1,281 research outputs found
Mass and Asymptotics associated to Fractional Hardy-Schr\"odinger Operators in Critical Regimes
We consider linear and non-linear boundary value problems associated to the
fractional Hardy-Schr\"odinger operator on domains of
containing the singularity , where and , the latter being the best constant in the
fractional Hardy inequality on . We tackle the existence of
least-energy solutions for the borderline boundary value problem
on
, where and is the critical fractional
Sobolev exponent. We show that if is below a certain threshold
, then such solutions exist for all , the latter being the first eigenvalue of
. On the other hand, for , we prove existence of such solutions only for those
in for which the domain
has a positive {\it fractional Hardy-Schr\"odinger mass} . This latter notion is introduced by way of an invariant of
the linear equation on
Design of a Novel Portable Flow Meter for Measurement of Average and Peak Inspiratory Flow
The maximum tolerable physical effort that workers can sustain is of significance across many industrial sectors. These limits can be determined by assessing physiological responses to maximal workloads. Respiratory response is the primary metric to determine energy expenditure in industries that use respirator masks to protect against airborne contaminants. Current studies fail to evaluate endurance under conditions that emulate employee operating environments. Values obtained in artificial laboratory settings may be poor indicators of respiratory performance in actual work environments. To eliminate such discrepancies, equipment that accurately measures peak respiratory flows in situ is needed. This study provides a solution in the form of a novel portable flow meter design that accurately measures average and peak inspiratory flow of a user wearing an M40A1 respirator mask
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