Search results for "philosophy of mathematics"
showing 10 items of 246 documents
A local chemical potential approach within the variable charge method formalism
2008
A new and computationally efficient implementation of the variable charge method of Streitz and Mintmire (1994 Phys. Rev. B 50 11996) is presented. In particular a local chemical potential approach that optimizes the charge on only those atoms expected to be ionic is developed. By doing so, the charge fluctuation problem experienced in regions far from any oxygen is solved, leading to a linear minimization problem of the electrostatic energy. In the dilute oxygen limit, such an approach can lead to at least an order of magnitude saving in computation.
Limitations of the TG-43 formalism for skin high-dose-rate brachytherapy dose calculations
2014
Purpose: In skin high-dose-rate (HDR) brachytherapy, sources are located outside, in contact with, or implanted at some depth below the skin surface. Most treatment planning systems use the TG-43 formalism, which is based on single-source dose superposition within an infinite water medium without accounting for the true geometry in which conditions for scattered radiation are altered by the presence of air. The purpose of this study is to evaluate the dosimetric limitations of the TG-43 formalism in HDR skin brachytherapy and the potential clinical impact. Methods: Dose rate distributions of typical configurations used in skin brachytherapy were obtained: a 5 cm × 5 cm superficial mould; a …
SU-E-T-516: Limitations and Clinical Implications of the TG-43 Formalism for High-Dose-Rate Skin Brachytherapy
2013
Purpose: In high‐dose‐rate (HDR) skin brachytherapy, sources are located outside, in contact with, or implanted at some depth below the skin surface. Nowadays, most TPS use the TG‐43 formalism that is based on sources within an infinite water medium, without accounting for the scatter defect due to surrounding air. The purpose of the present study is to evaluate the limitations of the TG‐43 formalism in HDR skin brachytherapy. Methods: This study examined two HDR sources (Ir‐192 and Co‐60) together with a hypothetical Yb‐169 source. Dose distributions were obtained using Monte Carlo methods (i.e., GEANT4). The following configurations were investigated: 1)A typical clinical case consisting …
Leon Henkin the Reviewer
2014
In this chapter, we intend to look at Henkin’s reviews, a total of forty-six. The books and papers reviewed deal with a large variety of subjects that range from the algebraic treatment of logical systems to issues concerning the philosophy of mathematics and, not surprisingly—given his active work in mathematical education—one on the teaching of this subject. Most of them were published in The Journal of Symbolic Logic and only one in the Bulletin of the American Mathematical Society. We will start by sorting these works into subjects and continue by providing a brief summary of each of them in order to point out those aspects that are originally from Henkin, and what we take to be mistake…
Interfaces as design tools for the InAs/GaSb/InSb short-period superlattice for mid-infrared emission
2011
We use a standard 8 × 8 envelope-function approximation (EFA) formalism taking into account the effect of anisotropic and other interface (IF) interactions to investigate the electronic and optical properties of short-period superlattice laser structures (InAs/GaSb/InSb)×N grown on a GaSb substrate. We find that the band gaps numerically calculated at different temperatures give a good fitting with the experimental data confirming the model used. The calculated modal gain demonstrates that it is possible to achieve lasing operation at room temperature for N > 12 and for a reasonable total optical loss αt = 25 cm−1. Therefore, the 8 × 8 EFA formalism with IF design serves as a tool to model…
Philosophy of Mathematics and Ontological Commitment
2000
This paper concerns Quine's classification of philosophies of mathematics as sketched in "On what there is" and offers a new reading of Quine's view. In his famous paper Quine defines three positions: Realism, Conceptualism, and Nominalism. Each of them, he says, has its modern expression, respectively, in Logicism, Intuitionism, and Formalism. According to Quine these foundational positions can be accepted or rejected on a clear and objective basis, according to their distinctive ontological commitments. Consistent with his own criterion for ontological commitment (buttressed by his view on impredicative definitions), Quine adopts the Realist (or the Platonist) position in mathematics. Lat…
Density functional calculation of stopping power of an electron gas for slow ions
1981
Abstract We describe the first calculation of the stopping power of an electron gas for slow ions using the density-functional formalism. We evaluate the nonlinear self-consistent potential around the ion and from scattering theory determine the energy loss directly. Comparison with the results of linear theory is made.
Neutron-proton pairing correlations in a single l-shell model
2017
The long standing problem of neutron-proton pairing correlations is revisited by employing the Hartree-Fock-Bogoliubov formalism with neutron-proton mixing in both the particle-hole and particle-hole channels. We compare numerical calculations performed within this method with an exact pairing model based on the $SO(8)$ algebra. The neutron-proton mixing is included in our calculations by performing rotations in the isospin space using the isocranking technique.
Generalization of the model-independent Laurent–Pietarinen single-channel pole-extraction formalism to multiple channels
2016
A method to extract resonance pole information from single-channel partial-wave amplitudes based on a Laurent (Mittag-Leffler) expansion and conformal mapping techniques has recently been developed. This method has been applied to a number of reactions and provides a model-independent extraction procedure which is particularly useful in cases where a set of amplitudes is available only at discrete energies. This method has been generalized and applied to the case of a multi-channel fit, where several sets of amplitudes are analyzed simultaneously. The importance of unitarity constraints is discussed. The final result provides a powerful, model-independent tool for analyzing partial-wave amp…
Interaction of vector mesons with baryons and nuclei
2012
After some short introductory remarks on particular issues on the vector mesons in nuclei, in this paper we present a short review of recent developments concerning the interaction of vector mesons with baryons and with nuclei from a modern perspective using the local hidden gauge formalism for the interaction of vector mesons. We present results for the vector baryon interaction and in particular for the resonances which appear as composite states, dynamically generated from the interaction of vector mesons with baryons, taking also the mixing of these states with pseudoscalars and baryons into account. We then venture into the charm sector, reporting on hidden charm baryon states around 4…