11,508 research outputs found
Lagrange's four squares theorem with one prime and three almost--prime variables
It is conjectured that every sufficiently large integer should be a sum of the squares of 4 primes. The best approximation to this in the literature is the result of Brüdern and Fouvry [J. Reine Angew. Math., 454 (1994), 59--96] who showed that every sufficiently large integer is a sum of the squares of 4 almost-primes, each of which has at most 34 prime factors.
The present paper proves such a result with the square of one prime and 3 almost-primes, which in this case have at most 101 prime factors each. The work of Brüdern and Fouvry was based on Kloosterman's approach to representations by quaternary forms, but this does not lend itself to situations in which one of the variables is restricted to be a prime. Instead the present paper works with an `almost all' result for the representation of numbers as sums of 3 squares. To use this approach one has to take of the form , and such numbers are too sparse for the standard theory. It is therefore necessary to use an `amplification' procedure, which emphasizes those integers for which is a square.
All this machinery is coupled with Kloosterman's version of the circle method. There are considerable technical complications, in which bounds for the Kloosterman sum play a key rôle. At one point in the argument a saving has to be extracted from a non-trivial averaging over the denominators of the Farey arcs. This is an instance of `the second Kloosterman refinement'
Density of non-residues in Burgess-type intervals and applications
We show that for any fixed \eps>0, there are numbers and with the following property: for every prime and every integer
such that p^{1/(4\sqrt{e})+\eps}\le N\le p, the sequence
contains at least quadratic non-residues modulo . We use this
result to obtain strong upper bounds on the sizes of the least quadratic
non-residues in Beatty and Piatetski--Shapiro sequences.Comment: In the new version we use an idea of Roger Heath-Brown (who is now a
co-author) to simply the proof and improve the main results of the previous
version, 14 page
Modelling the Northeast Atlantic circulation : implications for the spring invasion of shelf regions by Calanus finmarchicus
The appearance in spring of the copepod Calanus finmarchicus in continental shelf waters of the northeastern Atlantic has been hypothesized to be mainly attributable to invasion from across the continental slope rather than in situ overwintering. This paper describes the application of a hydrodynamic circulation model and a particle-tracking model to Northeast Atlantic waters in order to assess the influence of the flow field and ascent migration parameters on the spring invasion of C. finmarchicus. For hydrodynamic modelling, the Hamburg Shelf-Ocean Model (HAMSOM) was applied to the North Atlantic and Nordic Seas and forced with daily mean atmospheric data. Simulated flow fields from HAMSOM serve as forcing functions for a particle-tracking model of the same region. The robustness of the simulated shelf invasion in three target boxes of the Northeast Atlantic Shelf was assessed by means of a sensitivity analysis with respect to variations in four key migration parameters: overwintering depth, ascent rate, ascent timing, and depth during residence in upper layers. The invasion of the northern North Sea and Norwegian Shelf waters is more sensitive to ascent migration parameters than invasion of the Faroese Shelf. The main reason for enhanced sensitivity of the North Sea invasion is the time and space-dependent flow structure in the Faroe-Shetland Channel. Dense aggregations of overwintering C. finmarchicus are found in the Channel, but because of the complex flow field only a proportion of the overwintering stock has the capacity to reach the North Sea
The Clustering Of Galaxies Around Radio-Loud AGNs
We examine the hypothesis that mergers and close encounters between galaxies
can fuel AGNs by increasing the rate at which gas accretes towards the central
black hole. We compare the clustering of galaxies around radio-loud AGNs with
the clustering around a population of radio-quiet galaxies with similar masses,
colors and luminosities. Our catalog contains 2178 elliptical radio galaxies
with flux densities greater than 2.8 mJy at 1.4 GHz from the 6dFGS survey. We
find that radio AGNs with more than 200 times the median radio power have, on
average, more close (r<160 kpc) companions than their radio-quiet counterparts,
suggestive that mergers play a role in forming the most powerful radio
galaxies. For ellipticals of fixed stellar mass, the radio power is not a
function of large-scale environment nor halo mass, consistent with the radio
powers of ellipticals varying by orders of magnitude over billions of years.Comment: 12 pages, 6 figure
Zeldovich flow on cosmic vacuum background: new exact nonlinear analytical solution
A new exact nonlinear Newtonian solution for a plane matter flow superimposed
on the isotropic Hubble expansion is reported. The dynamical effect of cosmic
vacuum is taken into account. The solution describes the evolution of nonlinear
perturbations via gravitational instability of matter and the termination of
the perturbation growth by anti-gravity of vacuum at the epoch of transition
from matter domination to vacuum domination. On this basis, an `approximate' 3D
