Let M and N be smooth manifolds, where M ⊂ N and dim(N)− dim(M) ≥ 3. A disjunction lemma for embeddings proved recently by Goodwillie leads to a calculation up to extension problems of the base point component of the space of smooth embeddings of M in N . This is mostly in terms of imm(M,N), the space of smooth immersions, which is well understood, and embedding spaces emb(S,N) for finite subse...

Quasiminimality In this chapter we introduce Zilber’s notion [Zil05] of an abstract quasiminimalexcellent class and prove Theorem 2.23: Lω1,ω-definable quasiminimal-excellent classes satisfying the countable closure condition are categorical in all powers. In the next chapter we expound Zilber’s simplest concrete algebraic example. In Chapter 25, we will place this example in the context of She...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...

Amplified fragment length polymorphism (AFLP) analysis was conducted on the wabisuke camellia and its relative species. Genetic identified among ‘Uraku’ camellia, offspring ‘Tosa-uraku’ Camellia japonica, whereas two accessions of old showed monomorphism in all fragments. The results suggested that trees are asexually-propagated clonal strains. genetic distance between cultivars Chinese camelli...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...