Factorization of numbers with Gauss sums: I. Mathematical background

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.Comment: 21 pages, 8 figure

Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series: (i) a two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) a chirped one-photon transition in a two-level atom with a periodically modulated excited state, and (iii) a linearly chirped one-photon transition driven by a sequence of ultrashort pulses. For each of these quantum systems we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.Comment: 22 pages, 7 figure

A Membrane Approach to CO2 Capture

For the past eight years, Membrane Technology and Research, Inc. (MTR) sponsored by the U.S. Department of Energy, has been developing membrane technology to capture CO2 from power plant flue gas. A 20 ton/day test system has been built and operated at two field sites. The technology is moving to the 200 ton/day (10 MWe) demonstration scale. A block diagram of the MTR process is shown in Figure 1. One innovation of this process is the use of a two-step membrane design where the second step uses a membrane operating with air sweep to selectively recycle CO2 to the boiler. The use of combustion air to provide driving force for CO2 separation significantly reduces the energy cost. Because the air to the boiler already contains CO2, the CO2 concentration in the flue gas leaving the boiler increases from 13% CO2 to as much as 20% CO2. The removal rate required by the first step membrane is then reduced and the concentration of CO2 in the membrane permeate is increase to the 60 to 75% range. Please click Additional Files below to see the full abstract

Gauss sum factorization with cold atoms

We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193.Comment: 4 pages, 5 figure

New factorization algorithm based on a continuous representation of truncated Gauss sums

In this paper, we will describe a new factorization algorithm based on the continuous representation of Gauss sums, generalizable to orders j>2. Such an algorithm allows one, for the first time, to find all the factors of a number N in a single run without precalculating the ratio N/l, where l are all the possible trial factors. Continuous truncated exponential sums turn out to be a powerful tool for distinguishing factors from non-factors (we also suggest, with regard to this topic, to read an interesting paper by S. Woelk et al. also published in this issue [Woelk, Feiler, Schleich, J. Mod. Opt. in press]) and factorizing different numbers at the same time. We will also describe two possible M-path optical interferometers, which can be used to experimentally realize this algorithm: a liquid crystal grating and a generalized symmetric Michelson interferometer.Comment: 8 pages, 5 figure

Quantum Control of the Hyperfine Spin of a Cs Atom Ensemble

We demonstrate quantum control of a large spin-angular momentum associated with the F=3 hyperfine ground state of 133Cs. A combination of time dependent magnetic fields and a static tensor light shift is used to implement near-optimal controls and map a fiducial state to a broad range of target states, with yields in the range 0.8-0.9. Squeezed states are produced also by an adiabatic scheme that is more robust against errors. Universal control facilitates the encoding and manipulation of qubits and qudits in atomic ground states, and may lead to improvement of some precision measurements.Comment: 4 pages, 4 figures (color

Die Bedeutung intermediärer Regimes in der Konsolidierung der Demokratie Ostmitteleuropas

Der Autor skizziert verschiedene theoretische Positionen der wissenschaftlichen Debatte um die Bedeutung intermediärer Organisationen wie Verbände und politische Parteien in den westlichen Industriegesellschaften und konstatiert, wie umstritten deren Beitrag für die Qualität einer Demokratie ist. Die Debatte über Rolle, Funktion und Bedeutung von intermediären Organisationen in nicht konsolidierten Demokratien der Transformationsgesellschaft müsse daher gesondert geführt werden, so die These des Autors. Er führt dies am Beispiel von Parteien, Verbänden und zivilgesellschaftlichen Assoziationen aus. Eingangs stellt er die generelle Bedeutung von intermediären Organisationen innerhalb politischer Systeme dar, deren demokratische Konsolidierung noch nicht abgeschlossen ist und zeigt im Anschluß die Herausbildung von Partei- und Verbandsystemen auf. Er analysiert ihre jeweilige Bedeutung für die Stabilisierung der Demokratien Ostmitteleuropas und konstatiert abschließend ein Dilemma. Gerade unkonsolidierte Demokratien, die der "zivilkulturellen Unterfütterung der politischen Gesellschaft" mit moralischen, kognitiven und ökonomischen Ressourcen besonders bedürfen um die staatliche Macht zu kontrollieren und zu demokratisieren, können am wenigsten auf diese zurückgreifen. (rk

Coccolithophore fluxes in the open tropical North Atlantic: influence of thermocline depth, Amazon water, and Saharan dust

Coccolithophores are calcifying phytoplankton and major contributors to both the organic and inorganic oceanic carbon pumps. Their export fluxes, species composition, and seasonal patterns were determined in two sediment trap moorings (M4 at 12 degrees N, 49 degrees W and M2 at 14 degrees N, 37 degrees W) collecting settling particles synchronously from October 2012 to November 2013 at 1200 m of water depth in the open equatorial North Atlantic. The two trap locations showed a similar seasonal pattern in total coccolith export fluxes and a predominantly tropical coccolithophore settling assemblage. Species fluxes were dominated throughout the year by lower photic zone (LPZ) taxa (Florisphaera profunda, Gladiolithus flabellatus) but also included upper photic zone (UPZ) taxa (Umbellosphaera spp., Rhabdosphaera spp., Umbilicosphaera spp., Helicosphaera spp.). The LPZ flora was most abundant during fall 2012, whereas the UPZ flora was more important during summer. In spite of these similarities, the western part of the study area produced persistently higher fluxes, averaging 241 x 10(7) +/- 76 x 10(7) coccoliths m(-2) d(-1) at station M4 compared to only 66 x 10(7) +/- 31 x 10(7) coccoliths m(-2) d(-1) at station M2. Higher fluxes at M4 were mainly produced by the LPZ species, favoured by the westward deepening of the thermocline and nutricline. Still, most UPZ species also contributed to higher fluxes, reflecting enhanced productivity in the western equatorial North Atlantic. Such was the case of two marked flux peaks of the more opportunistic species Gephyrocapsa muellerae and Emiliania huxleyi in January and April 2013 at M4, indicating a fast response to the nutrient enrichment of the UPZ, probably by wind-forced mixing. Later, increased fluxes of G. oceanica and E. huxleyi in October-November 2013 coincided with the occurrence of Amazon-River-affected surface waters. Since the spring and fall events of 2013 were also accompanied by two dust flux peaks, we propose a scenario in which atmospheric dust also provided fertilizing nutrients to this area. Enhanced surface buoyancy associated with the river plume indicates that the Amazon acted not only as a nutrient source, but also as a surface density retainer for nutrients supplied from the atmosphere. Nevertheless, lower total coccolith fluxes during these events compared to the maxima recorded in November 2012 and July 2013 indicate that transient productivity by opportunistic species was less important than "background" tropical productivity in the equatorial North Atlantic. This study illustrates how two apparently similar sites in the tropical open ocean actually differ greatly in ecological and oceanographic terms. The results presented here provide valuable insights into the processes governing the ecological dynamics and the downward export of coccolithophores in the tropical North Atlantic.Netherlands Organization for Scientific Research (NWO) [822.01.008]; European Research Council (ERC) [311152]; University of Bremen; European Union [600411]info:eu-repo/semantics/publishedVersio