We study irreducibility of families of degree 4 Del Pezzo surface fibrations over curves.

In this paper, we study irreducibility in RNA structures. By RNA structure, we mean RNA secondary as well as RNA pseudoknot structures as abstract contact structures. We give an analysis contrasting random and minimum free energy (mfe) configurations and secondary versus pseudoknots structures. In the process, we compute various distributions: the numbers of irreducible substructures and their ...

Given a polynomial P in several variables over an algebraically closed field, we show that except in some special cases that we fully describe, if one coefficient is allowed to vary, then the polynomial is irreducible for all but at most deg(P ) − 1 values of the coefficient. We more generally handle the situation where several specified coefficients vary.

We find necessary and sufficient conditions of irreducibility of vacuum modules over affine Lie algebras and superalgebras. From this we derive conditions of simplicity of minimal W -algebras. Moreover, in the case of the Virasoro and Neveu–Schwarz algebras we obtain explicit formulas for the vacuum determinants. © 2006 Elsevier Inc. All rights reserved.

How are claims about what people ought to do related to claims about what ought to be the case? That is, how are claims about of personal obligation, of the form s ought to φ, related to claims about impersonal obligation, of the form it ought to be the case that p? Many philosophers have held that the former type of claim can be reduced to the latter. In particular, they have held a view known...