Calogero Conjecture and Hubble Law

Acceptance of the Calogero hypothesis on the cosmic origin of quantizationin the framework of Nelson stochastic mechanics would imply that the age ofuniverse is larger than the standard quantum mechanical interpretation of theredshift measurement implies. This is due to variation of h with the radius of theuniverse and thus with time.     

Pulse contrast enhancement of high-energy pulses by use of a gas-filled hollow waveguide

Using nonlinear ellipse rotation in a gas-filled hollow waveguide, we have increased the pulse contrast of a microjoule femtosecond laser pulse by several orders of magnitude. This scheme offers a number of advantages over competing techniques, including a high degree of tunability that allows for a broad range of input pulse parameters, higher throughput, greater stability, and an output pulse with high spatial quality that is compressible to a quarter of the original temporal width.     

A two-stage solution approach for the Directed Rural Postman Problem with Turn Penalties

In this paper, we consider the Directed Rural Postman Problem with Turn Penalties (DRPP-TP). A solution is a tour that traverses all required arcs of the graph. The total cost of the tour is the sum of the lengths of the traversed arcs plus the penalties associated with the turns. One solution approach involves transforming the arc routing problem into an equivalent node routing problem. An alternative direct approach (without graph transformation) that involves two stages has been proposed in the literature. In the first part of this paper, we investigate the applicability of the direct approach. We identify several characteristics of the input instance that make this approach effective and present several limitations of this approach. In the second part of this paper, we describe an integer linear program that is combined with a local search algorithm. This combination produces high-quality solutions to the DRPP-TP in a reasonable amount of computing time.     

On the approximation performance of fictitious play in finite games

We study the performance of Fictitious Play (FP), when used as a heuristic for finding an approximate Nash equilibrium of a two-player game. We exhibit a class of two-player games having payoffs in the range $[0,1]$ that show that FP fails to find a solution having an additive approximation guarantee significantly better than $1/2$ . Our construction shows that for $n\times n$ games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity $1/2 - O(1/n^{1-\delta })$ for arbitrarily small $\delta $ . We also show an essentially matching upper bound of $1/2 - O(1/n)$ .     

Stresses and momenta in electromagnetic materials

The notion of energy–momentum, or energy–stress, pertains typically to electromagnetism. Eshelby transferred such a notion into elasticity in 1951 and, afterward, into continuum mechanics, in order to account for the force acting on a material defect. Similarities and differences between the Maxwell tensor of electromagnetism and the Eshelby tensor are shown and commented hereby. Basing on a Lagrangian approach to electromagnetic materials, canonical momenta are shown to emerge in a natural way. On the basis of these canonical quantities, one can introduce the material momentum (or pseudomomentum) along with the classical momentum and the material stress (Eshelby stress) along with the Maxwell stress, which is a Cauchy-like stress.