terms in the propagation of intense laser beams in a bulk medium with Kerr nonlinearity. In this paper we investigate the cubic defocusing fourth order Schrödinger equation i∂tu +∆ 2 u + |u|u = 0 in arbitrary space dimension R for arbitrary initial data....

and Applied Analysis 3 Motivated by 14, 15 , here we study the existence of AL-solutions for 1.1 . The approach is completely different from the one used in 15 , in which an iteration process, jointly with a comparison with the linear equation y 4 q t y 2 0, is employed. Our tools are based on a topological method, certain integral inequalities, and some auxiliary functions. In particular, for ...

may be thought of as a nonlinear beam equation. In this paper we obtain both L-L estimates and space-time integrability estimates on solutions to the linear equation. We also use these estimates to study the local existence and asymptotic behavior of solutions to the nonlinear equation, for nonlinear terms which grow like a certain power of u. The main L-L estimate (Theorem 2.1) states that sol...

We present analytical and numerical results for a truncated version of the RS model for neural networks and also for the generalization of the Hopfield model that considers multineuron interactions. Static properties are analyzed in the replica mean-field approach and dynamical aspects are studied through numerical simulations using the multispin coding algorithm. The load capacity, the sizes o...

In the problem of blind separation of sources, we define usually a function ( cost, contrast, . . . ) and the solution is based on the search of the extremum of that function. The choice of cost function is then very important, both to have simple computation and to guarantee unicity and convergence to a good solution. In this paper, in the case of instantaneous mixtures of 2 sources, we study ...

A modification of the exponential time-differencing fourth-order Runge–Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison is made of the performance of this modified exponential time-differencing (ETD) scheme against the competi...

Recent work in the literature has studied fourth-order elliptic operators on manifolds with boundary. This paper proves that, in the case of the squared Laplace operator, the boundary conditions which require that the eigenfunctions and their normal derivative should vanish at the boundary lead to self-adjointness of the boundary-value problem. On studying, for simplicity, the squared Laplace o...

We calculate the bubble nucleation rate in a fourth-order gravity theory whose action contains an R term, under the thin-wall approximation, by two different methods. First the bounce solution is found for the Euclidean version of the original action. Next, we use a conformal transformation to transform the theory into general relativity with an additional scalar field and then proceed to find ...