The large deviation problem for sums of i.i.d. random vectors is considered. It is assumed that the underlying distribution is absolutely continuous and its density is of regular variation. An asymptotic expression for the probability of large deviations is established in the case of a non-normal stable limit law. The role of the maximal summand is also emphasized. AMS Subject Classification: P...

Starting from the symmetric group Sn , we construct two fiat 2-categories. One of them can be viewed as the fiat “extension” of the natural 2-category associated with the symmetric inverse semigroup (considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the symmetric inverse semigroup. The ot...

'Motion dazzle camouflage' is the name for the putative effects of highly conspicuous, often repetitive or complex, patterns on parameters important in prey capture, such as the perception of speed, direction and identity. Research into motion dazzle camouflage is increasing our understanding of the interactions between visual tracking, the confusion effect and defensive coloration. However, th...

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 ...