271,778 research outputs found
On Gorenstein Surfaces Dominated by P^2
In this paper we prove that a normal Gorenstein surface dominated by the
projective plane P^2 is isomorphic to a quotient P^2/G, where G is a finite
group of automorphisms of P^2 (except possibly for one surface V_8'). We can
completely classify all such quotients. Some natural conjectures when the
surface is not Gorenstein are also stated.Comment: Nagoya Mathematical Journal, to appea
Partial radiogenic heat model for Earth revealed by geoneutrino measurements
The Earth has cooled since its formation, yet the decay of radiogenic isotopes, and in particular uranium, thorium and
potassium, in the planet’s interior provides a continuing heat source. The current total heat flux from the Earth to space is 44:2±1.0 TW, but the relative contributions from residual primordial heat and radiogenic decay remain uncertain. However, radiogenic decay can be estimated from the flux of geoneutrinos, electrically neutral particles that are emitted during radioactive decay and can pass through the Earth virtually unaffected. Here we combine precise measurements of the geoneutrino flux from the Kamioka Liquid-Scintillator Antineutrino Detector, Japan, with existing measurements from the Borexino detector, Italy.We find that decay of uranium-238 and thorium-232 together contribute 20.0^(+8.8)_(-8.6)TW to Earth’s heat
flux. The neutrinos emitted from the decay of potassium-40 are below the limits of detection in our experiments, but are known to contribute 4TW. Taken together, our observations indicate that heat from radioactive decay contributes about half of Earth’s total heat flux. We therefore conclude that Earth’s primordial heat supply has not yet been exhausted
The Minimum Wiener Connector
The Wiener index of a graph is the sum of all pairwise shortest-path
distances between its vertices. In this paper we study the novel problem of
finding a minimum Wiener connector: given a connected graph and a set
of query vertices, find a subgraph of that connects all
query vertices and has minimum Wiener index.
We show that The Minimum Wiener Connector admits a polynomial-time (albeit
impractical) exact algorithm for the special case where the number of query
vertices is bounded. We show that in general the problem is NP-hard, and has no
PTAS unless . Our main contribution is a
constant-factor approximation algorithm running in time
.
A thorough experimentation on a large variety of real-world graphs confirms
that our method returns smaller and denser solutions than other methods, and
does so by adding to the query set a small number of important vertices
(i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International
Conference on Management of Dat
Critical comments on the paper "Crossing by a single scalar field on a Dvali-Gabadadze-Porrati brane" by H Zhang and Z-H Zhu [Phys.Rev.D75,023510(2007)]
It is demonstrated that the claim in the paper "Crossing by a
single scalar field on a Dvali-Gabadadze-Porrati brane" by H Zhang and Z-H Zhu
[Phys.Rev.D75,023510(2007)], about a prove that there do not exist scaling
solutions in a universe with dust in a Dvali-Gabadadze-Porrati (DGP) braneworld
scenario, is incorrect.Comment: 5 pages, 8 eps figure
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