Search results for "Mathematica"
showing 10 items of 7971 documents
Of Many, Many Other Things
2021
Propositions of everyday discourse can have, unlike those of formal languages, other components over and above the predicate and the terms needed to saturate it. These components are of two very different sorts: adverbs and further individual terms. Only adverbs have already been discussed by other writers in this connection; but they are not the whole story.
(Approximate) Low-Mode Averaging with a new Multigrid Eigensolver
2015
We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD computations. Since the $\gamma_5$-preserving aggregation based interpolation used in our multigrid method is valid for both, the Hermitian and the non-Hermitian case, inversions of very ill-conditioned shifted systems with the Hermitian operator become feasible. This enables the use of multigrid within shift-and-invert type eigensolvers. We show numerical results from our MPI-C implementation of a Rayleigh quotient iteration with multigrid. For state-of-the-art lat…
Intertwining operators between different Hilbert spaces: connection with frames
2009
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral self-adjoint operators living in different Hilbert spaces. Many examples are discussed in details. Many of them arise from the theory of frames in Hilbert spaces, others from the so-called g-frames.
Transformations that preserve learnability
1996
We consider transformations (performed by general recursive operators) mapping recursive functions into recursive functions. These transformations can be considered as mapping sets of recursive functions into sets of recursive functions. A transformation is said to be preserving the identification type I, if the transformation always maps I-identifiable sets into I-identifiable sets.
Researching (Algebraic) Problem Solving from the Perspective of Local Theoretical Models
2010
Concepts such as Local Theoretical Model, Mathematical Sign System, logico-semiotic outline, analytical reading, and formal competence model, elaborated within long term research programs developed in Mexico and Spain, are presented. Empirical data from a study carried out in Spain with students of a teacher training school are analyzed using this theoretical framework. The cases analyzed show to which extent the logico-semiotic outline determines the arithmetic or algebraic nature of the entire problem solving process, even in the case of pupils which had been instructed in general problem solving heuristics, management and control, including the explicit training in changing the plan of s…
Analysis of block random rocking on nonlinear flexible foundation
2020
Abstract In this paper the rocking response of a rigid block randomly excited at its foundation is examined. A nonlinear flexible foundation model is considered accounting for the possibility of uplifting in the case of strong excitation. Specifically, based on an appropriate nonlinear impact force model, the foundation is treated as a bed of continuously distributed springs in parallel with nonlinear dampers. The statistics of the rocking response is examined by an analytical procedure which involves a combination of static condensation and stochastic linearization methods. In this manner, repeated numerical integration of the highly nonlinear differential equations of motion is circumvent…
CLUSTER MONTE CARLO ALGORITHMS IN STATISTICAL MECHANICS
1992
The cluster Monte Carlo method, where variables are updated in groups, is very efficient at second order phase transitions. Much better results can be obtained with less computer time. This article reviews the method of Swendsen and Wang and some of its applications.
An introduction to knowledge computing
2014
This paper deals with the challenges related to self-management and evolution of massive knowledge collections. We can assume that a self-managed knowledge graph needs a kind of a hybrid of: an explicit declarative self-knowledge (as knowledge about own properties and capabilities) and an explicit procedural self-knowledge (as knowledge on how to utilize own properties and the capabilities for the self-management).We offer an extension to a traditional RDF model of describing knowledge graphs according to the Semantic Web standards so that it will also allow to a knowledge entity to autonomously perform or query from remote services different computational executions needed. We also introdu…
Imbalance Effects in the Lucas Model: An Analytical Exploration
2004
In this note, we use a technique analogous to Xie's method (1994) to solve analytically the Lucas model with externality in a specific parametric case. In particular, we characterize the shape of imbalance effects in this model. Our results are entirely consistent with the findings of the related computational literature. Moreover, our analytical investigation tends to show that these findings are robust to the presence of the Lucas externality as long as a unique equilibrium path exist.
Design of composite measure schemes for comparative severity assessment in animal-based neuroscience research: A case study focussed on rat epilepsy …
2020
PLOS ONE 15(5), e0230141 (2020). doi:10.1371/journal.pone.0230141