1,042 research outputs found
On computational complexity of Siegel Julia sets
It has been previously shown by two of the authors that some polynomial Julia
sets are algorithmically impossible to draw with arbitrary magnification. On
the other hand, for a large class of examples the problem of drawing a picture
has polynomial complexity. In this paper we demonstrate the existence of
computable quadratic Julia sets whose computational complexity is arbitrarily
high.Comment: Updated version, to appear in Commun. Math. Phy
Intersection cohomology of Drinfeld's compactifications
Let be a smooth complete curve, be a reductive group and
a parabolic.
Following Drinfeld, one defines a compactification \widetilde{\on{Bun}}_P
of the moduli stack of -bundles on .
The present paper is concerned with the explicit description of the
Intersection Cohomology sheaf of \widetilde{\on{Bun}}_P. The description is
given in terms of the combinatorics of the Langlands dual Lie algebra
.Comment: An erratum adde
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Intersection cohomology of Drinfeld‚s compactifications
Let X be a smooth complete curve, G be a reductive group and a parabolic. Following Drinfeld, one defines a (relative) compactification of the moduli stack of P-bundles on X. The present paper is concerned with the explicit description of the Intersection Cohomology sheaf of . The description is given in terms of the combinatorics of the Langlands dual Lie algebra
Essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs
We give sufficient conditions for essential self-adjointness of magnetic
Schr\"odinger operators on locally finite graphs. Two of the main theorems of
the present paper generalize recent results of Torki-Hamza.Comment: 14 pages; The present version differs from the original version as
follows: the ordering of presentation has been modified in several places,
more details have been provided in several places, some notations have been
changed, two examples have been added, and several new references have been
inserted. The final version of this preprint will appear in Integral
Equations and Operator Theor
Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via K-theory of affine Laumon spaces
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps
from the projective line to the flag variety of GL_n. We construct the action
of the quantum loop algebra U_v(Lsl_n) in the equivariant K-theory of Laumon
spaces by certain natural correspondences. Also we construct the action of the
quantum toroidal algebra U^{tor}_v(Lsl}_n) in the equivariant K-theory of the
affine version of Laumon spaces. We write down explicit formulae for this
action in the affine Gelfand-Tsetlin base, corresponding to the fixed point
base in the localized equivariant K-theory.Comment: v2: multiple typos fixed, proofs of Theorems 4.13 and 4.19 expanded,
23 pages. v3: formulas of Theorems 4.9 and 4.13 corrected, resulting minor
changes added. arXiv admin note: text overlap with arXiv:0812.4656,
arXiv:math/0503456, arXiv:0806.0072 by other author
Spatial and temporal characterization of a Bessel beam produced using a conical mirror
We experimentally analyze a Bessel beam produced with a conical mirror,
paying particular attention to its superluminal and diffraction-free
properties. We spatially characterized the beam in the radial and on-axis
dimensions, and verified that the central peak does not spread over a
propagation distance of 73 cm. In addition, we measured the superluminal phase
and group velocities of the beam in free space. Both spatial and temporal
measurements show good agreement with the theoretical predictions.Comment: 5 pages, 6 figure
On algebraic integrability of the deformed elliptic Calogero--Moser problem
Algebraic integrability of the elliptic Calogero--Moser quantum problem
related to the deformed root systems \pbf{A_{2}(2)} is proved. Explicit
formulae for integrals are found
Mesoscopic Superconducting Disc with Short-Range Columnar Defects
Short-range columnar defects essentially influence the magnetic properties of
a mesoscopic superconducting disc.They help the penetration of vortices into
the sample, thereby decrease the sample magnetization and reduce the upper
critical field. Even the presence of weak defects split a giant vortex state
(usually appearing in a clean disc in the vicinity of the transition to a
normal state) into a number of vortices with smaller topological charges. In a
disc with a sufficient number of strong enough defects vortices are always
placed onto defects. The presence of defects lead to the appearance of
additional magnetization jumps related to the redistribution of vortices which
are already present on the defects and not to the penetration of new vortices.Comment: 14 pgs. RevTex, typos and figures corrected. Submitted to Phys. Rev.
Molecular Identification, Phylogenetic Status, and Geographic Distribution of Culicoides oxystoma (Diptera: Ceratopogonidae) in Israel
Culicoides oxystoma (Diptera: Ceratopogonidae) is an important vector species, reported mainly from Asia, with high potential to transmit viral diseases affecting livestock. In Japan, many arboviruses have been isolated from C. oxystoma, suggesting it as a key player in the epidemiology of several Culicoides-borne diseases. Over the years, C. oxystoma has also been reported in the Middle East region, including Israel. In this region, however, C. oxystoma cannot be easily distinguished morphologically from its sibling species included in the Culicoides schultzei complex. We therefore used genomic data for species identification and phylogeny resolution. Phylogenetic analyses based on internal transcribed spacer 1 (ITS-1) of ribosomal DNA and the mitochondrial gene encoding cytochrome oxidase subunit I (COI) showed that C. oxystoma from Israel is closely related to C. oxystoma from Japan. Using differential probing PCR, we showed that C. oxystoma is distributed all over the country, especially in Mediterranean climate regions. Culicoides oxystoma is less common or even absent in arid regions, while the other genetic cluster of C. schultzei complex was found only in the east of the country (mostly arid and semiarid regions). The molecular finding of C. oxystoma in wide geographical regions, together with its high proportion in the general Culicoides population and its vectoring potential, imply that it may be an important vector species in the Middle East
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