70,085 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Hybridization of multi-objective deterministic particle swarm with derivative-free local searches
The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based on the hypervolume metric. The hybridization scheme uses two parameters to control the local search activation and the number of function calls used by the local algorithm. The most promising values of these parameters were identified using forty analytical tests representative of the SBDO problem of interest. The resulting hybrid algorithm was finally applied to two SBDO problems for hull-form design. For both analytical tests and SBDO problems, the hybrid method achieves better performance than its global and local counterparts
Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis
The Boubaker polynomials are investigated in this paper. Using Riordan
matrices analysis, a sequence of relations outlining the relations with
Chebyshev and Fermat polynomials have been obtained. The obtained expressions
are a meaningful supply to recent applied physics studies using the Boubaker
polynomials expansion scheme (BPES).Comment: 12 pages, LaTe
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Convergence and Optimality of Adaptive Mixed Finite Element Methods
The convergence and optimality of adaptive mixed finite element methods for
the Poisson equation are established in this paper. The main difficulty for
mixed finite element methods is the lack of minimization principle and thus the
failure of orthogonality. A quasi-orthogonality property is proved using the
fact that the error is orthogonal to the divergence free subspace, while the
part of the error that is not divergence free can be bounded by the data
oscillation using a discrete stability result. This discrete stability result
is also used to get a localized discrete upper bound which is crucial for the
proof of the optimality of the adaptive approximation
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