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This paper has been superseded by math-ph/0102032, "Bures geometry of the three-level quantum systems.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

The International Congress of Mathematicians (ICM), inaugurated in 1897, is the greatest effort of the mathematical community to strengthen international communication and connections across all mathematical fields. Meetings of the ICM have historically hosted some of the most prominent mathematicians of their time. Receiving an invitation to present a talk at an ICM signals the high international reputation of the recipient, and is akin to entering a `hall of fame for mathematics'. Women mathematicians attended the ICMs from the start. With the invitation of Laura Pisati to present a lecture in 1908 in Rome and the plenary talk of Emmy Noether in 1932 in Zurich, they entered the grand international stage of their field. At the congress in 2014 in Seoul, Maryam Mirzakhani became the first woman to be awarded the Fields Medal, the most prestigious award in mathematics. In this article, we dive into assorted data sources to follow the footprints of women among the ICM invited speakers, analyzing their demographics and topic distributions, and providing glimpses into their diverse biographies.

Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR), linked with CRISPR associated (CAS) genes, play a profound role in the interactions between phage and their bacterial hosts. It is now well understood that CRISPR-CAS systems can confer adaptive immunity against bacteriophage infections. However, the possibility of failure of CRISPR immunity may lead to a productive infection by the phage (cell lysis) or lysogeny. Recently, CRISPR-CAS genes have been implicated in changes to group behaviour, including biofilm formation, of the bacterium Pseudomonas aeruginosa when lysogenized. For lysogens with a CRISPR system, another recent experimental study suggests that bacteriophage re-infection of previously lysogenized bacteria may lead to cell death. Thus CRISPR immunity can have complex effects on phage-host-lysogen interactions, particularly in a biofilm. In this contribution, we develop and analyse a series of models to elucidate and disentangle these interactions. From a therapeutic standpoint, CRISPR immunity increases biofilm resistance to phage therapy. Our models predict that lysogens may be able to displace CRISPR-immune bacteria in a biofilm, and thus suggest strategies to eliminate phage resistant biofilms.