989 research outputs found
Large subsets of discrete hypersurfaces in contain arbitrarily many collinear points
In 1977 L.T. Ramsey showed that any sequence in with bounded
gaps contains arbitrarily many collinear points. Thereafter, in 1980, C.
Pomerance provided a density version of this result, relaxing the condition on
the sequence from having bounded gaps to having gaps bounded on average. We
give a higher dimensional generalization of these results. Our main theorem is
the following.
Theorem: Let , let be a
Lipschitz map and let have positive upper Banach
density. Then contains arbitrarily many collinear points.
Note that Pomerance's theorem corresponds to the special case . In our
proof, we transfer the problem from a discrete to a continuous setting,
allowing us to take advantage of analytic and measure theoretic tools such as
Rademacher's theorem.Comment: 16 pages, small part of the argument clarified in light of
suggestions from the refere
Microdeflectometry - a novel tool to acquire 3D microtopography with nanometer height resolution
We introduce "microdeflectometry", a novel technique for measuring the
microtopography of specular surfaces. The primary data is the local slope of
the surface under test. Measuring the slope instead of the height implies high
information efficiency and extreme sensitivity to local shape irregularities.
The lateral resolution can be better than one micron whereas the resulting
height resolution is in the range of one nanometer. Microdeflectometry can be
supplemented by methods to expand the depth of field, with the potential to
provide quantitative 3D imaging with SEM-like features.Comment: 3 pages, 11 figures, latex, zip-file, accepted for publication at
Optics Letter
A meta-analysis on the effects of IT capability toward agility and performance: New directions for information systems research
Information technology (IT) capability is an organizational capability that enables organizations to acquire, deploy, combine, and reconfigure IT resources. As such, it is often investigated in conjunction with organizational agilityâan organizationâs ability to sense and respond to changesâand organizational performance. Studies on IT capability distinguish between reactive and proactive IT capability and identify varying effects in relation to agility and performance. While reactive IT capability supports and enhances work processes, proactive IT capability supports and enhances business strategies. In the light of the mixed results of prior research, we conduct a meta-analytical investigation into the varying effects that reactive and proactive IT capability have on organizational agility and organizational performance. We identified 6.436 studies from multiple sources that we systematically reduced to include 72 empirical studies in our analysis. Contrary to previous results and widely held opinion, our meta-analysis neither finds support for differences in effect size between reactive (r(+) = 0.39, k = 34, 95% Confidence Interval (CI) [0.34, 0.44]) and proactive IT capability (r(+) = 0.38, k = 21, 95% CI [0.31, 0.45]) toward agility (z = 0.68, p = 0.25), nor from reactive IT capability (r(+) = 0.31, k = 43, 95% CI [0.26, 0.37]) and proactive IT capability (r(+) = 0.33, k = 25, 95% CI [0.27, 0.40]) toward performance (z = 1.11, p = 0.13). Given the importance of IT capability, we discuss possible explanations and propose four areas for future research: latency, sequence, configurational, and theoretical multiplicity of IT capability
Photon counting intensity interferometry in the blue at a 0.5 m telescope
Intensity interferometry is a re-emerging interferometry tool that alleviates
some of the challenges of amplitude interferometry at the cost of reduced
sensitivity. We demonstrate the feasibility of intensity interferometry with
fast single photon counting detectors at small telescopes by utilising a
telescope of diameter of merely \,m. The entire measurement setup,
including collimation, optical filtering, and two single photon detectors, is
attached directly to the telescope without the use of optical fibres,
facilitated by the large area of our single photon detectors. For digitisation
and timing, we utilise a Time-To-Amplitude-Converter. Observing Lyrae
(Vega) for a total exposure time of \,h over the course of six nights, an
auto-correlation signal with a contrast of and a
coherence time of ps at a SNR of 2.8 is measured. The result
fits well to preceding laboratory tests as well as expectations calculated from
the optical and electronic characteristics of our measurement setup. This
measurement, to our knowledge, constitutes the first time that a bunching
signal with starlight was measured in the B band with single photon counting
detectors. Simultaneously, this is to date the stellar intensity interferometry
measurement utilising the smallest telescope. Our successful measurement shows
that intensity interferometry can be adopted not only at large scale
facilities, but also at readily available and inexpensive smaller telescopes
A proof of a sumset conjecture of Erd\H{o}s
In this paper we show that every set with positive
density contains for some pair of infinite subsets of ,
settling a conjecture of Erd\H{o}s. The proof features two different
decompositions of an arbitrary bounded sequence into a structured component and
a pseudo-random component. Our methods are quite general, allowing us to prove
a version of this conjecture for countable amenable groups.Comment: 54 pages. Corrected proof of Theorem 3.22 and added Example 3.27
Keywords: sum sets, almost periodic functions, ultrafilter
Lines and Conics in a Family of Quartic Surfaces
42 pagesThis thesis is primarily concerned with the fact that the general quartic surface does not contain a line or a conic section. More formally, the set of quartic surfaces containing lines or conic sections has measure zero.
This result follows from an important result in algebraic geometry, the Noether-Lefschetz theo-rem; however, this paper will use elemenary techniques in algebra and analysis to come to the same conclusion. In addition, this paper will introduce the idea of curves, surfaces, and their parameter spaces
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