On the Correspondence between Display Postulates and Deep Inference in Nested Sequent Calculi for Tense Logics

We consider two styles of proof calculi for a family of tense logics, presented in a formalism based on nested sequents. A nested sequent can be seen as a tree of traditional single-sided sequents. Our first style of calculi is what we call "shallow calculi", where inference rules are only applied at the root node in a nested sequent. Our shallow calculi are extensions of Kashima's calculus for tense logic and share an essential characteristic with display calculi, namely, the presence of structural rules called "display postulates". Shallow calculi enjoy a simple cut elimination procedure, but are unsuitable for proof search due to the presence of display postulates and other structural rules. The second style of calculi uses deep-inference, whereby inference rules can be applied at any node in a nested sequent. We show that, for a range of extensions of tense logic, the two styles of calculi are equivalent, and there is a natural proof theoretic correspondence between display postulates and deep inference. The deep inference calculi enjoy the subformula property and have no display postulates or other structural rules, making them a better framework for proof search

Analysis of the low-energy η\etaNN-dynamics within a three-body formalism

The interaction of an $\eta$-meson with two nucleons is studied within a three-body approach. The major features of the $\eta NN$-system in the low-energy region are accounted for by using a s-wave separable ansatz for the two-body $\eta N$- and $NN$-amplitudes. The calculation is confined to the $(J^\pi;T)=(0^-;1)$ and $(1^-;0)$ configurations which are assumed to be the most promising candidates for virtual or resonant $\eta NN$-states. The eigenvalue three-body equation is continued analytically into the nonphysical sheets by contour deformation. The position of the poles of the three-body scattering matrix as a function of the $\eta N$-interaction strength is investigated. The corresponding trajectory, starting on the physical sheet, moves around the $\eta NN$ three-body threshold and continues away from the physical area giving rise to virtual $\eta NN$-states. The search for poles on the nonphysical sheets adjacent directly to the upper rim of the real energy axis gives a negative result. Thus no low-lying s-wave $\eta NN$-resonances were found. The possible influence of virtual poles on the low-energy $\eta NN$-scattering is discussed.Comment: 16 pages revtex including 10 figure

Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation

In this work, we consider a spatially homogeneous Kac's equation with a non cutoff cross section. We prove that the weak solution of the Cauchy problem is in the Gevrey class for positive time. This is a Gevrey regularizing effect for non smooth initial datum. The proof relies on the Fourier analysis of Kac's operators and on an exponential type mollifier

QCDMAPT: program package for Analytic approach to QCD

A program package, which facilitates computations in the framework of Analytic approach to QCD, is developed and described in details. The package includes the explicit expressions for relevant spectral functions calculated up to the four-loop level and the subroutines for necessary integrals.Comment: 18 pages, 4 figures; QCDMAPT package is available from http://cpc.cs.qub.ac.uk/summaries/AEGP_v1_0.htm

From Proof Nets to the Free *-Autonomous Category

In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We show the standard results of sequentialization and strong normalization of cut elimination. In the second part of the paper we show that the identifications enforced on proofs are such that the class of two-conclusion proof nets defines the free *-autonomous category.Comment: LaTeX, 44 pages, final version for LMCS; v2: updated bibliograph