Let M be a closed oriented 3-manifold which can be triangulated with N simplices. We prove that any map from M to a genus 2 surface has Hopf invariant at most C . Let X be a closed oriented hyperbolic 3-manifold with injectivity radius less than ǫ at one point. If there is a degree non-zero map from M to X, then we prove that ǫ is at least C . In the 1970’s, Thurston invented simplex straighten...

We show that the recipe for computing expansions [Formula: see text] and of outgoing ingoing null geodesics normal to a surface admits covariance group with nonconstant scalar text], corresponding mapping text]. Under this mapping, product is invariant, thus marginal computed from vanishing which used define apparent horizon, invariant. This naturally appears in comparing different choices coor...

let a be a bounded linear operator on a banach space x. we investigate the conditions of existing rank-one operator b such that i+f(a)b is invertible for every analytic function f on sigma(a). also we compare the invariant subspaces of f(a)b and b. this work is motivated by an operator method on the banach space ell^2 for solving some pdes which is extended to general operator space under some ...

background: invariant natural killer cells (inkt) are an important immunoregulatory t cell subset. currently several flow cytometry-based approaches exist for the identifi-cation of inkt cells, which rely on using the 6b11 monoclonal antibody or a combina-tion of anti-vα24 and anti-vβ11 antibodies. objective: the aim of this study was to compare the ability of two flow cytometry-based methods f...