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...

Kress, W. 2003. High Order Finite Difference Methods in Space and Time. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 880. 28 pp. Uppsala. ISBN 91-554-5721-5 In this thesis, high order accurate discretization schemes for partial differential equations are investigated. In the first paper, the linearized two-dimensiona...

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 ...

We consider the operator H = d 4 dt4 + d dtp d dt + q with 1-periodic coefficients on the real line. The spectrum of H is absolutely continuous and consists of intervals separated by gaps. We describe the spectrum of this operator in terms of the Lyapunov function, which is analytic on a two-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov...

The general quasi-linear autonomous fourth order diffusion equation ut = −[G(u)uxxx + h(u, ux, uxx)]x with positive variable diffusivity G(u) and lower-order flux component h is considered on the real line. A direct algorithm produces a general class of equations for which the Shannon entropy density obeys a reaction-diffusion equation with a positive irreducible source term. Such equations may...