10,212 research outputs found
Rationality of Euler-Chow series and finite generation of Cox rings
In this paper we work with a series whose coefficients are the Euler
characteristic of Chow varieties of a given projective variety. For varieties
where the Cox ring is defined, it is easy to see that in this case the ring
associated to the series is the Cox ring. If this ring is noetherian then the
series is rational. It is an open question whether the converse holds. In this
paper we give an example showing the converse fails. However we conjecture that
it holds when the variety is rationally connected. As an evidence of this
conjecture, It is proved that the series is not rational, and in a sense
defined, not algebraic, in the case of the blowup of the projective plane at
nine or more points in general position. Furthermore, we also treat some other
examples of varieties with infinitely generated Cox ring, studied by Mukai and
Hassett-Tschinkel. These are the first examples known where the series is not
rational. We also compute the series for Del Pezzo surfaces.Comment: 26 pages. In this last version we correct many typos and add a cite
of a work of Artebani and Laface in Theorem 1.6 which was brought to our
attention. More typo correction
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Parental divorce is not uniformly disruptive to children's educational attainment.
Children whose parents divorce tend to have worse educational outcomes than children whose parents stay married. However, not all children respond identically to their parents divorcing. We focus on how the impact of parental divorce on children's education varies by how likely or unlikely divorce was for those parents. We find a significant negative effect of parental divorce on educational attainment, particularly college attendance and completion, among children whose parents were unlikely to divorce. Families expecting marital stability, unprepared for disruption, may experience considerable adjustment difficulties when divorce occurs, leading to negative outcomes for children. By contrast, we find no effect of parental divorce among children whose parents were likely to divorce. Children of high-risk marriages, who face many social disadvantages over childhood irrespective of parental marital status, may anticipate or otherwise accommodate to the dissolution of their parents' marriage. Our results suggest that family disruption does not uniformly disrupt children's attainment
Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection
Explicit formulas for the rotation frequency and the long-wavenumber
diffusion coefficients of global spirals with arms in Rayleigh-Benard
convection are obtained. Global spirals and parallel rolls share exactly the
same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals
seem not to have a characteristic frequency or a typical size ,
but their product is a constant under given experimental
conditions. The ratio of the radii of any two dislocations (,
) inside a multi-armed spiral is also predicted to be constant. Some of
these results have been tested by our numerical work.Comment: To appear in Phys. Rev. E as Rapid Communication
Laboratory Transferability of Optimally Shaped Laser Pulses for Quantum Control
Optimal control experiments can readily identify effective shaped laser
pulses, or "photonic reagents", that achieve a wide variety of objectives. For
many practical applications, an important criterion is that a particular
photonic reagent prescription still produce a good, if not optimal, target
objective yield when transferred to a different system or laboratory, {even if
the same shaped pulse profile cannot be reproduced exactly. As a specific
example, we assess the potential for transferring optimal photonic reagents for
the objective of optimizing a ratio of photoproduct ions from a family of
halomethanes through three related experiments.} First, applying the same set
of photonic reagents with systematically varying second- and third-order chirp
on both laser systems generated similar shapes of the associated control
landscape (i.e., relation between the objective yield and the variables
describing the photonic reagents). Second, optimal photonic reagents obtained
from the first laser system were found to still produce near optimal yields on
the second laser system. Third, transferring a collection of photonic reagents
optimized on the first laser system to the second laser system reproduced
systematic trends in photoproduct yields upon interaction with the homologous
chemical family. Despite inherent differences between the two systems,
successful and robust transfer of photonic reagents is demonstrated in the
above three circumstances. The ability to transfer photonic reagents from one
laser system to another is analogous to well-established utilitarian operating
procedures with traditional chemical reagents. The practical implications of
the present results for experimental quantum control are discussed
Magnetism of Cold Fermionic Atoms on p-Band of an Optical Lattice
We carry out \textit{ab initio} study of ground state phase diagram of
spin-1/2 cold fermionic atoms within two-fold degenerate -band of an
anisotropic optical lattice. Using the Gutzwiller variational approach, we show
that a robust ferromagnetic phase exists for a vast range of band fillings and
interacting strengths. The ground state crosses over from spin density wave
state to spin-1 Neel state at half filling. Additional harmonic trap will
induce spatial separation of varies phases. We also discuss several relevant
observable consequences and detection methods. Experimental test of the results
reported here may shed some light on the long-standing issue of itinerant
ferromagnetism.Comment: 5 pages, 4 figure
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