5,684 research outputs found
Equations for Hereditary Substitution in Leivant's Predicative System F: A Case Study
This paper presents a case study of formalizing a normalization proof for
Leivant's Predicative System F using the Equations package. Leivant's
Predicative System F is a stratified version of System F, where type
quantification is annotated with kinds representing universe levels. A weaker
variant of this system was studied by Stump & Eades, employing the hereditary
substitution method to show normalization. We improve on this result by showing
normalization for Leivant's original system using hereditary substitutions and
a novel multiset ordering on types. Our development is done in the Coq proof
assistant using the Equations package, which provides an interface to define
dependently-typed programs with well-founded recursion and full dependent
pattern- matching. Equations allows us to define explicitly the hereditary
substitution function, clarifying its algorithmic behavior in presence of term
and type substitutions. From this definition, consistency can easily be
derived. The algorithmic nature of our development is crucial to reflect
languages with type quantification, enlarging the class of languages on which
reflection methods can be used in the proof assistant.Comment: In Proceedings LFMTP 2015, arXiv:1507.07597. www:
http://equations-fpred.gforge.inria.fr
Selected topics on Low Energy Antiproton Physics
Some of the last results on low energy antiproton physics are reviewed. First
Faddeev calculations for \={n}d scattering length are presented.Comment: 10 pages, 11 figures Invited talk to the Biennial Conference on Low
Energy Antiproton Physics (LEAP 2000), Venice 20-26 August (2000). To appear
in Nuclear Physics
Role of Surface Texture on Workpiece Angular Deformation in Cross Wedge Rolling
The cross wedge rolling process is commonly used for the manufacturing of shaft or for preforms, being used for preliminary operation of forming cycle. The presence of angular deformation produced during the rolling process is analyzed in this paper. This work shows some experimental results obtained on parts made of steel in semi-industrial condition. Visioplasticity technique is used to measure the angular displacement occurring in some sections with reference to the adjacent ones. Thus the test samples are prepared to include surface grooves filled up with quite similar steel grade. After rolling process, angular deformations are highlighted by observations and external deformation profile. Influence of surface texture of the forming area is experimentally demonstrated. Moreover, the numerical simulation with the software FORGE is used to verify the adequacy between the observed phenomena and forecasts which can be obtained today.Conclusions about the relative influence of friction factors on the internal stresses creation are finally presented to better identify potential occurrence of these phenomena. Strain diagrams are used to bring out the magnitude of angular variations depending on local plastic strain on parts. Possible consequences for process optimization are raised
Contact Pressure Measurement System in Cross Wedge Rolling
In the cross wedge rolling process (CWR), plastic deformation is geared by a driving torque transmitted by friction on die surface. Friction plays a role which has to be further identified in this metal forming process. The local contact pressure between a cylindrical billet and flat dies seems to be a relevant parameter to characterize the severe contact conditions during the rolling. This paper deals with an experimental measurement technology, which has been designed and implemented on a semi-industrial CWR test bench with plate configuration. This measurement system using pin and piezoelectric sensor is presented, with an analysis of the system operation and design detail. Characterization of systematic error and calibration tests are then explained. Additional tests performed on hot steel preforms allow to check the ability of the contact pressure measurement system to resist under severe operating conditions. Realistic results for varying temperatures are then discussed
Relativistic wave functions and energies for nonzero angular momentum states in light-front dynamics
Light-front dynamics (LFD) is a powerful approach to the theory of
relativistic composite systems (hadrons in the quark models and relativistic
nucleons in nuclei). Its explicitly covariant version has been recently applied
with success to describe the new CEBAF/TJNAF data on the deuteron
electromagnetic form factors. The solutions used in were however not obtained
from solving exactly the LFD equations but by means of a perturbative
calculation with respect to the non relativistic wave function. Since, a
consequent effort has been made to obtain exact solutions of LFD equations. The
first results concerning J=0 states in a scalar model have been published in
nucl-th/9912050. The construction of states in LFD is complicated by
the two following facts. First, the generators of the spatial rotations contain
interaction and are thus difficult to handle. Second, one is always forced to
work in a truncated Fock space, and consequently, the Poincar\'e group
commutation relations between the generators -- ensuring the correct properties
of the state vector under rotation -- are in practice destroyed. In the
standard approach, with the light-front plane defined as , this
violation of rotational invariance manifests by the fact that the energy
depends on the angular momentum projection on -axis.
We present here a method to construct states in the explicitly
covariant formulation of LFD and show how it leads to a restoration of
rotational invariance.Comment: To appear in Nucl.Phys.B, 3 pages, 2 figures, .tar.gz fil
Stability of bound states in the light-front Yukawa model
We show that in the system of two fermions interacting by scalar exchange,
the solutions for J= bound states are stable without any cutoff
regularization for coupling constant below some critical value.Comment: 5 pages, 2 figures, submitted to publicatio
Two-Body Bound States in Light-Front Dynamics
We present the main features of the explicitly covariant Light-Front Dynamics
formalism and a summary of our recent works on this topic. They concern the
bound states of two scalar particles in the Wick-Cutkosky model and of two
fermions interacting via the usual OBEP ladder kernels.Comment: Invited contribution to the XIVth International School on Nuclear
Physics, Varna, Bulgaria, Sept 25-30. 20 pages, 23 figure
Universal dual amplitudes and asymptotic expansions for and in four dimensions
Though the one-loop amplitudes of the Higgs boson to massless gauge bosons
are finite because there is no direct interaction at tree-level in the Standard
Model, a well-defined regularization scheme is still required for their correct
evaluation. We reanalyze these amplitudes in the framework of the
four-dimensional unsubtraction and the loop-tree duality (FDU/LTD), and show
how a local renormalization solves potential regularization ambiguities. The
Higgs boson interactions are also used to illustrate new additional advantages
of this formalism. We show that LTD naturally leads to very compact integrand
expressions in four space-time dimensions of the one-loop amplitude with
virtual electroweak gauge bosons. They exhibit the same functional form as the
amplitudes with top quarks and charged scalars, thus opening further
possibilities for simplifications in higher-order computations. Another
outstanding application is the straightforward implementation of asymptotic
expansions by using dual amplitudes. One of the main benefits of the LTD
representation is that it is supported in a Euclidean space. This
characteristic feature naturally leads to simpler asymptotic expansions.Comment: 11 pages, no figures. Minor modifications, discussion improved. Final
version published in EPJ
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