In this article, we prove that we can introduce a small ~ parameter in the six Painlevé equations through their corresponding Lax pairs and Hamiltonian formulations. Moreover, we prove that these ~-deformed Lax pairs satisfy the Topological Type property proposed by Bergère, Borot and Eynard for any generic choice of the monodromy parameters. Consequently we show that one can reconstruct the fo...

The Lax-Wendroff theorem stipulates that a discretely conservative operator is necessary to accurately capture discontinuities. The discrete operator, however, need not be derived from the divergence form of the continuous equations. Indeed, conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm ske...

BACKGROUND Quantification of left ventricular (LV) volume from cardiovascular magnetic resonance images relies on subjective and often challenging selection of short-axis (SAX) slices. We hypothesized that this could be solved by defining mitral annular (MA) plane and apex in long-axis (LAX) views, which could be combined with automated LV volume analysis that does not rely on manual tracing of...

The inventory of 15 German full vowels realized by speakers of Northern Standard German (NSG) and Austrian Standard German (ASG) is investigated acoustically. The vowels were produced in phonotactically regular nonsense words (bVp and dVt environments) embedded in a sentence frame. The analyses revealed that the main difference between both varieties can be found in a different acoustic realiza...

We combine two research directions of the past decade, namely the development of a lax-algebraic framework for categories of interest to topologists and analysts, and the exploration of key topological concepts, like separation and compactness, in an abstract category which comes equipped with an axiomatic notion “closed” or “proper” map. Hence, we present various candidates for such notions in...

We present a method for numerical wave propagation in a heterogeneous medium. The medium is defined in terms of an extended scatterer or target which is surrounded by many small scatterers. By extending the classic Foldy-Lax formulation we developed an efficient algorithm for numerical wave propagation in two dimension. In the method that we set forth multiple scattering among the point scatter...

We study the C2 Ruijsenaars-Schneider(RS) models with interaction potentials of rational and trigonometric types. The Lax pairs for these models are constructed and the involutive Hamiltonians are also given. Taking nonrelativistic limit, we obtain the Lax pair of C2 Calogero-Moser model. PACS: 02.20.+b, 11.10.Lm, 03.80.+r

We generalize the work by Sobociński on relational presheaves and their connection with weak (bi)simulation for labelled transistion systems to a coalgebraic setting. We show that the coalgebraic notion of saturation studied in our previous work can be expressed in the language of lax functors in terms of existence of a certain adjunction between categories of lax functors. This observation all...