We complete a study of the splitting/non-splitting properties of the enumeration degrees below 0′e by proving an analog of Harrington’s non-splitting theorem for the Σ2 enumeration degrees. We show how non-splitting techniques known from the study of the c.e. Turing degrees can be adapted to the enumeration degrees.

Moriah and Schultens have demonstrated that an irreducible Heegaard splitting of an orientable Seifert fibered space over an orientable base surface is either vertical or horizontal. In this paper it is determined precisely which vertical and horizontal splittings are irreducible. Let M be a Seifert fibered space which admits a horizontal splitting at the fiber f . If the genus of the horizonta...

We present a splitting moving mesh method for multi-dimensional reaction-diffusion problems with nonlinear forcing terms over rectangular domains. The structure of the adaptive algorithm is an elegant combination of an operator splitting and one-dimensional moving mesh. It is motivated by the nature of splitting method, which splits a multi-dimensional problems into a few one-dimensional proble...

System splitting problem, also known as controlled system separation problem, is to determine the proper splitting points for splitting the entire power network into islands when island operation of system is unavoidable. By “proper” we mean that the splitting strategies should guarantee both the power balance and satisfaction to capacity constraints of transmission lines and other facilities i...

We find exact solutions of the string equations of motion and constraints describing the classical splitting of a string into two. We show that for the same Cauchy data, the strings that split have smaller action than the string without splitting. This phenomenon is already present in flat space-time. The mass, energy and momentum carried out by the strings are computed. We show that the splitt...

In this paper we consider the solutions of linear systems of saddle point problems‎. ‎By using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method‎.

S U M M A R Y Measurements of the splitting or birefringence of seismic shear waves constitute a powerful and popular technique for characterizing azimuthal anisotropy in the upper mantle. The increasing availability of data sets from dense broad-band seismic arrays has driven interest in the development of techniques for the tomographic inversion of shear wave splitting data and in comparing s...

Splitting a tree is defined as removing all edges of a chain and disconnecting one from the other edges incident with that chain. Splitting a forest is simultaneously splitting each of its non-trivial trees. The splitting number a(T) of a tree T is the minimum number of successive forest splittings which lead to deletion of all of T’s edges. An O(N) algorithm is proposed to get an upper bound c...

Besides conjoining an assertion into the common ground (Stalnaker 1978), another kind of move that we often propose and accept in discourse is to change our notion of what is a thing and what is the same thing. For example, depending on how a conversation goes, in the middle of it we might start treating ‘a’ and ‘A’ as different letters, while preserving our common knowledge that it is a vowel....

A common presupposition in the concepts literature is that concepts constitute a singular natural kind. If, on the contrary, concepts split into more than one kind, this literature needs to be recast in terms of other kinds of mental representation. We offer two new arguments that concepts, in fact, divide into different kinds: (a) concepts split because different kinds of mental representation...