128 research outputs found
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Femtosecond Pump-Probe Diagnostics Of Preformed Plasma Channels
We report on recent ultrafast pump-probe experiments 28 in He plasma waveguides using 800 nm, 80 fs pump pulses of 0.2 x 1018 W/cm2 peak guided intensity, and single orthogonally-polarized 800 nm probe pulses with similar to0.1% of pump intensity. The main results are: (1) We observe frequency-domain interference between the probe and a weak, depolarized component of the pump that differs substantially in mode shape from the injected pump pulse; (2) we observe spectral blue-shifts in the transmitted probe that are not evident in the transmitted pump. The evidence indicates that pump depolarization and probe blue-shifts both originate near the channel entrance.Physic
Criteria for flatness and injectivity
Let be a commutative Noetherian ring. We give criteria for flatness of
-modules in terms of associated primes and torsion-freeness of certain
tensor products. This allows us to develop a criterion for regularity if
has characteristic , or more generally if it has a locally contracting
endomorphism. Dualizing, we give criteria for injectivity of -modules in
terms of coassociated primes and (h-)divisibility of certain \Hom-modules.
Along the way, we develop tools to achieve such a dual result. These include a
careful analysis of the notions of divisibility and h-divisibility (including a
localization result), a theorem on coassociated primes across a \Hom-module
base change, and a local criterion for injectivity.Comment: 19 page
The amalgamated duplication of a ring along a multiplicative-canonical ideal
After recalling briefly the main properties of the amalgamated duplication of
a ring along an ideal , denoted by R\JoinI, we restrict our attention
to the study of the properties of R\JoinI, when is a multiplicative
canonical ideal of \cite{hhp}. In particular, we study when every regular
fractional ideal of is divisorial
Almost clean rings and arithmetical rings
It is shown that a commutative B\'ezout ring with compact minimal prime
spectrum is an elementary divisor ring if and only if so is for each
minimal prime ideal . This result is obtained by using the quotient space
of the prime spectrum of the ring modulo the equivalence
generated by the inclusion. When every prime ideal contains only one minimal
prime, for instance if is arithmetical, is Hausdorff and
there is a bijection between this quotient space and the minimal prime spectrum
, which is a homeomorphism if and only if is
compact. If is a closed point of , there is a pure ideal
such that . If is almost clean, i.e. each element is the
sum of a regular element with an idempotent, it is shown that is totally disconnected and, , is
almost clean; the converse holds if every principal ideal is finitely
presented. Some questions posed by Facchini and Faith at the second
International Fez Conference on Commutative Ring Theory in 1995, are also
investigated. If is a commutative ring for which the ring of
quotients of is an IF-ring for each proper ideal , it is proved that
is a strongly discrete valuation ring for each maximal ideal and
is semicoherent for each proper ideal
Perverse coherent t-structures through torsion theories
Bezrukavnikov (later together with Arinkin) recovered the work of Deligne
defining perverse -structures for the derived category of coherent sheaves
on a projective variety. In this text we prove that these -structures can be
obtained through tilting torsion theories as in the work of Happel, Reiten and
Smal\o. This approach proves to be slightly more general as it allows us to
define, in the quasi-coherent setting, similar perverse -structures for
certain noncommutative projective planes.Comment: New revised version with important correction
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Plasma Channels And Laser Pulse Tailoring For Gev Laser-Plasma Accelerators
We have demonstrated distortion-free guiding of I TW pulses at near relativistic intensity (0.2 x 10(18) W/cm(2)) over 60 Rayleigh lengths at 20 Hz repetition rate in a preformed helium plasma channel. As steps toward efficient channeled Laser Wakefield Acceleration up to the dephasing limit, we have upgraded our laser system from I to 4 TW, adapted femtosecond interferometric diagnostics to probe plasma density fluctuations inside the channel, and developed detailed strategies for managing ionization distortions at the channel entrance and exit at the upgraded intensity. We also report simulations, and preliminary experiments, that explore a strategy for Raman-seeding laser pulses to coherently control both unchanneled and channeled LWFA in order to lower the laser energy threshold and increase the repetition rate of election pickup and acceleration.Physic
On the support of general local cohomology modules and filter regular sequences
Let R be a commutative Noetherian ring with non-zero identity and a an ideal of R. In the present paper, we examine the question whether the support of Hn a (N;M) must be closed in Zariski topology, where Hn a (N;M) is the nth general local cohomology module of nitely generated R-modules M and N with respect to the ideal a
On Albanese torsors and the elementary obstruction
We show that the elementary obstruction to the existence of 0-cycles of
degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed
in terms of the Albanese 1-motives associated with dense open subsets of X.
Arithmetic applications are given
Algebraic entropy in locally linearly compact vector spaces
We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in Giordano Bruno and Salce (Arab J Math 1:69\u201387, 2012). We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem
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