Search results for "philosophy of mathematics"
showing 10 items of 246 documents
Size-consistent single-reference methods for electronic correlation: a unified formulation through intermediate hamiltonian theory
1996
Using the intermediate hamiltonian theory as a unique conceptual frame and the technique of CI matrix dressing, a wide series of single-reference methods for the treatment of the ground state correlation are reviewed, compared, and sometimes improved. These methods range from independent excitation approximation (the very next step beyond MP2) to coupled cluster, going through the so-called electron pair approximations and the (SC)2CI formalism. A hierarchy of these methods can be established according to two criteria: These formulations in terms of diagonalizations of dressed CI matrices avoid convergence problems, but their main advantage is their flexibility, since they apply to multi-re…
CTR: A calculus of timed refinement
1995
This paper presents CTR — a process algebraic framework for loose specification of time quantity sensitive operational behaviour of reactive systems. CTR terms are provided both with operational and specification semantics (via the notion of specification refinement). Besides the intuitive justification of appropriateness of the refinement notion, a preservation theorem is proved for a timed variant of Hennessy-Milner logic. A comparison of CTR with the related formalism of Timed Modal Specifications, and with the timed process calculi TCCS due to Wang is given. Some pragmatics of the application of CTR is sketched on a critical resource access example.
Density functional theory calculations on magnetic properties of actinide compounds
2010
We have performed a detailed analysis of the magnetic (collinear and noncollinear) order and atomic and the electron structures of UO2, PuO2 and UN on the basis of density functional theory with the Hubbard electron correlation correction (DFT+U). We have shown that the 3-k magnetic structure of UO2 is the lowest in energy for the Hubbard parameter value of U=4.6 eV (and J=0.5 eV) consistent with experiments when Dudarev's formalism is used. In contrast to UO2, UN and PuO2 show no trend for a distortion towards rhombohedral structure and, thus, no complex 3-k magnetic structure is to be anticipated in these materials.
On parameterizing thermodynamic descriptions of minerals for petrological calculations
2014
A new regularization approach, termed micro-ϕ, is outlined for parameterizing activity–composition (a–x) relations and other aspects of the thermodynamic descriptions of minerals for petrological calculations. In the context of the symmetric formalism, a formulation of a–x relations that is easily generalizable to multi-component minerals, parameterization with micro-ϕ extends from where there are good data available to constrain, for example, interaction energies, to where there are little or no data. This involves decomposing the interaction energies, which are macroscopic between end-members, into their microscopic components involving interactions between elements on sites. Micro-ϕ invo…
Discovering temporal relationships in databases of newspapers
1998
This paper is mainly dedicated to analyse the problem of discovering frequent temporal patterns in event sequences extracted from a large repository of newspapers. The proposed formalism and algorithms rely on Toodor, which is a document retrieval system that allows users to specify conditions over the structure, contents and temporal features of the stored documents. We develop in this work several algorithms for recognising frequent temporal patterns in terms of arc-consistency, which consist of discarding temporal occurrences that do not satisfy a temporal structure.
Use of parallel computing to improve the accuracy of calculated molecular properties
1998
Calculation of electron correlation energy in molecules is unavoidable in accurate studies of chemical reactivity. However, these calculations involve, a computational effort several, even in the simplest cases, orders of magnitude larger than the computer power nowadays available. In this work the possibility of parallelize the calculations of the electron correlation energy is studied. The formalism chosen is the dressing of matrices in both distributed and shared memory parallel systems MIMD. Algorithms developed on PVM are presented, and the results are evaluated on several platforms. These results show that the parallel techniques are useful in order to decrease very appreciably the ti…
Varieties of Vagueness, Fuzziness and a few foundational (and ontological) questions
2011
In this paper we discuss the multifaceted nature of vagueness, the limits of (standard) set theory in dealing with the foundational aspects that a really innovating theory of vagueness should manifest, and the difficul- ties in outlining the possible features that such a type of new formalism should exhibit in order to be able to deal with such innovative aspects. We shall highlight some aspects of the role that Fuzzy Set Theory (FST) can play in this process.
The microscopic theory of diffusion-controlled defect aggregation
1998
Abstract The kinetics of diffusion-controlled aggregation of primary Frenkel defects ( F and H centers) in irradiated CaF 2 crystals is theoretically studied. Microscopic theory is based on the discrete-lattice formalism for the single defect densities (concentrations) and the coupled joint densities of similar and dissimilar defects treated in terms of the Kirkwood superposition approximation. Conditions and dynamics of the efficient F center aggregation during crystal heating after irradiation are analyzed.
The Poincar\'e-Cartan Form in Superfield Theory
2018
An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincar\'e-Cartan form. Noether theorem and examples from superfield theory and supermechanics are also discussed.
Semiclassical geons at particle accelerators
2014
We point out that in certain four-dimensional extensions of general relativity constructed within the Palatini formalism stable self-gravitating objects with a discrete mass and charge spectrum may exist. The incorporation of nonlinearities in the electromagnetic field may effectively reduce their mass spectrum by many orders of magnitude. As a consequence, these objects could be within (or near) the reach of current particle accelerators. We provide an exactly solvable model to support this idea.