1,290 research outputs found
Diagonalizing operators over continuous fields of C*-algebras
It is well known that in the commutative case, i.e. for being a
commutative C*-algebra, compact selfadjoint operators acting on the Hilbert
C*-module (= continuous families of such operators , ) can
be diagonalized if we pass to a bigger W*-algebra which can be obtained from by completing it with respect to the weak
topology. Unlike the "eigenvectors", which have coordinates from , the
"eigenvalues" are continuous, i.e. lie in the C*-algebra . We discuss here
the non-commutative analog of this well-known fact. Here the "eigenvalues" are
defined not uniquely but in some cases they can also be taken from the initial
C*-algebra instead of the bigger W*-algebra. We prove here that such is the
case for some continuous fields of real rank zero C*-algebras over a
one-dimensional manifold and give an example of a C*-algebra for which the
"eigenvalues" cannot be chosen from , i.e. are discontinuous. The main point
of the proof is connected with a problem on almost commuting operators. We
prove that for some C*-algebras if is a selfadjoint, is a
unitary and if the norm of their commutant is small enough then one can
connect with the unity by a path so that the norm of
would be also small along this path.Comment: 21 pages, LaTeX 2.09, no figure
Resonance-continuum interference in the di-photon Higgs signal at the LHC
A low mass Standard Model Higgs boson should be visible at the Large Hadron
Collider through its production via gluon-gluon fusion and its decay to two
photons. We compute the interference of this resonant process, gg -> H -> gamma
gamma, with the continuum QCD background, gg -> gamma gamma induced by quark
loops. Helicity selection rules suppress the effect, which is dominantly due to
the imaginary part of the two-loop gg -> gamma gamma scattering amplitude. The
interference is destructive, but only of order 5% in the Standard Model, which
is still below the 10-20% present accuracy of the total cross section
prediction. We comment on the potential size of such effects in other Higgs
models.Comment: 10 pages, 2 figure
Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
We compute the leading-color (planar) three-loop four-point amplitude of N=4
supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent
expansion about epsilon = 0 including the finite terms. The amplitude was
constructed previously via the unitarity method, in terms of two Feynman loop
integrals, one of which has been evaluated already. Here we use the
Mellin-Barnes integration technique to evaluate the Laurent expansion of the
second integral. Strikingly, the amplitude is expressible, through the finite
terms, in terms of the corresponding one- and two-loop amplitudes, which
provides strong evidence for a previous conjecture that higher-loop planar N =
4 amplitudes have an iterative structure. The infrared singularities of the
amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on
resummation. Based on the four-point result and the exponentiation of infrared
singularities, we give an exponentiated ansatz for the maximally
helicity-violating n-point amplitudes to all loop orders. The 1/epsilon^2 pole
in the four-point amplitude determines the soft, or cusp, anomalous dimension
at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a
prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the
leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and
Vogt. Following similar logic, we are able to predict a term in the three-loop
quark and gluon form factors in QCD.Comment: 54 pages, 7 figures. v2: Added references, a few additional words
about large spin limit of anomalous dimensions. v3: Expanded Sect. IV.A on
multiloop ansatz; remark that form-factor prediction is now confirmed by
other work; minor typos correcte
The Maximal Denumerant of a Numerical Semigroup
Given a numerical semigroup S = and n in S, we
consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >=
0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over
all such factorizations of n. We provide an algorithm for computing the maximum
number of maximal factorizations possible for an element in S, which is called
the maximal denumerant of S. We also consider various cases that have
connections to the Cohen-Macualay and Gorenstein properties of associated
graded rings for which this algorithm simplifies.Comment: 13 Page
Parasites (Trematoda, Nematoda, Phthiraptera) of Two Arkansas Raptors (Accipitriformes: Accipitridae; Strigiformes: Strigidae)
Very little is known about the helminth parasites of hawks and owls of Arkansas. We had the opportunity to salvage 2 road-killed raptors, a red-shouldered hawk (Buteo lineatus) and a great horned owl (Bubo virginianus) from the state and examine them for ecto- and endoparasites. Found were chewing lice (Degeeriella fulva) and a nematode (Porrocaecum angusticolle) on/in B. lineatus, and 3 digenean trematodes (Echinoparyphium sp., Strigea elegans, Neodiplostomum americanum), and nematode eggs (Capillaria sp.) in B. virginianus. We document 6 new distributional records for these parasites
Deformed Shape Calculation of a Full-Scale Wing Using Fiber Optic Strain Data from a Ground Loads Test
A ground loads test of a full-scale wing (175-ft span) was conducted using a fiber optic strain-sensing system to obtain distributed surface strain data. These data were input into previously developed deformed shape equations to calculate the wing s bending and twist deformation. A photogrammetry system measured actual shape deformation. The wing deflections reached 100 percent of the positive design limit load (equivalent to 3 g) and 97 percent of the negative design limit load (equivalent to -1 g). The calculated wing bending results were in excellent agreement with the actual bending; tip deflections were within +/- 2.7 in. (out of 155-in. max deflection) for 91 percent of the load steps. Experimental testing revealed valuable opportunities for improving the deformed shape equations robustness to real world (not perfect) strain data, which previous analytical testing did not detect. These improvements, which include filtering methods developed in this work, minimize errors due to numerical anomalies discovered in the remaining 9 percent of the load steps. As a result, all load steps attained +/- 2.7 in. accuracy. Wing twist results were very sensitive to errors in bending and require further development. A sensitivity analysis and recommendations for fiber implementation practices, along with, effective filtering methods are include
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