In the theory of progressive enlargements of filtrations, the supermartingale Zt = P (g > t | Ft) associated with an honest time g, and its additive (Doob-Meyer) decomposition, play an essential role. In this paper, we propose an alternative approach, using a multiplicative representation for the supermartingale Zt, based on Doob’s maximal identity. We thus give new examples of progressive enla...

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, is in fact also used as a necessary condition. I argue that Lorentz-invariant elements of reality can be defined but, as Vaidman pointed out, they won...

In this paper, related to RBMO, we prove the sharp maximal inequalities for the Morrey spaces with the measure μ satisfying the growth condition. As an application we obtain the boundedness of commutators for these spaces.

We prove that the Lorentzian helicoid and Enneper’s surface are the unique properly embedded maximal surfaces bounded by a lightlike regular arc of mirror symmetry.

We discuss the efficiency of a heat engine operating in a nonequilibrium steady state maintained by two heat reservoirs. Within the general framework of linear irreversible thermodynamics we derive a universal upper bound on the efficiency of the engine operating at arbitrary fixed power. Furthermore, we show that a slight decrease of the power below its maximal value can lead to a significant ...

Pentatomid bugs communicate using substrate-borne vibrational signals that are transmitted along herbaceous plant stems in the form of bending waves with a regular pattern of minimal and maximal amplitude values with distance. We tested the prediction that amplitude variation is caused by resonance, by measuring amplitude profiles of different vibrational pulses transmitted along the stem of a ...

Thus our generators are not quite canonically normalized, but are all normalized equally, and β is positive definite. This is related to the fact, which we have already seen, that the group is compact. In writing down our generators, we have chosen, arbitrarily, one direction to make diagonal. Any rotation can be, by similarity transformation with at rotation, rotated into the z direction, so a...

The purpose of this study was to investigate the effects of loaded and unloaded plyometric training strategies on speed and power performance of elite young soccer players. Twenty-three under-17 male soccer players (age: 15.9 ± 1.2 years, height: 178.3 ± 8.1 cm, body-mass (BM): 68.1 ± 9.3 kg) from the same club took part in this study. The athletes were pair-matched in two training groups: load...

In contrast to most other primates, great apes have feet in which the heel supports body weight during standing, walking and running. One possible advantage of this plantigrade foot posture is that it may enhance fighting performance by increasing the ability to apply free moments (i.e. force couples) to the ground. We tested this possibility by measuring performance of human subjects when perf...

We prove sharp power-weighted L, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic analysis related to Bessel operators.