Detecting codimension one manifold factors with topographical techniques

We prove recognition theorems for codimension one manifold factors of dimension n?4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X×R is a manifold in the cases when X is a resolvable generalized manifold of finite dimension n?3 with either: (1) the crinkled ribbons property; (2) the twisted crinkled ribbons property and the disjoint point disk property; or (3) the fuzzy ribbons property.     

On character sums of binary quadratic forms

We establish character sum bounds of the form

     

A new approach to spectral approximation

A new technique for approximating eigenvalues and eigenvectors of a self-adjoint operator is presented. The method does not incur spectral pollution, uses trial spaces from the form domain, has a self-adjoint algorithm, and exhibits superconvergence.     

Multivariate Failure Times Regression with a Continuous Auxiliary Covariate

How to take advantage of the available auxiliary covariate information when the primary covariate of interest is not measured is a frequently encountered question in biomedical study. In this paper, we consider the multivariate failure times regression analysis in which the primary covariate is assessed only in a validation set, but a continuous auxiliary covariate for it is available for all subjects in the study cohort. Under the frame of marginal hazard model, we propose to estimate the induced relative risk function in the non-validation set through kernel smoothing method and then obtain an estimated pseudo-partial likelihood function. The proposed estimator which maximizes the estimated pseudo-partial likelihood is shown to be consistent and asymptotically normal. We also give an estimator of the marginal cumulative baseline hazard function. Simulation studies are conducted to evaluate the finite sample performance of our proposed estimator. The proposed method is illustrated by analyzing a heart disease data from the Study of Left Ventricular Dysfunction (SOLVD).     

Inference on periodograms of infinite dimensional discrete time periodically correlated processes

In this work we shall consider two classes of weakly second-order periodically correlated and strongly second-order periodically correlated processes with values in separable Hilbert spaces. The periodogram for these processes is introduced and its statistical properties are studied. In particular, it is proved that the periodogram is asymptotically unbiased for the spectral density of the processes, where the type of the convergence is fully specified.     

Central extensions of gerbes

We introduce the notion of central extension of gerbes on a topological space X. We show that there are obstruction classes to lifting objects and isomorphisms in a central extension. We also discuss pronilpotent gerbes. These results are used in the paper [15] by A. Yekutieli to study twisted deformation quantization on algebraic varieties.     

The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces

This article gives a natural decomposition of the suspension of generalized moment-angle complexes or partial product spaces which arise as polyhedral product functors described below. The geometrical decomposition presented here provides structure for the stable homotopy type of these spaces including spaces appearing in work of Goresky-MacPherson concerning complements of certain subspace arrangements, as well as Davis-Januszkiewicz and Buchstaber-Panov concerning moment-angle complexes. Since the stable decompositions here are geometric, they provide corresponding homological decompositions for generalized moment-angle complexes for any homology theory.     

Which compacta are noncommutative ARs?

We give a short answer to the question in the title: dendrits. Precisely we show that the C^*-algebra C(X) of all complex-valued continuous functions on a compactum X is projective in the category C¹ of all (not necessarily commutative) unital C^*-algebras if and only if X is an absolute retract of dimension dimX?1 or, equivalently, that X is a dendrit.     

Any chart with at most one crossing is a ribbon chart

In this paper, we shall show the one written in the title.