The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L− L∞ ∩ L∞ = {0}, where the cl...

Materials and structures exhibiting coupled behaviors between mechanics and other physics (especially magnetics, electrics and thermics – phase transformation –) and submitted to multiaxial stress are considered. The most practical applications concern sensors and actuators. The multiaxial stress is usually inherited from forming process or appears in use. In the area of coupling between mechan...

Using a two-player Tullock-type contest we show that intuitively and structurally different contests can be strategically equivalent. Strategically equivalent contests generate the same best response functions and, as a result, the same equilibrium efforts. However, strategically equivalent contests may yield different equilibrium payoffs. We propose a simple two-step procedure to identify stra...

Skin, the largest organ in the body, performs many important roles including protection against physical and chemical insults, regulation of temperature and fluid loss, and immunity and sensory roles. Once damaged, skin cannot perform these normal tasks and numerous complications such as infection or fluid loss can occur. To restore these roles, the body needs to close the wound as quickly as p...

Hwang and Xu defined equivalent double-loop networks and gave one such result showing that the L-shapes of the two equivalent networks are recombinations of three rectangles. Recently, Rödseth gave an elegant algebraic theorem for equivalent multi-loop networks. We show that its double-loop version yields equivalent networks of the 3rectangle version. We also show that other seemingly different...

In Ambisonics sound is encoded and stored in multichannel sound files and is decoded for playback. In the enand decoding process complicated functions are used. In this paper panning functions equivalent to the result of enand decoding are presented which can be used for real-time panning in an arbitrary high ambisonic order. In the function equivalent to the socalled in-phase decoding the orde...