Mirror principle is a general method developed in [LLY1]-[LLY4] to compute characteristic classes and characteristic numbers on moduli spaces of stable maps in terms of hypergeometric type series. The counting of the numbers of curves in Calabi-Yau manifolds from mirror symmetry corresponds to the computation of Euler numbers. This principle computes quite general Hirzebruch multiplicative clas...

We show that the notion of asymptotic lift generalizes naturally to normal positive maps φ : M → M acting on von Neumann algebras M . We focus on cases in which the domain of the asymptotic lift can be embedded as an operator subsystem M∞ ⊆ M , and characterize when M∞ is a Jordan subalgebra of M in terms of the asymptotic multiplicative properties of φ.

We investigate the multiplicative loops of finite semifields. We show that the group generated by the left and right multiplication maps contains the special linear group. This result solves a BCC18 problem of A. Drápal. Moreover, we study the question of whether the bigMathieu groups can occur asmultiplication groups of loops. © 2009 Elsevier Ltd. All rights reserved.

We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some connectome graphs are described.

In this paper we describe the form of those continuous multiplicative maps on B(H) (H being a separable complex Hilbert space of dimension not less than 3) which preserve the rank, or the corank. Furthermore, we characterize those continuous *-semigroup endomorphisms of B(H) which are spectrum non-increasing.

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Abstract In finite group theory, chief factors play an important and well-understood role in the structure theory. We here develop a theory of for Polish groups. development this we prove version Schreier refinement theorem. also trichotomy topologically characteristically simple The requires two independently interesting lines study. First consider injective, continuous homomorphisms with dens...