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 $J \ne 0$ 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 $t+z=0$, this violation of rotational invariance manifests by the fact that the energy depends on the angular momentum projection on $z$-axis. We present here a method to construct $J\ne0$ 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

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

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$^{\pi}$=$0^+$ bound states are stable without any cutoff regularization for coupling constant below some critical value.Comment: 5 pages, 2 figures, submitted to publicatio

Universal dual amplitudes and asymptotic expansions for gg→Hgg\to H and H→γγH\to \gamma\gamma 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