Radial limits of solutions to elliptic partial differential equations

For certain elliptic differential operators $L,$ we study the behaviour of solutions to $Lu=0,$ as we tend to the boundary along radii in strictly starlike domains in $\R^n, n\ge 3.$ Analogous results are obtained in other special domains. Our approach involves introducing harmonic line bundles as instances of Brelot harmonic spaces and approximating continuous functions by harmonic functions on appropriate subsets. These approximation theorems on harmonic spaces yield interesting examples for approximation by solutions of $Lu=0$ on some domains in $\R^n.

The FLRW cosmological model revisited: relation of the local time with th e local curvature and consequences on the Heisenberg uncertainty principle

version to be published in Advanced Studies in Theoretical PhysicsInternational audienceBy using the FLRW cosmological model, we calculated the relation between the local time and the local curvature in the case of a vacuum dominated universe. We showed that except for special values of the different constants which enter this equation, the time cannot be equal to zero. By using this assumption, we showed also that the demonstration of the uncertainty principle of Heisenberg is only an approximatio

Security of high-dimensional quantum key distribution protocols using Franson interferometers

Franson interferometers are increasingly being proposed as a means of securing high-dimensional energy-time entanglement-based quantum key distribution (QKD) systems. Heuristic arguments have been proposed that purport to demonstrate the security of these schemes. We show, however, that such systems are vulnerable to attacks that localize the photons to several temporally separate locations. This demonstrates that a single pair of Franson interferometers is not a practical approach to securing high-dimensional energy-time entanglement based QKD. This observations leads us to investigate the security of modified Franson-based-protocols, where Alice and Bob have two or more Franson interferometers. We show that such setups can improve the sensitivity against attacks that localize the photons to multiple temporal locations. While our results do not constituting a full security proof, they do show that a single pair of Franson interferometers is not secure and that multiple such interferometers could be a promising candidate for experimentally realizable high-dimensional QKD.Comment: 14 pages (single column format

Ventilation-on-Demand: Quantity or Quality — A Pilot Trial at Barrick Gold\u27s Bousquet Mine

Common to many established mines in Canada, is the problem that their ventilation systems are continually being stretched to meet new needs that were not anticipated in the original design. This can be the result of a variety of different factors, such as the discovery of new reserves at depth, accelerated production, new worker exposure regulations or a change of mining method. At Bousquet, the ventilation of a new multilevel mining block over 1 km away from the existing bottom of the mine presents a challenge. The airflow available for this region is limited to 57 m3/s by the size of a ventilation drift and raise, and by the total volume the mine can supply. This volume is sufficient only if it can be directed to the desired locations, namely where the diesel equipment is operating and with minimal losses (\u3c10%). Due to the mobile nature of the mining equipment and changing production areas, such tight management of air can only be achieved with Ventilation on Demand . This paper describes a pilot trial, within the existing mine, of an automated demand based ventilation management system. Vehicle tracking and identification determine ventilation demand, location and duration. Specific air volumes are achieved with remote controlled regulators, and auxiliary fan systems and verified with airflow monitors. Air quality is monitored with gas sensors. Based upon this trial the mine will be able to determine the viability of an air quality driven system over an engine based air quantity dictated system. This would then, with the approval of the local regulators, allow the mine to operate its ventilation more efficiently and gain the maximum benefit of cleanengine technology and exhaust treatment devices

Rational approximation on products of planar domains

We consider A(Ω), the Banach space of functions f from Ω¯¯¯¯=∏i∈IUi¯¯¯¯¯ to C that are continuous with respect to the product topology and separately holomorphic, where I is an arbitrary set and Ui are planar domains of some type. We show that finite sums of finite products of rational functions of one variable with prescribed poles off Ui¯¯¯¯¯ are uniformly dense in A(Ω). This generalizes previous results where Ui=D is the open unit disc in C or Ui¯¯¯¯¯c is connected