Leak detector

A detector for sensing a leaking of fluid pressures is reported. The detector is characterized by an hermetically sealed housing confining therewithin a first normalized pressure, a connector for coupling the housing in direct communication with a suspected leak established within a substantially sealed body, an electrical circuit having a first or normalized configuration and including a pair of circuit completing electrical contacts and means mounting at least one contact of said pair of contacts on a flexible wall of the housing supporting the contact for movement from a first position along a linear path to a second position in response to an altering of the pressure confined within the housing for thereby altering the configuration of the circuit

Two Weight Inequalities for Discrete Positive Operators

We characterize two weight inequalities for general positive dyadic operators. We consider both weak and strong type inequalities, and general (p,q) mapping properties. Special cases include Sawyers Fractional Integral operator results from 1988, and the bilinear embedding inequality of Nazarov-Treil-Volberg from 1999. The method of proof is an extension of Sawyer's argument.Comment: 20 pages, 3 figures. v2 correction of minor typos v3: Correction of typos. v4: Two references adde

A Two Weight Inequality for the Hilbert transform Assuming an Energy Hypothesis

Subject to a range of side conditions, the two weight inequality for the Hilbert transform is characterized in terms of (1) a Poisson A_2 condition on the weights (2) A forward testing condition, in which the two weight inequality is tested on intervals (3) and a backwards testing condition, dual to (2). A critical new concept in the proof is an Energy Condition, which incorporates information about the distribution of the weights in question inside intervals. This condition is a consequence of the three conditions above. The Side Conditions are termed 'Energy Hypotheses'. At one endpoint they are necessary for the two weight inequality, and at the other, they are the Pivotal Conditions of Nazarov-Treil-Volberg. This new concept is combined with a known proof strategy devised by Nazarov-Treil-Volberg. A counterexample shows that the Pivotal Condition are not necessary for the two weight inequality.Comment: 60 pages, 1 figure. v3. An important revision: The Energy Condition is reformulated, a key concept of the proof, is reformulated. The main result is unchanged. v4. important display corrected. v6: The earlier versions incorrectly claimed a characterization, as was pointed out to us by S. Treil v7. Corrections in Section

Mean lattice point discrepancy bounds, II: Convex domains in the plane

We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.Comment: Revised version, to appear in Journal d'Analyse Mathematiqu

Turbulence, combustion, pollutant, and stability characterization of a premixed, step combustor

A two dimensional combustion tunnel was constructed to study a lean premixed turbulent propane/air flame stablized behind a rearward facing step. Studied were: (1) the existence and importance of large coherent structures in turbulent reacting and nonreacting free shear layers behind the steps; (2) the effect of inlet temperature and reference velocity on combustion efficiency; (3) CO, NO2 and NO sub x production in the flame; and (4) the blowout and upstream propagation of the flame. In the ranges studied, the large coherent structures dominated both the reacting and the nonreacting free shear layers behind the step. The growth of the vortices and the propagation of the flamer were intimately linked. Vortex pairing was observed to be one of the mechanisms for introduction of fresh reactants into the shear layer and growth of the shear layer. Probe composition measurements of the flame showed that, in the recirculation zone, the reaction was above 99 percent complete, CO and unburnt hydrocarbons were above the equilibrium level NO sub x concentration was far below the equilibrium level and NO2 comprised a negligible fraction of NO sub x