The Energy of n Identical Bosons in a Finite Volume at O(L^{-7})

The volume dependence of the ground-state energy of n identical bosons with short-range interactions in a periodic spatial volume with sides of length L is calculated at order L^{-7} in the large volume expansion. This result will enable a refined determination of the pi^+ pi^+ pi^+ interaction from lattice QCD calculations.Comment: 3 page

Quark resonances and high E_t jets

Possible spin-3/2 quark resonances would have a significant effect on high E_{\mbox{\rm t}} jet production through their contribution to the subprocess $q+{\bar q}\rightarrow g+g$. Such enhancements are compared to a, recently reported, anomaly in inclusive jet production at the CDF detector.Comment: 7 pages set in RevTex with four postscript figures appended- all uuencode

Molecular Gas and Star Formation in the Cartwheel

Atacama Large Millimeter/submillimeter Array (ALMA) 12CO(J=1-0) observations are used to study the cold molecular ISM of the Cartwheel ring galaxy and its relation to HI and massive star formation (SF). CO moment maps find $(2.69\pm0.05)\times10^{9}$ M$_{\odot}$ of H$_2$ associated with the inner ring (72%) and nucleus (28%) for a Galactic I(CO)-to-N(H2) conversion factor ($\alpha_{\rm CO}$). The spokes and disk are not detected. Analysis of the inner ring's CO kinematics show it to be expanding ($V_{\rm exp}=68.9\pm4.9$ km s$^{-1}$) implying an $\approx70$ Myr age. Stack averaging reveals CO emission in the starburst outer ring for the first time, but only where HI surface density ($\Sigma_{\rm HI}$) is high, representing $M_{\rm H_2}=(7.5\pm0.8)\times10^{8}$ M$_{\odot}$ for a metallicity appropriate $\alpha_{\rm CO}$, giving small $\Sigma_{\rm H_2}$ ($3.7$ M$_{\odot}$ pc$^{-2}$), molecular fraction ($f_{\rm mol}=0.10$), and H$_2$ depletion timescales ($\tau_{\rm mol} \approx50-600$ Myr). Elsewhere in the outer ring $\Sigma_{\rm H_2}\lesssim 2$ M$_{\odot}$ pc$^{-2}$, $f_{\rm mol}\lesssim 0.1$ and $\tau_{\rm mol}\lesssim 140-540$ Myr (all $3\sigma$). The inner ring and nucleus are H$_2$-dominated and are consistent with local spiral SF laws. $\Sigma_{\rm SFR}$ in the outer ring appears independent of $\Sigma_{\rm H_2}$, $\Sigma_{\rm HI}$ or $\Sigma_{\rm HI+H_2}$. The ISM's long confinement in the robustly star forming rings of the Cartwheel and AM0644-741 may result in either a large diffuse H$_2$ component or an abundance of CO-faint low column density molecular clouds. The H$_2$ content of evolved starburst rings may therefore be substantially larger. Due to its lower $\Sigma_{\rm SFR}$ and age the Cartwheel's inner ring has yet to reach this state. Alternately, the outer ring may trigger efficient SF in an HI-dominated ISM.Comment: 10-pages text; 5-figure

Comparison of the INRIM and PTB lattice-spacing standards

To base the kilogram definition on the atomic mass of the silicon 28 atom, the present relative uncertainty of the silicon 28 lattice parameter must lowered to 3E-9. To achieve this goal, a new experimental apparatus capable of a centimetre measurement-baseline has been made at the INRIM. The comparison between the determinations of the lattice parameter of crystals MO*4 of INRIM and WASO4.2a of PTB is intended to verify the measurement capabilities and to assess the limits of this experiment.Comment: 10 pages, 8 figures, submitted to Metrologi

Regularization-robust preconditioners for time-dependent PDE constrained optimization problems

In this article, we motivate, derive and test �effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two diff�erent functionals, and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the eff�ectiveness of our preconditioners in each case is an eff�ective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are eff�ective for a wide range of regularization parameter values, as well as mesh sizes and time-steps

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

Fast iterative solution of reaction-diffusion control problems arising from chemical processes

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs