Expressive Power in First Order Topology

A first order representation (fo.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions one f.o.r. is at least as expressive as another relative to a class of spaces and one class of spaces is definable in another relative to an f.o.r. , and prove some general statements. Following this we compare some well-known classes of spaces and first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of zero-sets are elementarily equivalent then their respective rings of bounded continuous real-valued functions satisfy the same positiveuniversal sentences. The proof of this uses the technique of constructing ultraproducts as direct limits of products in a category theoretic setting

On the topology of conformally compact Einstein 4-manifolds

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally compact Einstein 4-manifold is diffeomorphic to $B^4$ and its conformal infinity is diffeomorphic to $S^3$.Comment: 16 page

The mediation between participative leadership and employee exploratory innovation: Examining intermediate knowledge mechanisms

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.We examine mediation effects of coworker knowledge sharing and absorptive capacity on the participative leadership–employee exploratory innovation relationship in R&D units of Taiwanese technology firms. Deploying a time-lagged questionnaire method implemented over four business quarters, data is generated from 1600 paired samples (managers and employees) in R&D units of Taiwanese technology firms. The structural equation modeling results reveal that (1) participative leadership is positively related to employee exploratory innovation; (2) coworker knowledge and (3) absorptive capacity partially mediate the relationship between participative leadership and employee exploratory innovation independently; and, (4) coworker knowledge sharing in combination with absorptive capacity partially mediates this relationship. The results extend previous research on participative leadership and innovation by demonstrating that participative leadership is related to employee exploratory innovation (Lee and Meyer-Doyle, 2017; Mom et al., 2009).Results also confirm that participative leadership drives employee exploratory innovation through employee absorptive capacity. This reinforces the need highlighted by Lane et al. (2006) to investigate the role of absorptive capacity at the individual-level. Collectively, while participative leadership is important for employee exploratory innovation it is the knowledge mechanisms existing and interacting at the employee-level that are central to generating increased employee exploratory innovation from this leadership approach

Selling Australia as "clean and green"

"Green and clean" has been used as a key marketing tool to promote Australian products overseas. The rationale is that consumers are generally concerned about personal health and the environment and will choose, and pay price premiums, for products that are perceived to be clean (good for them) and green (good for the environment) over alternative products. But is Australia seen as clean and green? Is it really why people buy Australian? This paper attempts to investigate such questionsexport marketing, clean green image, Marketing,

Some Progress in Conformal Geometry

This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $\sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Optical nanofiber temperature monitoring via double heterodyne detection

Tapered optical fibers (nanofibers) whose diameters are smaller than the optical wavelength are very fragile and can be easily destroyed if excessively heated by energy dissipated from the transmitted light. We present a technique for monitoring the nanofiber temperature using two-stage heterodyne detection. The phase of the heterodyne output signal is determined by that of the transmitted optical field, which, in turn, depends on the temperature through the refractive index. From the phase data, by numerically solving the heat exchange equations, the temperature distribution along the nanofiber is determined. The technique is applied to the controlled heating of the nanofiber by a laser in order to remove rubidium atoms adsorbed on its surface that substantially degrade its transmission. Almost 90% of the nanofiber's original transmission is recovered