955 research outputs found
The Morse-Sard theorem revisited
Let be positive integers with . We establish an abstract
Morse-Sard-type theorem which allows us to deduce, on the one hand, a previous
result of De Pascale's for Sobolev functions with and, on the other hand, also the following
new result: if satisfies
for every
(that is, is a Stepanov function), then the set
of critical values of is Lebesgue-null in . In the case that
we also show that this limiting condition holding for every
, where is a set of zero
-dimensional Hausdorff measure for some , is
sufficient to guarantee the same conclusion.Comment: We corrected some misprints and made some changes in the introductio
Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO
We consider QCD radiative corrections to the production of W and Z bosons in
hadron collisions. We present a fully exclusive calculation up to
next-to-next-to-leading order (NNLO) in QCD perturbation theory. To perform
this NNLO computation, we use a recently proposed version of the subtraction
formalism. The calculation includes the gamma-Z interference, finite-width
effects, the leptonic decay of the vector bosons and the corresponding spin
correlations. Our calculation is implemented in a parton level Monte Carlo
program. The program allows the user to apply arbitrary kinematical cuts on the
final-state leptons and the associated jet activity, and to compute the
corresponding distributions in the form of bin histograms. We show selected
numerical results at the Tevatron and the LHC.Comment: 7 pages, 3 ps figure
Universality of transverse-momentum resummation and hard factors at the NNLO
We consider QCD radiative corrections to the production of colourless
high-mass systems in hadron collisions. The logarithmically-enhanced
contributions at small transverse momentum are treated to all perturbative
orders by a universal resummation formula that depends on a single
process-dependent hard factor. We show that the hard factor is directly related
to the all-order virtual amplitude of the corresponding partonic process. The
direct relation is universal (process independent), and it is expressed by an
all-order factorization formula that we explicitly evaluate up to the
next-to-next-to-leading order (NNLO) in QCD perturbation theory. Once the NNLO
scattering amplitude is available, the corresponding hard factor is directly
determined: it controls NNLO contributions in resummed calculations at full
next-to-next-to-leading logarithmic accuracy, and it can be used in
applications of the q_T subtraction formalism to perform fully-exclusive
perturbative calculations up to NNLO. The universality structure of the hard
factor and its explicit NNLO form are also extended to the related formalism of
threshold resummation.Comment: References added. Version accepted for publication on NP
Threshold resummation at NLL accuracy and soft-virtual cross sections at NLO
We consider QCD radiative corrections to the production of colourless
high-mass systems in hadron collisions. We show that the recent computation of
the soft-virtual corrections to Higgs boson production at NLO [1] together
with the universality structure of soft-gluon emission can be exploited to
extract the general expression of the hard-virtual coefficient that contributes
to threshold resummation at NLL accuracy. The hard-virtual coefficient is
directly related to the process-dependent virtual amplitude through a universal
(process-independent) factorization formula that we explicitly evaluate up to
three-loop order. As an application, we present the explicit expression of the
soft-virtual NLO corrections for the production of an arbitrary colourless
system. In the case of the Drell-Yan process, we confirm the recent result of
Ref.[2].Comment: Slightly expanded text, one reference added, version published on NP
A method for calculating transient thrust and flow-rate levels for Mariner type attitude control nitrogen gas jets
The purpose of this report is to define and program the transient pneumatic flow equations necessary to determine, for a given set of conditions (geometry, pressures, temperatures, valve on time, etc.), the total nitrogen impulse and mass flow per pulse for the single pulsing of a Mariner type reaction control assembly valve. The rates of opening and closing of the valves are modeled, and electrical pulse durations from 20 to 100 ms are investigated. In developing the transient flow analysis, maximum use was made of the steady-state analysis. The impulse results are also compared to an equivalent square-wave impulse for both the Mariner Mars 1971 (MM'71) and Mariner Mars 1964 (MM'64) systems. It is demonstrated that, whereas in the MM'64 system, the actual impulse was as much as 56 percent higher than an assumed impulse (which is the product of the steady-state thrust and value on time i.e., the square wave), in the MM'71 system, these two values were in error in the same direction by only approximately 4 percent because of the larger nozzle areas and shorter valve stroke used
Solar electric propulsion system tests
Design and performance of solar-powered electric propulsion system for interplanetary space exploratio
Airbag Products Liability Litigation: State Common Law Tort Claims Are Not Automatically Preempted by Federal Legislation
This article addresses an important and recurring issue of federalism, and attempts to resolve the tensions that exist between federal and state laws in the context of recent automobile airbag litigation. The authors trace the evolution of the preemption doctrine as it relates to airbag litigation, and write further as to how manufacturers adapt, developing business and ethical strategies of compliance to concurrent state and federal regulation. Two recent important decisions involving no airbag litigation, Tebbetts v. Ford Motor Co. and Wilson v. Pleasant, are interpretive of two provisions of the Safety Act. The former case discussed a preemption clause, and the latter a state common law savings clause. These cases have posed important and controversial legal and ethical issues that have an enormous impact on auto manufacturers\u27 exposure to liability. This article will discuss the issues emanating from the decisions in Tebbetts and Wilson with major emphasis on the doctrine of preemption, the Supremacy Clause of the U.S. Constitution, state police powers, the potential of the judiciary to shape business policy, and the ethical obligations of auto manufacturers to the many stakeholders involved. In addition, the authors proffer suggestions regarding the best road to travel when there are different options for meeting the overlapping layers of federal and state safety requirements
How does the geodesic rule really work for global symmetry breaking first order phase transitions?
The chain of events usually understood to lead to the formation of
topological defects during phase transitions is known as the Kibble mechanism.
A central component of the mechanism is the so-called ``geodesic rule''.
Although in the Abelian Higgs model the validity of the geodesic rule has been
questioned recently, it is known to be valid on energetic grounds for a global
U(1) symmetry breaking transition. However, even for these globally symmetric
models no dynamical analisys of the rule has been carried to this date, and
some points as to how events proceed still remain obscure. This paper tries to
clarify the dynamics of the geodesic rule in the context of a global U(1)
model. With an appropriate ansatz for the field modulus we find a family of
analytical expressions, phase walls, that accounts for both geodesic and
nongeodesic configurations. We then show how the latter ones are unstable and
decay into the former by nucleating pairs of defects. Finnally, we try to give
a physical perspective of how the geodesic rule might really work in these
transitions.Comment: 10 pages, 9 multiple figre
Smooth Approximation of Lipschitz functions on Riemannian manifolds
We show that for every Lipschitz function defined on a separable
Riemannian manifold (possibly of infinite dimension), for every continuous
, and for every positive number , there exists
a smooth Lipschitz function such that
for every and
. Consequently, every separable
Riemannian manifold is uniformly bumpable. We also present some applications of
this result, such as a general version for separable Riemannian manifolds of
Deville-Godefroy-Zizler's smooth variational principle.Comment: 10 page
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