We construct A-stable and L-stable diagonally implicit Runge-Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge-Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge-Kutta methods are suitable methods for integrating shallow water problems in the sense that the stab...

The implicit function theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of equations, as functions of the remaining variables. We derive a lower bound for the radius of this ball in the case of Lipschitz maps. Under a sign-preserving condition, we prove that an implicit function exists in the case of a set of inequ...

There is mounting evidence for the idea that performance in a visuomotor rotation task can be supported by both implicit and explicit forms of learning. The implicit component of learning has been well characterized in previous experiments and is thought to arise from the adaptation of an internal model driven by sensorimotor prediction errors. However, the role of explicit learning is less cle...

In this paper, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a metric space satisfying a weak Meir-Keeler type contractive condition by using a class of implicit relations. In particular, our result generalizes and improves a result of K. Jha, R.P. Pant, S.L. Singh, by removing the assumption of continuity, relaxing compatibility to weakly com...

We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi-infinite cylinder in one more spatial dimension. We write our evolution ...

So far, several approaches have been studied to bridge the problem of the Semantic Gap, the bottleneck in image and video retrieval. However, no approach is successful enough to increase retrieval performances significantly. One reason is the lack of understanding the user’s interest, a major condition towards adapting results to a user. This is partly due to the lack of appropriate interfaces ...

This paper presents a semi-implicit numerical method for the simulation of grain growth in two dimensions with a multi phase field model. To avoid the strong stability condition of traditional explicit methods, a first-order, semi-implicit discretisation scheme is employed, which offers a good compromise with regard to memory intensity and computational requirements. A nonlinear multigrid solve...

We studied an individual with multiple personality disorder in whom each of several personalities claimed to have no direct awareness of the others and to be unable to consciously remember the experiences of other personalities. A broad selection of implicit and explicit memory tests was used to determine the extent to which one personality had access to knowledge acquired by another and the ci...

The present commentary addresses the main results obtained in the Butler and Klein [Butler, B. C., & Klein, R. (2009). Inattentional blindness for ignored words: Comparison of explicit and implicit memory tasks. Consciousness and Cognition, 18, 811-819.] study and discusses them in relation to the Perceptual Load Theory of Lavie [Lavie, N. (1995). Perceptual load as a necessary condition for se...