We present a (partial) historical summary of the mathematical analysis finite difference and volume methods, paying special attention to Lax–Richtmyer Lax–Wendroff theorems. then state consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates recent generalization flux notion designed cope with general discrete functions.

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...

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...

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

The water hammer phenomenon is the main problem in long-distance pipeline networks. MOC (Method of characteristics) and finite difference methods lead to severe constraints on mesh Courant number, while volume method second-order Godunov scheme has limited intermittent capture capability. These will produce numerical dissipation, affecting computational efficiency at low numbers. Based lax-Frie...

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...

The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears...