The D7 degeneration of the Painleve-III equation has solutions that are rational functions $x^{1/3}$ for certain parameter values. We apply isomonodromy method to obtain a Riemann-Hilbert representation these solutions. demonstrate utility this by analyzing rigorously behavior in large limit.

Many alternative formulations of Einstein’s evolution have lately been examined, in an effort to discover one which yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations, we instead develop analytic tools to discover which formulations are particularly ill-behaved. Specifically, we examine the growth of approximate (geometric...

In this paper we propose and study models of long-term Human Immunodeficiency Virus (HIV-1) infection. Our aim is to identify model mechanisms that allow to explain the trends observed in clinical measurements of the number of CD4+ Tcells and virus throughout the long-term HIV-1 infection, from the acute phase until the onset of AIDS. To achieve our goal we apply some standard methods of modeli...

In this paper, we classify all values of the parameters α, β, γ and δ of the Painlevé VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlevé VI equation.

Therefore 0 + l)* s P + 1 mod p\ Now put t=<r + vp, (0 < c r < p 1). Then ^ = cr̂ , 0 + l)*' s (er + 1)*" mod p. Therefore (er + l)* = a + 1 mod p, (0 < a < p 1). This is relation (7) of my previous note; from this follows (1) as in the earlier treatment. Hence (1) is satisfied by all primes of the form Qn + 1. Therefore the test can be useful only when the exponent p is 3 or is of the form 6n — 1.

The 120-year old so-called Painlevé paradox involves the loss of determinism in models of planar rigid bodies in point contact with a rigid surface, subject to Coulomb-like dry friction. The phenomenon occurs due to coupling between normal and rotational degrees-of-freedom such that the effective normal force becomes attractive rather than repulsive. Despite a rich literature, the forward evolu...

Scaling models of random N x N hermitian matrices and passing to the limit N -» oo leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order. For the Gaussian Unitary Ensemble, and for many others' as well, the kernel one obtains by scaling in the "bulk" of the spectrum is the "sine kernel" — — . Rescal...