3,997 research outputs found
Diode pumped Nd:YAG laser development
A low power Nd:YAG laser was constructed which employs GaAs injection lasers as a pump source. Power outputs of 125 mW TEM CW with the rod at 250 K and the pump at 180 K were achieved for 45 W input power to the pump source. Operation of the laser, with array and laser at a common heat sink temperature of 250 K, was inhibited by difficulties in constructing long-life GaAs LOC laser arrays. Tests verified pumping with output power of 20 to 30 mW with rod and pump at 250 K. Although life tests with single LOC GaAs diodes were somewhat encouraging (with single diodes operating as long as 9000 hours without degradation), failures of single diodes in arrays continue to occur, and 50 percent power is lost in a few hundred hours at 1 percent duty factor. Because of the large recent advances in the state of the art of CW room temperature AlGaAs diodes, their demonstrated lifetimes of greater than 5,000 hours, and their inherent advantages for this task, it is recommended that these sources be used for further CW YAG injection laser pumping work
Linear resolutions of powers and products
The goal of this paper is to present examples of families of homogeneous
ideals in the polynomial ring over a field that satisfy the following
condition: every product of ideals of the family has a linear free resolution.
As we will see, this condition is strongly correlated to good primary
decompositions of the products and good homological and arithmetical properties
of the associated multi-Rees algebras. The following families will be discussed
in detail: polymatroidal ideals, ideals generated by linear forms and Borel
fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi
deformation
Four generated, squarefree, monomial ideals
Let be two squarefree monomial ideals of a polynomial algebra
over a field generated in degree , resp. . Suppose that
is either generated by three monomials of degrees and a set of monomials of
degrees , or by four special monomials of degrees . If the Stanley
depth of is then the usual depth of is too.Comment: to appear in "Bridging Algebra, Geometry, and Topology", Editors
Denis Ibadula, Willem Veys, Springer Proceed. in Math. and Statistics, 96,
201
Absolutely Koszul algebras and the Backelin-Roos property
We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos
property and their behavior under standard algebraic operations. In particular,
we identify some Veronese subrings of polynomial rings that have the
Backelin-Roos property and conjecture that the list is indeed complete. Among
other things, we prove that every universally Koszul ring defined by monomials
has the Backelin-Roos property
The 10Be contents of SNC meteorites
Several authors have explored the possibility that the Shergottites, Nakhlites, and Chassigny (SNC) came from Mars. The spallogenic gas contents of the SNC meteorites have been used to: constrain the sizes of the SNC's during the last few million years; to establish groupings independent of the geochemical ones; and to estimate the likelihood of certain entries in the catalog of all conceivable passages from Mars to Earth. The particular shielding dependence of Be-10 makes the isotope a good probe of the irradiation conditions experienced by the SNC meteorites. The Be-10 contents of nine members of the group were measured using the technique of accelerator mass spectrometry. The Be-10 contents of Nakhla, Governador Valadares, Chassigny, and probably Lafayette, about 20 dpm/kg, exceed the values expected from irradiation of the surface of a large body. The Be-10 data therfore do not support scenario III of Bogard et al., one in which most of the Be-10 in the SNC meteorites would have formed on the Martian surface; they resemble rather the Be-10 contents found in many ordinary chondrites subjected to 4 Pi exposures. The uncertainties of the Be-10 contents lead to appreciable errors in the Be-10 ages, t(1) = -1/lambda ln(1 Be-10/Be-10). Nonetheless, the Be-10 ages are consistent with the Ne-21 ages calculated assuming conventional, small-body production rates and short terrestrial ages for the finds. It is believed that this concordance strengthens the case for at least 3 different irradiation ages for the SNC meteorites. Given the similar half-thicknesses of the Be-10 and Ne-21 production rates, the ratios of the Be-10 and Ne-21 contents do not appear consistent with common ages for any of the groups. In view of the general agreement between the Be-10 and Ne-21 ages it does not seem useful at this time to construct multiple-stage irradiation histories for the SNC meteorites
Study of Giant Pairing Vibrations with neutron-rich nuclei
We investigate the possible signature of the presence of giant pairing states
at excitation energy of about 10 MeV via two-particle transfer reactions
induced by neutron-rich weakly-bound projectiles. Performing particle-particle
RPA calculations on Pb and BCS+RPA calculations on Sn, we
obtain the pairing strength distribution for two particles addition and removal
modes. Estimates of two-particle transfer cross sections can be obtained in the
framework of the 'macroscopic model'. The weak-binding nature of the projectile
kinematically favours transitions to high-lying states. In the case of (~^6He,
\~^4He) reaction we predict a population of the Giant Pairing Vibration with
cross sections of the order of a millibarn, dominating over the mismatched
transition to the ground state.Comment: Talk presented in occasion of the VII School-Semina r on Heavy Ion
Physics hosted by the Flerov Laboratory (FLNR/JINR) Dubna, Russia from May 27
to June 2, 200
Powers of componentwise linear ideals
We give criteria for graded ideals to have the property that all their powers
are componentwise linear. Typical examples to which our criteria can be applied
include the vertex cover ideals of certain finite graphs
Wall Crossing, Quivers and Crystals
We study the spectrum of BPS D-branes on a Calabi-Yau manifold using the 0+1
dimensional quiver gauge theory that describes the dynamics of the branes at
low energies. The results of Kontsevich and Soibelman predict how the
degeneracies change. We argue that Seiberg dualities of the quiver gauge
theories, which change the basis of BPS states, correspond to crossing the
"walls of the second kind." There is a large class of examples, including local
del Pezzo surfaces, where the BPS degeneracies of quivers corresponding to one
D6 brane bound to arbitrary numbers of D4, D2 and D0 branes are counted by
melting crystal configurations. We show that the melting crystals that arise
are a discretization of the Calabi-Yau geometry. The shape of the crystal is
determined by the Calabi-Yau geometry and the background B-field, and its
microscopic structure by the quiver Q. We prove that the BPS degeneracies
computed from Q and Q' are related by the Kontsevich Soibelman formula, using a
geometric realization of the Seiberg duality in the crystal. We also show that,
in the limit of infinite B-field, the combinatorics of crystals arising from
the quivers becomes that of the topological vertex. We thus re-derive the
Gromov-Witten/Donaldson-Thomas correspondence
Exceptional collections and D-branes probing toric singularities
We demonstrate that a strongly exceptional collection on a singular toric
surface can be used to derive the gauge theory on a stack of D3-branes probing
the Calabi-Yau singularity caused by the surface shrinking to zero size. A
strongly exceptional collection, i.e., an ordered set of sheaves satisfying
special mapping properties, gives a convenient basis of D-branes. We find such
collections and analyze the gauge theories for weighted projective spaces, and
many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong
exceptionality for all p in the Y^{p,p-1} case, and similarly for the
Y^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio
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