Every ring type spanner in a wedge is spherical

A ring type spanner in a wedge is a compact embedded annular surface of constant mean curvature which meets the planes of the wedge in constant angles along its boundary. In this paper we show that every ring type spanner in a wedge is spherical.     

The semigroup of values of a one-dimensional local ring with two minimal primes

In this paper, we give a new simple algebraic proof of the involutivity of the characteristic variety after Gabber, which is one of the most important results of D-module theory.     

Local cohomology over homogeneous rings with one-dimensional local base ring

Let be a homogeneous Noetherian ring with local base ring and let be a finitely generated graded -module. Let be the -th local cohomology module of with respect to 0}R_n$">. If , the -modules , and are Artinian for all . As a consequence, much can be said on the asymptotic behaviour of the -modules for .

     

The orthogonal group over a local ring is 4-reflectional

LetV be a free finite-dimensional module over a commutative local ringR where 2 is a unit. Letf:V × V R be a regular symmetric bilinear form. We prove that every element of the orthogonal group O(V) is a product of four involutions in O(V).     

On modules whose endomorphism ring is local

The paper is a study of modules with a local endomorphism ring. We consider decompositions of modules and give a simple proof of Azumaya’s theorem. We also define an equivalence relation on the family of direct summands of a module, and show that the properties of a decomposition are closely related to the properties of this equivalence relation. Supported by the Norwegian Research Council for Science and the Humanities.     

Every Proposition is a Counterfactual

I present and discuss two logical results. The first shows that a non-trivial counterfactual analysis exists for any contingent proposition that is false in at least two possible worlds. The second result identifies a set of conditions that are individually necessary and jointly sufficient for the success of a counterfactual analysis. I use these results to shed light on the question whether disposition ascribing propositions can be analyzed as Stalnaker-Lewis conditional propositions. The answer is that they can, but, in order for a counterfactual analysis to work, the antecedent and consequent must be related in a particular way, and David Lewis’s Time’s Arrow constraints on comparative world similarity must be relaxed. The upshot is that counterfactual analyses are easy to come by, in principle, even if not in practice. In that sense, it’s easy to be iffy.     

Every surface is a leaf

FOR EACH integer n≥3, there are open, connected n-manifolds that cannot be realized as leaves in any compact, C⁰-foliated (n+1)-manifold [8] (for the C² case, cf. [10]). For n=2, the corresponding question has been thought to be hard. Here we give a proof, announced in [7], that all open surfaces are realizable. This answers a basic question posed in [14].In the following, L denotes an open, connected 2-manifold, M a closed, connected 3-manifold.     

Every Finite Topology is Generated by a Partial Pseudometric

Given any preorder on a finite set , we present an algorithm to construct a partial pseudometric on which generates in the sense that if and only if . The specialization topology generated by agrees with the topology generated by the partial pseudometric -balls, and consequently any topology on is generated by a partial pseudometric.     

Every Projective Variety is a Quiver Grassmannian

The claim in the title is proved.     

Every connected graph is a query graph

Let V be a set of bit strings of length k, i.e., V ? {0, 1}^k. The query graph Q(V) is defined as follows: the vertices of Q(V) are the elements of V, and {ū, v?} is an edge of Q(V) if and only if no other w? ? V agrees with ū in all the positions in which v? does. If V represents the set of keys for a statistical data base in which queries that match only one key are rejected, then the security of the individual data is related to the graph Q(V). Ernst Leiss showed that graphs belonging to any of several classes could be represented as query graphs and asked whether any connected graph could be so represented. We answer his question in the affirmative by making use of a spanning tree with special properties.     

An answer to Hirasaka and Muzychuk: Every p-Schur ring over Cp3 is Schurian

In Hirasaka and Muzychuk [An elementary abelian group of rank 4 is a CI-group, J. Combin. Theory Ser. A 94 (2) (2001) 339–362] the authors, in their analysis on Schur rings, pointed out that it is not known whether there exists a non-Schurian p-Schur ring over an elementary abelian p-group of rank 3. In this paper we prove that every p-Schur ring over an elementary abelian p-group of rank 3 is in fact Schurian.     

Every point is critical

We show that, for any compact Alexandrov surface S$S$ (without boundary) and any point y$y$ in S$S$, there exists a point x$x$ in S$S$ for which y$y$ is a critical point. Moreover, we prove that uniqueness characterizes the surfaces homeomorphic to the sphere among smooth orientable surfaces.