On summability of pairs of convolution sequences of probability measures on locally compact semigroups

In this paper we study the problem of convergence in the weak and the vague topology of the sequence

On Strong Uniform Distribution II

 Let ? be a class of real valued integrable functions on [0,1). We will call a strictly increasing sequence of natural numbers an sequence if for every f in ? we have

Independent Sets In Association Schemes

Let X be k-regular graph on v vertices and let τ denote the least eigenvalue of its adjacency matrix A(X). If α(X) denotes the maximum size of an independent set in X, we have the following well known bound:

Isomorphic factorizations VIII: Bisectable trees

A tree is called even if its line set can be partitioned into two isomorphic subforests; it is bisectable if these forests are trees. The problem of deciding whether a given tree is even is known (Graham and Robinson) to be NP-hard. That for bisectability is now shown to have a polynomial time algorithm. This result is contained in the proof of a theorem which shows that if a treeS is bisectable then there is a unique treeT that accomplishes the bipartition. With the help of the uniqueness ofT and the observation that the bisection ofS into two copies ofT is unique up to isomorphism, we enumerate bisectable trees. Visiting Professor, University of Newcastle, 1976 and 1977 when this work was begun. Visiting Scholar, University of Michigan, 1981–82 on leave from Newcastle University (Australia) when this work was completed. The research was supported by grants from the Australian Research Grants Commission. The computing reported herein was performed by A. Nymeyer.     

Optimal Edge-Colourings for a Class of Planar Multigraphs

  Let G be a multigraph containing no minor isomorphic to or (where denotes without one of its edges). We show that the chromatic index of G is given by , where is the maximum valency of G and is defined as

Calculus of functors,operad formality,and rational homology of embedding spaces

Let M be a smooth manifold and V a Euclidean space. Let [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V) be the homotopy fiber of the map Emb(M,V) → Imm(M,V). This paper is about the rational homology of [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V). We study it by applying embedding calculus and orthogonal calculus to the bifunctor (M,V)↦ HQ ∧ [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V)₊. Our main theorem states that if

Finite Proper Covers in a Class of Finite Semigroups with Commuting Idempotents

   Abstract. Weakly left ample semigroups are a class of semigroups that are (2,1) -subalgebras of semigroups of partial transformations, where the unary operation takes a transformation α to the identity map in the domain of α . It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroup

Almost Periodic Compactifications of Semidirect Products of Flows

   Abstract. Let

Boundaries and complements of infinite- dimensional manifolds in the model space

Let M be a manifold modeled on a locally convex linear metric space E≌E^ω (or ≌E^ω_f and N a Z-submanifold of M. Then N is collared in M. In this paper, we study the following problem [1, 3]: Under what conditions can M be embedded in E so that N is the topological boundary of M in E? We gain a more mild sufficient condition than the previous papers [7, 8] and a necessary and sufficient condition in the case M has the homotopy type of Sⁿ (and each component of N is simply connected if n?2) and in the case N has the homotopy type of Sⁿ (n?2). Also we obtain a necessary and sufficient condition under which M can be embedded in E so that bd M = N and cl(E\M) has the homotopy type of Sⁿ (we assume that M and N are simply connected if n ? 2).     

Maximum andk-th maximal spanning trees of a weighted graph

LetA be a maximum spanning tree andP be an arbitrary spanning tree of a connected weighted graphG. Then we prove that there exists a bijectionψ fromA/P intoP/A such that for any edgea∈A/P, (P/ψ(a)) ∪a is a spanning tree ofG whose weight is greater than or equal to that ofP. We apply this theorem to some problems concerning spanning trees of a weighted graph.     

Packing random rectangles

A random rectangle is the product of two independent random intervals, each being the interval between two random points drawn independently and uniformly from [0,1]. We prove that te number C _n of items in a maximum cardinality disjoint subset of n random rectangles satisfies

Convergence of the method of chords for solving generalized equations

In this article, we study an iterative procedure of the following form

Some remarks on multiplication ideals,ii

Let R bea commutative ring with identity. An R-module (ideal of R) A is called a multiplication module (ideal) if for each submodule N of A there exists an ideal I of R with N = I A. We give several characterizations of multiplication modules. Using the method of idealization we show how to reduce questions concerning multiplication modules to multiplication ideals. For example, we show that if S is a commutative R-algebra and ψ: M→an R-module homomorphism where M is a multiplication R-module and N is an S-module, then Sψ(M) is a multiplication S-module.     

A lower bound for the recognition of digraph properties

The complexity of a digraph property is the number of entries of the adjacency matrix which must be examined by a decision tree algorithm to recognize the property in the worst case, Aanderaa and Rosenberg conjectured that there is a constant such that every digraph property which is monotone (not destroyed by the deletion of edges) and nontrivial (holds for some but not all digraphs) has complexity at leastv ² wherev is the number of nodes in the digraph. This conjecture was proved by Rivest and Vuillemin and a lower bound ofv ²/4–o(v ²) was subsequently found by Kahn, Saks, and Sturtevant. Here we show a lower bound ofv ²/2–o(v ²). We also prove that a certain class of monotone, nontrivial bipartite digraph properties is evasive (requires that every entry in the adjacency matrix be examined in the worst case).     

Constructing a 3-tree for a 3-connected matroid

In an earlier paper with Whittle, we showed that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid M. The purpose of this paper is to give a polynomial-time algorithm for constructing such a tree for M.     

Algebraic representation of mappings between submodule lattices

We show that under certain weak conditions on the module _R M, every mapping

A note on localizations of mapping spaces

We show that if A is a simply connected, finite, pointed CW-complex, then the mapping spaces Map_*(A,X) are preserved by the localization functors only if A has the rational homotopy type of a wedge of spheres V _l S ^k .     

On a Variation of Schur Numbers

 For every m≥3, let n=R (L ₃ (m)) be the least integer such that for every 2-coloring of the set S={1, 2, …, n}, there exists in S a monochromatic solution to the following system.?