Kleene algebra with domain

We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressiveness of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and well-foundedness; second, an algebraic reconstruction of propositional Hoare logic.Comment: 40 page

Which finitely generated Abelian groups admit isomorphic Cayley graphs?

We show that Cayley graphs of finitely generated Abelian groups are rather rigid. As a consequence we obtain that two finitely generated Abelian groups admit isomorphic Cayley graphs if and only if they have the same rank and their torsion parts have the same cardinality. The proof uses only elementary arguments and is formulated in a geometric language.Comment: 16 pages; v2: added reference, reformulated quasi-convexity, v3: small corrections; to appear in Geometriae Dedicat

Correlation studies of fission fragment neutron multiplicities

We calculate neutron multiplicities from fission fragments with specified mass numbers for events having a specified total fragment kinetic energy. The shape evolution from the initial compound nucleus to the scission configurations is obtained with the Metropolis walk method on the five-dimensional potential-energy landscape, calculated with the macroscopic-microscopic method for the three-quadratic-surface shape family. Shape-dependent microscopic level densities are used to guide the random walk, to partition the intrinsic excitation energy between the two proto-fragments at scission, and to determine the spectrum of the neutrons evaporated from the fragments. The contributions to the total excitation energy of the resulting fragments from statistical excitation and shape distortion at scission is studied. Good agreement is obtained with available experimental data on neutron multiplicities in correlation with fission fragments from $^{235}$U(n$_{\rm th}$,f). At higher neutron energies a superlong fission mode appears which affects the dependence of the observables on the total fragment kinetic energy.Comment: 12 pages, 10 figure

We can believe the Error Theory

Bart Streumer argues that it is not possible for us to believe the error theory, where by ‘error theory’ he means the claim that our normative beliefs are committed to the existence of normative properties even though such properties do not exist. In this paper, we argue that it is indeed possible to believe the error theory. First, we suggest a critical improvement to Streumer’s argument. As it stands, one crucial premise of that argument—that we cannot have a belief while believing that there is no reason to have it—is implausibly strong. We argue that for his purposes, Streumer’s argument only requires a weaker premise, namely that we cannot rationally have a belief while believing that there is no reason to have it. Secondly, we go on to refute the improved argument. Even in its weaker form, Streumer’s argument is either invalid or the crucial premise should be rejected

Changes in r-process abundances at late times

We explore changes in abundance patterns that occur late in the r process. As the neutrons available for capture begin to disappear, a quasiequilibrium funnel shifts material into the large peaks at A=130 and A=195, and into the rare-earth "bump" at A=160. A bit later, after the free-neutron abundance has dropped and beta-decay has begun to compete seriously with neutron capture, the peaks can widen. The degree of widening depends largely on neutron-capture rates near closed neutron shells and relatively close to stability. We identify particular nuclei the capture rates of which should be examined experimentally, perhaps at a radioactive beam facility.Comment: 8 pages, 14 figures included in tex

The TESLA accelerator module test facility

The superconducting TESLA linear accelerator will consist of about 1800 cryomodules. Before their installation in the TESLA tunnel, the acceleratorcryomodules have to be qualified after the assembly in random tests. The qualification includes the check of the general mechanical dimensions and the measurement of the cryogenic performance of all systems, in particular,the performance of the cavities. In addition, all about 21000 single cavities have to be tested before the assembly in the cryomodules at a rate of about 24 per day. The paper presents the layout of the test facility

An O(M(n) log n) algorithm for the Jacobi symbol

The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n) log n), using Sch\"onhage's fast continued fraction algorithm combined with an identity due to Gauss. We give a different O(M(n) log n) algorithm based on the binary recursive gcd algorithm of Stehl\'e and Zimmermann. Our implementation - which to our knowledge is the first to run in time O(M(n) log n) - is faster than GMP's quadratic implementation for inputs larger than about 10000 decimal digits.Comment: Submitted to ANTS IX (Nancy, July 2010

Dynamical approach to heavy-ion induced fission using actinide target nuclei at energies around the Coulomb barrier

In order to describe heavy-ion fusion reactions around the Coulomb barrier with an actinide target nucleus, we propose a model which combines the coupled-channels approach and a fluctuation-dissipation model for dynamical calculations. This model takes into account couplings to the collective states of the interacting nuclei in the penetration of the Coulomb barrier and the subsequent dynamical evolution of a nuclear shape from the contact configuration. In the fluctuation-dissipation model with a Langevin equation, the effect of nuclear orientation at the initial impact on the prolately deformed target nucleus is considered. Fusion-fission, quasi-fission and deep quasi-fission are separated as different Langevin trajectories on the potential energy surface. Using this model, we analyze the experimental data for the mass distribution of fission fragments (MDFF) in the reactions of $^{34,36}$S+$^{238}$U and $^{30}$Si+$^{238}$U at several incident energies around the Coulomb barrier. We find that the time scale in the quasi-fission as well as the deformation of fission fragments at the scission point are different between the $^{30}$Si+$^{238}$U and $^{36}$S+$^{238}$U systems, causing different mass asymmetries of the quasi-fission.Comment: 11 figure