solution is suggested as an analog of the Zeldovich ansatz.Comment: 9 pages, 1 figure
Halo detection via large-scale Bayesian inference
We present a proof-of-concept of a novel and fully Bayesian methodology
designed to detect halos of different masses in cosmological observations
subject to noise and systematic uncertainties. Our methodology combines the
previously published Bayesian large-scale structure inference algorithm, HADES,
and a Bayesian chain rule (the Blackwell-Rao Estimator), which we use to
connect the inferred density field to the properties of dark matter halos. To
demonstrate the capability of our approach we construct a realistic galaxy mock
catalogue emulating the wide-area 6-degree Field Galaxy Survey, which has a
median redshift of approximately 0.05. Application of HADES to the catalogue
provides us with accurately inferred three-dimensional density fields and
corresponding quantification of uncertainties inherent to any cosmological
observation. We then use a cosmological simulation to relate the amplitude of
the density field to the probability of detecting a halo with mass above a
specified threshold. With this information we can sum over the HADES density
field realisations to construct maps of detection probabilities and demonstrate
the validity of this approach within our mock scenario. We find that the
probability of successful of detection of halos in the mock catalogue increases
as a function of the signal-to-noise of the local galaxy observations. Our
proposed methodology can easily be extended to account for more complex
scientific questions and is a promising novel tool to analyse the cosmic
large-scale structure in observations.Comment: 17 pages, 13 figures. Accepted for publication in MNRAS following
moderate correction
Mapping the optoelectronic property space of small aromatic molecules
Small aromatic molecules and their quinone derivatives find use in organic transistors, solar-cells, thermoelectrics, batteries and photocatalysts. These applications exploit the optoelectronic properties of these molecules and the ease by which such properties can be tuned by the introduction of heteroatoms and/or the addition of functional groups. We perform a high-throughput virtual screening using the xTB family of density functional tight-binding methods to map the optoelectronic property space of ~250,000 molecules. The large volume of data generated allows for a broad understanding of how the presence of heteroatoms and functional groups affect the ionisation potential, electron affinity and optical gap values of these molecular semiconductors, and how the structural features – on their own or in combination with one another – allow access to particular regions of the optoelectronic property space. Finally, we identify the apparent boundaries of the optoelectronic property space for these molecules: regions of property space that appear off limits for any small aromatic molecule
Quantum Field Theory of Forward Rates with Stochastic Volatility
In a recent formulation of a quantum field theory of forward rates, the
volatility of the forward rates was taken to be deterministic. The field theory
of the forward rates is generalized to the case of stochastic volatility. Two
cases are analyzed, firstly when volatility is taken to be a function of the
forward rates, and secondly when volatility is taken to be an independent
quantum field. Since volatiltiy is a positive valued quantum field, the full
theory turns out to be an interacting nonlinear quantum field theory in two
dimensions. The state space and Hamiltonian for the interacting theory are
obtained, and shown to have a nontrivial structure due to the manifold moving
with a constant velocity. The no arbitrage condition is reformulated in terms
of the Hamiltonian of the system, and then exactly solved for the nonlinear
interacting case.Comment: 7 Figure
On certain other sets of integers
We show that if A is a subset of {1,...,N} containing no non-trivial
three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).Comment: 29 pp. Corrected typos. Added definitions for some non-standard
notation and remarks on lower bound
Using high-throughput virtual screening to explore the optoelectronic property space of organic dyes; finding diketopyrrolopyrrole dyes for dye-sensitized water splitting and solar cells
Organic dyes based on conjugated chromophores such as diketopyrrolopyrrole (DPP) have a large range of uses beyond providing colour to other materials, such as in dye-sensitized solar cells, dye-sensitized photoelectrochemical cells, dye-sensitized colloidal photocatalysts and organic photovoltaics. We perform a high-throughput virtual screening using the xTB family of density functional tight-binding methods to map the optoelectronic property space of ∼45 000 DPP dyes. The large volume of data at our disposal allows us to probe the difference between symmetric and asymmetric dyes and to identify the apparent boundaries of the optoelectronic property space for these dyes, as well as which substituents give access to particular combinations of properties. Finally, we use our dataset to screen for DPP dyes that can drive the reduction of protons to molecular hydrogen when illuminated as part of dye-sensitized photoelectrochemical cells or dye-sensitized colloidal photocatalysts, or as dyes for TiO2-based dye-sensitized solar cells
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