In [8], I. M. Krichever invented the space of matrices parametrizing the cotangent bundle of moduli space of stable vector bundles over a compact Riemann surface, which is named as the Hitchin system after the investigation [5]. We study a necessary and sufficient condition for the linearity of flows on the space of Krichever-Lax matrices in a Lax representation in terms of cohomological classe...

Lax representation in terms of 2 × 2 matrices is constructed for separable multiply–periodic systems splitting on two tori. Hyperelliptic Kleinian functions and their reduction to elliptic functions are used. Introduction. Completely integrable systems with two degree of freedoms and with dynamics splitting on two tori have been largely investigated during the past years as examples of separabl...

We investigate a peculiar intuitionistic modal logic, called Propositional Lax Logic (PLL), which has promising applications to the formal veri cation of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints | a central notion in hardware veri cation | as a logical modality. As a modal logic it is special since it features a single modal...

“A`−1” stands for the A`−1 root system that underlies this model. Similarly, an elliptic Calogero-Moser system can be defined for each irreducible (but not necessary reduced) root system. Furthermore, for non-simply laced root systems, a kind of variants called “twisted model” and “extended twisted models” are also known. Those elliptic Calogero-Moser systems are known to possess an isospectral...

four explicit finite difference schemes, including lax-friedrichs, nessyahu-tadmor, lax-wendroff and lax-wendroff with a nonlinear filter are applied to solve water hammer equations. the schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. the computational results are compared with those of the method of characteristics (moc), a...