19,164 research outputs found
Tractability of multivariate problems for standard and linear information in the worst case setting: part II
We study QPT (quasi-polynomial tractability) in the worst case setting for
linear tensor product problems defined over Hilbert spaces. We assume that the
domain space is a reproducing kernel Hilbert space so that function values are
well defined. We prove QPT for algorithms that use only function values under
the three assumptions:
1) the minimal errors for the univariate case decay polynomially fast to
zero,
2) the largest singular value for the univariate case is simple and
3) the eigenfunction corresponding to the largest singular value is a
multiple of the function value at some point.
The first two assumptions are necessary for QPT. The third assumption is
necessary for QPT for some Hilbert spaces
Supergravity-matter actions in three dimensions and Chern-Simons terms
We study off-shell N-extended Yang-Mills multiplets coupled to conformal
supergravity in three spacetime dimensions. Superform formulations are
presented for the non-Abelian Chern-Simons actions in the cases N=1, 2, 3, and
the corresponding component actions are explicitly worked out. Such a
Chern-Simons action does not exist for N=4. In the latter case, a superform
formulation is given for the BF term that describes the coupling of two Abelian
vector multiplets with self-dual and anti-self-dual superfield strengths
respectively. The superform results obtained are used to construct linear
multiplet action principles in the cases N=2, 3, 4. The N=3 and N=4 actions are
demonstrated to be universal in the sense that all known off-shell
supergravity-matter systems (with the exception of pure conformal supergravity)
may be described using such an action. Starting from the N=3 and N=4 Abelian
vector multiplets, we also construct composite O(2) multiplets which are
analogues of the four-dimensional construction of an N=2 reduced chiral scalar
engineered from the improved tensor multiplet. Using these composites, we
present the superfield equations of motion for N=3 and N=4 anti-de Sitter and
topologically massive supergravity theories. We also sketch the construction of
a large family of higher derivative couplings for N=3 and N=4 vector
multiplets.Comment: 64 pages; V3: published versio
On curvature squared terms in N = 2 supergravity
We present the N = 2 supersymmetric completion of a scalar curvature squared
term in a completely gauge independent form. We also elaborate on its component
structure.Comment: 15 pages; V2: 17 pages, typos corrected, discussion comments and
acknowledgement added; V3: published versio
On supersymmetric Chern-Simons-type theories in five dimensions
We present a closed-form expression for the supersymmetric non-Abelian
Chern-Simons action in conventional five-dimensional N=1 superspace. Our
construction makes use of the superform formalism to generate supersymmetric
invariants. Similar ideas are applied to construct supersymmetric actions for
off-shell supermultiplets with an intrinsic central charge. In particular, the
large tensor multiplet is described in superspace for the first time.Comment: 26 pages; V2: comments added and typos corrected, published versio
The operational processing of wind estimates from cloud motions: Past, present and future
Current NESS winds operations provide approximately 1800 high quality wind estimates per day to about twenty domestic and foreign users. This marked improvement in NESS winds operations was the result of computer techniques development which began in 1969 to streamline and improve operational procedures. In addition, the launch of the SMS-1 satellite in 1974, the first in the second generation of geostationary spacecraft, provided an improved source of visible and infrared scanner data for the extraction of wind estimates. Currently, operational winds processing at NESS is accomplished by the automated and manual analyses of infrared data from two geostationary spacecraft. This system uses data from SMS-2 and GOES-1 to produce wind estimates valid for 00Z, 12Z and 18Z synoptic times
New superconformal multiplets and higher derivative invariants in six dimensions
Within the framework of six-dimensional conformal
supergravity, we introduce new off-shell multiplets , where
and use them to construct higher-rank extensions of the linear
multiplet action. The multiplets may be viewed as being
dual to well-known superconformal multiplets. We provide
prepotential formulations for the and
multiplets coupled to conformal supergravity. For every
multiplet, we construct a higher derivative invariant which is superconformal
on arbitrary superconformally flat backgrounds. We also show how our results
can be used to construct new higher derivative actions in supergravity.Comment: 17 pages; V2: comments and reference adde
Symmetries of curved superspace in five dimensions
We develop a formalism to construct supersymmetric backgrounds within the
superspace formulation for five-dimensional (5D) conformal supergravity given
in arXiv:0802.3953. Our approach is applicable to any off-shell formulation for
5D minimal Poincare and anti-de Sitter supergravity theories realized as the
Weyl multiplet coupled with two compensators. For those superspace backgrounds
which obey the equations of motion for (gauged) supergravity, we naturally
reproduce the supersymmetric solutions constructed a decade ago by Gauntlett et
al. For certain supersymmetric backgrounds with eight supercharges, we
construct a large family of off-shell supersymmetric sigma models such that the
superfield Lagrangian is given in terms of the Kahler potential of a real
analytic Kahler manifold.Comment: 47 pages; V2: references added, minor modifications, published
versio
Higher derivative couplings and massive supergravity in three dimensions
We develop geometric superspace settings to construct arbitrary higher
derivative couplings (including R^n terms) in three-dimensional supergravity
theories with N=1,2,3 by realising them as conformal supergravity coupled to
certain compensators. For all known off-shell supergravity formulations, we
construct supersymmetric invariants with up to and including four derivatives.
As a warming-up exercise, we first give a new and completely geometric
derivation of such invariants in N=1 supergravity. Upon reduction to
components, they agree with those given in arXiv:0907.4658 and arXiv:1005.3952.
We then carry out a similar construction in the case of N=2 supergravity for
which there exist two minimal formulations that differ by the choice of
compensating multiplet: (i) a chiral scalar multipet; (ii) a vector multiplet.
For these formulations all four derivative invariants are constructed in
completely general and gauge independent form. For a general supergravity model
(in the N=1 and minimal N=2 cases) with curvature-squared and lower order
terms, we derive the superfield equations of motion, linearise them about
maximally supersymmetric backgrounds and obtain restrictions on the parameters
that lead to models for massive supergravity. We use the non-minimal
formulation for N = 2 supergravity (which corresponds to a complex linear
compensator) to construct a novel consistent theory of massive supergravity. In
the case of N = 3 supergravity, we employ the off-shell formulation with a
vector multiplet as compensator to construct for the first time various higher
derivative invariants. These invariants may be used to derive models for N = 3
massive supergravity. As a bi-product of our analysis, we also present
superfield equations for massive higher spin multiplets in (1,0), (1,1) and
(2,0) anti-de Sitter superspaces.Comment: 84 pages; V3: references added, minor modifications, published
versio
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