In this paper we provide a pricing-hedging duality for the model-independent superhedging price with respect to a prediction set $Ξ\subseteq C[0,T]$, where the superhedging property needs to hold pathwise, but only for paths lying in $Ξ$. For any Borel measurable claim $ξ$ which is bounded from below, the superhedging price coincides with the supremum over all pricing functionals $\mathbb{E}_{\mathbb{Q}}[ξ]$ with respect to martingale measures $\mathbb{Q}$ concentrated on the prediction set $Ξ$. This allows to include beliefs in future paths of the price process expressed by the set $Ξ$, while eliminating all those which are seen as impossible. Moreover, we provide several examples to justify our setup.

A mathematical model to describe period-memorizing behavior in Physarum plasmodium are reported. In constructing the model, we first examine the basic characteristics required for the class of models, then create a minimal linear model to fulfill these requirements. We also propose two modifications of the minimal model, nonlinearization and noise addition, which improve the reproducibility of experimental evidences. Differences in the mechanisms and in the reproducibility of experiments between our models and the previous models are discussed.

Using transfer-matrix methods, we investigate the response of a multilayered metamaterial system containing defects to an incident acoustic plane wave at normal or oblique incidence. The transmission response is composed of pass-bands with oscillatory behaviour, separated by band gaps and covers a wide frequency range. The presence of gain and loss in the layers leads to the emergence of symmetry breaking and re-entrant phases. In the general case, a system containing defects will display a more general property, pseudo-Hermiticity (PH), of which $\mathcal{PT}$ systems are a subset. In the PH-symmetric phase, unidirectional responses of the reflection, accomplished by reversing the parity $\mathcal{P}$, can be found but the response sometimes deviates from the predictions of simple scattering theory which call for a pseudo-unitarity relation relating the transmission and the two directions of reflections to hold. The converse of reversing the parity, reversing the time operator $\mathcal{T}$ in a spatially-asymmetric system within the PH-symmetric regime can lead to different transmissions: a pass-band versus a stop-band. As regions of stable PH-symmetric pass-band transmission oscillations occur over a wide spectral range, there is a large flexibility in system parameters such as layer thicknesses, for leading to the desired unidirectional traits. In addition, we find that while defects in general lead to a near or complete loss of PH symmetry at all frequencies, they can be exploited to produce highly-sensitive responses, making such systems good candidates for sensor applications.

A new concept called biased derivative is proposed. It has a potential to better understand and model some aspects of dynamical systems associated with creating bubbles.

Politics is everywhere. In this paper, I propose a simple model to demonstrate political behavior in human society.

Extends results of math-ph/0407067

Extends results of math-ph/0407067

Extends results of math-ph/0407067

This paper has been superseded by math-ph/0102032, "Bures geometry of the three-level quantum systems. II".

The goal of this note is to give an elementary and very short solution to equations of motion for the Kovalevskaya top. For this we use some results from original papers by Kovalevskay, Kötter and Weber and also the authors Lax representation (see math-ph/0111024)