3,457 research outputs found
Raising and lowering operators, factorization and differential/difference operators of hypergeometric type
Starting from Rodrigues formula we present a general construction of raising
and lowering operators for orthogonal polynomials of continuous and discrete
variable on uniform lattice. In order to have these operators mutually adjoint
we introduce orthonormal functions with respect to the scalar product of unit
weight. Using the Infeld-Hull factorization method, we generate from the
raising and lowering operators the second order self-adjoint
differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission
S-duality and 2d Topological QFT
We study the superconformal index for the class of N=2 4d superconformal
field theories recently introduced by Gaiotto. These theories are defined by
compactifying the (2,0) 6d theory on a Riemann surface with punctures. We
interpret the index of the 4d theory associated to an n-punctured Riemann
surface as the n-point correlation function of a 2d topological QFT living on
the surface. Invariance of the index under generalized S-duality
transformations (the mapping class group of the Riemann surface) translates
into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for
which the 4d SCFTs have a Lagrangian realization, the structure constants and
metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma
functions. Associativity then holds thanks to a remarkable symmetry of an
elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure
Superconformal indices of three-dimensional theories related by mirror symmetry
Recently, Kim and Imamura and Yokoyama derived an exact formula for
superconformal indices in three-dimensional field theories. Using their
results, we prove analytically the equality of superconformal indices in some
U(1)-gauge group theories related by the mirror symmetry. The proofs are based
on the well known identities of the theory of -special functions. We also
suggest the general index formula taking into account the global
symmetry present for abelian theories.Comment: 17 pages; minor change
Advanced Method for Forecasting and Warning of Severe Convective Weather and Local-scale Hazards
Hurricane Ida ferociously affected many south-eastern and eastern parts of the United States, making it one of the strongest hurricanes in recent years. Advanced forecast and warning tool has been used to track the path of the ex-Hurricane, Ida, as it left New Orleans on its way towards the northeast, accurately predicting significant supercell development above New York City on September 01, 2021. This advanced method accurately detected the area with the highest possible level of convective instability with 24-h lead time and even Level 5, devised in the categorical outlooks legend of the system. Therefore, an extreme level implied a very high probability of the local-scale hazard occurring above the NYC. Cloud model output fields (updrafts and downdrafts, wind shear, near-surface convergence, the vertical component of relative vorticity) show the rapid development of a strong supercell storm with rotating updrafts and a mesocyclone. The characteristic hook-shaped echo signature visible in the reflectivity patterns indicates a signal for a highly precipitable (HP) supercell with the possibility of tornado initiation. Open boundary conditions represent a good basis for simulating a tornado that evolved from a supercell storm, initialized with initial data obtained from a real-time simulation in the period when the bow echo and tornado-like signature occurred. Тhe modeled results agree well with the observations
q-Ultraspherical polynomials for q a root of unity
Properties of the -ultraspherical polynomials for being a primitive
root of unity are derived using a formalism of the algebra. The
orthogonality condition for these polynomials provides a new class of
trigonometric identities representing discrete finite-dimensional analogs of
-beta integrals of Ramanujan.Comment: 7 pages, LATE
Distinct Patterns of Expression and Evolution of Intronless and Intron-Containing Mammalian Genes
Comparison of expression levels and breadth and evolutionary rates of intronless and intron-containing mammalian genes shows that intronless genes are expressed at lower levels, tend to be tissue specific, and evolve significantly faster than spliced genes. By contrast, monomorphic spliced genes that are not subject to detectable alternative splicing and polymorphic alternatively spliced genes show similar statistically indistinguishable patterns of expression and evolution. Alternative splicing is most common in ancient genes, whereas intronless genes appear to have relatively recent origins. These results imply tight coupling between different stages of gene expression, in particular, transcription, splicing, and nucleocytosolic transport of transcripts, and suggest that formation of intronless genes is an important route of evolution of novel tissue-specific functions in animals
An E7 Surprise
We explore some curious implications of Seiberg duality for an SU(2)
four-dimensional gauge theory with eight chiral doublets. We argue that two
copies of the theory can be deformed by an exactly marginal quartic
superpotential so that they acquire an enhanced E7 flavor symmetry. We argue
that a single copy of the theory can be used to define an E7-invariant
superconformal boundary condition for a theory of 28 five-dimensional free
hypermultiplets. Finally, we derive similar statements for three-dimensional
gauge theories such as an SU(2) gauge theory with six chiral doublets or Nf=4
SQED.Comment: 27 page
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