116 research outputs found
An explicit height bound for the classical modular polynomial
For a prime m, let Phi_m be the classical modular polynomial, and let
h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we
prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we
find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values
is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To
appear in the Ramanujan Journal. 17 pages
Quantifying the noise of a quantum channel by noise addition
In this paper we introduce a way to quantify the noise level associated to a
given quantum transformation. The key mechanism lying at the heart of the
proposal is "noise addition": in other words we compute the amount of extra
noise we need to add to the system, through convex combination with a reference
noisy map or by reiterative applications of the original map, before the
resulting transformation becomes entanglement-breaking. We also introduce the
notion of entanglement-breaking channels of order n (i.e. maps which become
entanglement-breaking after n iterations), and the associated notion of
amendable channels (i.e. maps which can be prevented from becoming
entanglement-breaking after iterations by interposing proper quantum
transformations). Explicit examples are analyzed in the context of qubit and
one-mode Guassian channels.Comment: 14 pages, 6 figure
Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics
The atmospheric greenhouse effect, an idea that many authors trace back to
the traditional works of Fourier (1824), Tyndall (1861), and Arrhenius (1896),
and which is still supported in global climatology, essentially describes a
fictitious mechanism, in which a planetary atmosphere acts as a heat pump
driven by an environment that is radiatively interacting with but radiatively
equilibrated to the atmospheric system. According to the second law of
thermodynamics such a planetary machine can never exist. Nevertheless, in
almost all texts of global climatology and in a widespread secondary literature
it is taken for granted that such mechanism is real and stands on a firm
scientific foundation. In this paper the popular conjecture is analyzed and the
underlying physical principles are clarified. By showing that (a) there are no
common physical laws between the warming phenomenon in glass houses and the
fictitious atmospheric greenhouse effects, (b) there are no calculations to
determine an average surface temperature of a planet, (c) the frequently
mentioned difference of 33 degrees Celsius is a meaningless number calculated
wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the
assumption of a radiative balance is unphysical, (f) thermal conductivity and
friction must not be set to zero, the atmospheric greenhouse conjecture is
falsified.Comment: 115 pages, 32 figures, 13 tables (some typos corrected
Fundamental limits on quantum dynamics based on entropy change
It is well known in the realm of quantum mechanics and information theory that the entropy is non-decreasing for the class of unital physical processes. However, in general, the entropy does not exhibit monotonic behavior. This has restricted the use of entropy change in characterizing evolution processes. Recently, a lower bound on the entropy change was provided in the work of Buscemi, Das, and Wilde [Phys. Rev. A 93(6), 062314 (2016)]. We explore the limit that this bound places on the physical evolution of a quantum system and discuss how these limits can be used as witnesses to characterize quantum dynamics. In particular, we derive a lower limit on the rate of entropy change for memoryless quantum dynamics, and we argue that it provides a witness of non-unitality. This limit on the rate of entropy change leads to definitions of several witnesses for testing memory effects in quantum dynamics. Furthermore, from the aforementioned lower bound on entropy change, we obtain a measure of non-unitarity for unital evolutions
Strategien und Technologien einer pluralistischen Fern- und Nahwärmeversorgung in einem liberalisierten Energiemarkt unter besonderer Berücksichtigung der Kraft-Wärme-Kopplung und erneuerbarer Energien : Kurzfassung der Studie
Die Zusammenfassung dient zwei Zielen: Zunächst werden die wesentlichen Ergebnisse der Langfassung der o.g. Studie referiert; auf dieser Basis werden dann mögliche Maßnahmen und Strategien diskutiert, die kurzfristig (2000-2001) ergriffen werden könnten. Als Akteure kommen hierbei nicht nur die Bundesregierung, die wichtige Rahmenbedingungen zum Marktgeschehen wird setzen müssen, in den Fokus, sondern auch die Betreiber von Heizkraftwerken und KWK-Anlagen und deren Verbände, aber auch andere Akteure wie z. B. Contracting-Unternehmen und Forschungseinrichtungen. Da die Übergangsphase der Liberalisierung der europäischen Stromwirtschaft in den Jahren 2000-2005 eine besondere Herausforderung für die KWK-Entwicklung darstellt, wird auch ein kurzfristig wirksames Maßnahmenbündel zur Diskussion gestellt.
Dem Leser sei zum Verständnis in Erinnerung gerufen, dass diese vorgelegte Analyse im Rahmen einer Vorstudie durchgeführt wurde und langfristig abgesicherte Aussagen auch Analysen mit einschließen müssten, die bis 2010 und 2020 reichen. Weiterführende Arbeiten sollen in einer geplanten Hauptstudie erfolgen
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