Asymptotics and total integrals of the PI2\mathrm{P}_{\rm I}^{2} tritronqu\'{e}e solution and its Hamiltonian

We study the tritronqu\'{e}e solution $u(x,t)$ of the $\mathrm{P}_{\rm I}^{2}$ equation, the second member of the Painlev\'{e} I hierarchy. This solution is pole-free on the real line and has various applications in mathematical physics. We obtain a full asymptotic expansion of $u(x,t)$ as $x\to\pm \infty$, uniformly for the parameter $t$ in a large interval. Based on this result, we successfully derive the total integrals of $u(x,t)$ and the associated Hamiltonian.Comment: 23 pages, 3 figure

Tool Support for Testing Java Monitors

The Java programming language supports monitors. Monitor implementations, like other concurrent programs, are hard to test due to the inherent non-determinism. This paper presents the ConAn (Concurrency Analyser) tool for generating drivers for the testing of Java monitors. To obtain adequate controllability over the interactions between Java threads, the generated driver contains processes that are synchronized by a clock. The driver automatically executes the calls in the test sequence in the prescribed order and compares the outputs against the expected outputs specified in the test sequence. The method and tool are illustrated in detail on an asymmetric producer-consumer monitor, and their application to two other monitors is discussed