We give an extension of the two-component KP hierarchy by considering additional time variables. We obtain the linear 2× 2 system by taking into consideration the hierarchy through a reduction procedure. The Lax pair of the Schlesinger system and the sixth Painlevé equation is given from this linear system. A unified approach to treat the other Painlevé equations from the usual two-component KP...

The full Kostant–Toda hierarchy on a semisimple Lie algebra is system of Lax equations, in which the flows are determined by gradients Chevalley invariants. This paper concerned with even orthogonal algebra. By using Pfaffian matrix as one invariants, we construct an explicit form flow associated to this invariant. As main result, introduce extension Schur’s Q-functions time variables, and use ...

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...

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...

The activation of T cells and the initiation of an immune response is tightly controlled through the crosstalk of both positive and negative regulators. Two adaptors that function as negative regulators of T cell activation are adaptor in lymphocytes of unknown function X (ALX) and linker for activation of X cell (LAX). Previously, we showed that T cells from mice deficient in ALX and LAX displ...

The gauge-invariant description of zero-curvature representations of evolution equations is applied to the problem of how to distinguish the fake Lax pairs from the true Lax pairs. The main difference between the true Lax pairs and the fake ones is found in the structure of their cyclic bases. In this note, we use the gauge-invariant description of zero-curvature representations of evolution eq...

Lax Logic is an intuitionistic modal logic which has so far been investigated at the propositional level. It has shown itself to have applications in the formal veriication of hardware|a logical modality is used to capture and express the correctness of speciicationsùp to' behavioural constraints. A translation from Quantiied Lax Logic to a quantiied classical modal logic is presented which ena...