Let u be a weak solution of the initial boundary value problem for the semilinear parabolic system of order 2m : u′(t) + Au(t) + f(t, ., u, ...,∇u) = 0. Let f satisfy controllable growth conditions. Then u is smooth. This result is proved by a kind of continuity method, where the time t is the parameter of continuity. Classification: 35D10, 35K60, 35K50.

An analysis is given of ∗-representations of rank 2 single vertex graphs. We develop dilation theory for the nonselfadjoint algebras Aθ and Au which are associated with the commutation relation permutation θ of a 2 graph and, more generally, with commutation relations determined by a unitary matrix u in Mm(C)⊗Mn(C). We show that a defect free row contractive representation has a unique minimal ...

A method is given for a study of a nonlinear evolution equation for finding “slow” invariant manifolds. The method is studied for the evolution problem u̇=−Au + Au ,u / u ,u u, u 0 =u0, where A is a linear, self-adjoint, possibly unbounded operator in a Hilbert space. Global existence and uniqueness of the solution to this problem are proven. Asymptotic behavior of the solution as t→ is studied....

The purpose of this note is to show that there exist non-trivial families of algebraic varieties for which all the fibers above rational points (or even above points of odd degree) are torsors of abelian varieties representing nonzero elements of their Shafarevich-Tate groups. More precisely, we will prove the following theorem. (Throughout this paper, P unadorned denotes PQ.) Theorem 1. There ...

Comparing trees with regard to their topology is in itself an interesting theoretical problem in computer science, and furthermore researchers working in the interdisciplinary field of computational biology need tools to compare phylogenetic trees, i.e. trees that describe the relation of species according to evolutionary history. Different methods and different information can result in differ...

Extending the idea of our previous algorithm [17, 18] we developed a new sequential quartet-based phylogenetic tree construction method. This new algorithm reconstructs the phylogenetic tree iteratively by examining at each merge step every possible super-quartet which is formed by four subtrees instead of simple quartet in our previous algorithm. Because our new algorithm evaluates super-quart...

A collection P of phylogenetic trees is compatible if there exists a single phylogenetic tree that displays each of the trees in P. Despite its computational difficulty, determining the compatibility of P is a fundamental task in evolutionary biology. Characterizations in terms of chordal graphs have been previously given for this problem as well as for the closely-related problems of (i) deter...

Classical clustering algorithms as well as intrinsic evaluation criteria impose predefined structures onto a data set. If the structures do not fit the data, the clustering will fail and the evaluation criteria will lead to erroneous conclusions. Recently, the abstract U-matrix has been defined for emergent self-organizing maps (ESOM). In this work the abstract forms of the Pand the U* are defi...