Monodromy approach to the scaling limits in the isomonodromy systems

The isomonodromy deformation method is applied to the scaling limits in the linear NxN matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves which describe the local behavior of the reduced versions for the relevant isomonodromy deformation equations. The approach is illustrated by the study of the algebraic curve associated to the n-large asymptotics in the sequence of the bi-orthogonal polynomials with cubic potentials.Comment: Latex, 15 pages, 1 figure; submitted to the proceedings of the conference NEEDS 2002; in compare to the original version, there are minor changes in the references and in the main body of the articl

Omniscience, the Incarnation, and Knowledge de se

A knowledge argument is offered that presents unique difficulties for Christians who wish to assert that God is essentially omniscient. The difficulties arise from the doctrine of the incarnation. Assuming that God the Son did not necessarily have to become incarnate, then God cannot necessarily have knowledge de se of the content of a non-divine mind. If this is right, then God’s epistemic powers are not fixed across possible worlds and God is not essentially omniscient. Some options for Christian theists are discussed, including rejecting traditional theism in favour of some version of pantheism or panentheism

Conservative constraint satisfaction re-revisited

Conservative constraint satisfaction problems (CSPs) constitute an important particular case of the general CSP, in which the allowed values of each variable can be restricted in an arbitrary way. Problems of this type are well studied for graph homomorphisms. A dichotomy theorem characterizing conservative CSPs solvable in polynomial time and proving that the remaining ones are NP-complete was proved by Bulatov in 2003. Its proof, however, is quite long and technical. A shorter proof of this result based on the absorbing subuniverses technique was suggested by Barto in 2011. In this paper we give a short elementary prove of the dichotomy theorem for the conservative CSP