Random walk on surfaces with hyperbolic cusps

We consider the operator associated to a random walk on finite volume surfaces with hyperbolic cusps. We study the spectral gap (upper and lower bound) associated to this operator and deduce some rate of convergence of the iterated kernel towards its stationary distribution.Comment: 28 page

Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

More security or less insecurity

We depart from the conventional quest for ‘Completely Secure Systems’ and ask ‘How can we be more Secure’. We draw heavily from the evolution of the Theory of Justice and the arguments against the institutional approach to Justice. Central to our argument is the identification of redressable insecurity, or weak links. Our contention is that secure systems engineering is not really about building perfectly secure systems but about redressing manifest insecurities.Final Accepted Versio

Existence and stability of solitons for the nonlinear Schr\"odinger equation on hyperbolic space

We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space.Comment: New: As noted in Banica-Duyckaerts (arXiv:1411.0846), Section 5 should read that for sufficiently large mass, sub-critical problems can be solved via energy minimization for all d \geq 2 and as a result Cazenave-Lions results can be applied in Section 6 with the same restriction. These requirements were addressed by the subsequent work with Metcalfe and Taylor in arXiv:1203.361

The Challenges of Capacity Building in the Aligning Forces for Quality Alliances

Summarizes the challenges and trade-offs in infrastructure and governance as well as stakeholder relations and participation, such as inclusive versus efficient decision making, in an alliance to coordinate regional healthcare improvement activities

Near Sharp Strichartz estimates with loss in the presence of degenerate hyperbolic trapping

We consider an $n$-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schr\"odiner equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension $n$ and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary $\beta>0$ loss. This is in contrast to \cite{ChWu-lsm}, where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension

High-temperature, high-pressure oxygen metering valve

A control valve includes a body defining a central cavity arranged between a fluid inlet and outwardly-diverging first and second fluid outlets respectively disposed in a common transverse plane. A valve member is arranged in the cavity for rotation between first and second operating positions where a transverse fluid passage through the valve member alternatively communicates the fluid inlet with one or the other of the fluid outlets. To minimize fluid turbulence when the valve member is rotated to an alternate operating position, the fluid passage has a convergent entrance for maintaining the passage in permanent communication with the fluid inlet as well as an oblong exit opening with spaced side walls for enabling the exit opening to temporarily span the first and second fluid outlets as the valve member is turned between its respective operating positions

A Dialectical Basis for Software Development Tool Building

We identify typical problems in the interactions of people with current software-based systems. In particular we observe the need to expend significant on-going effort to adapt these systems to reflect changes in the world about them, the need for people to adapt their working practices to fit in with these systems, and the inflexibility of these systems when faced with unusual circumstances or the need for change. We believe that these problems follow, at least in part, from these systems being developed and evolved using mechanisms each based on one Inquiry System only. This basis leads to assumptions being embedded in the mechanisms’ analysis outputs, and in system designs and implementations. We suggest that the problems noted may be mitigated by the use of a dialectical approach to Inquiry System selection for software development, based on the work of Hegel, which places in opposition different models of a situation based on different Inquiry Systems. We claim that such a mechanism has the potential to make explicit some of the assumptions which would otherwise be embedded implicitly in the delivered system without being questioned. We outline a research programme intended to test this hypothesis, and suggest other research directions