171 research outputs found
The Laplace equation for the exterior of the Hankel contour and novel identities for hypergeometric functions
By employing conformal mappings, it is possible to express the solution of
certain boundary value problems for the Laplace equation in terms of a single
integral involving the given boundary data. We show that such explicit formulae
can be used to obtain novel identities for special functions. A convenient tool
for deriving this type of identities is the so-called \emph{global relation},
which has appeared recently in a wide range of boundary value problems. As a
concrete application, we analyze the Neumann boundary value problem for the
Laplace equation in the exterior of the so-called Hankel contour, which is the
contour that appears in the definition of both the gamma and the Riemann zeta
functions. By utilizing the explicit solution of this problem, we derive a
plethora of novel identities involving the hypergeometric function
Dynamic model of spherical perturbations in the Friedman universe. III. Automodel solutions
A class of exact spherically symmetric perturbations of retarding automodel
solutions linearized around Friedman background of Einstein equations for an
ideal fluid with an arbitrary barotrope value is obtained and investigated.Comment: 12 pages, 4 figures, 8 reference
A Feynman integral in Lifshitz-point and Lorentz-violating theories in R<sup>D</sup> âš R<i><sup>m</sup></i>
We evaluate a 1-loop, 2-point, massless Feynman integral ID,m(p,q) relevant for perturbative field theoretic calculations in strongly anisotropic d=D+m dimensional spaces given by the direct sum RD âš Rm . Our results are valid in the whole convergence region of the integral for generic (noninteger) codimensions D and m. We obtain series expansions of ID,m(p,q) in terms of powers of the variable X:=4p2/q4, where p=|p|, q=|q|, p Đ RD, q Đ Rm, and in terms of generalised hypergeometric functions 3F2(âX), when X<1. These are subsequently analytically continued to the complementary region Xâ„1. The asymptotic expansion in inverse powers of X1/2 is derived. The correctness of the results is supported by agreement with previously known special cases and extensive numerical calculations
On beta-function of tube of light cone
We construct -function of the Hermitian symmetric space
\OO(n,2)/\OO(n)\times \OO(2) or equivalently of the tube in $C^{n+1}Comment: 7 page
More three-point correlators of giant magnons with finite size
In the framework of the semiclassical approach, we compute the normalized
structure constants in three-point correlation functions, when two of the
vertex operators correspond to heavy string states, while the third vertex
corresponds to a light state. This is done for the case when the heavy string
states are finite-size giant magnons with one or two angular momenta, and for
two different choices of the light state, corresponding to dilaton operator and
primary scalar operator. The relevant operators in the dual gauge theory are
Tr(F_{\mu\nu}^2 Z^j+...) and Tr(Z^j). We first consider the case of AdS_5 x S^5
and N = 4 super Yang-Mills. Then we extend the obtained results to the
gamma-deformed AdS_5 x S^5_\gamma, dual to N = 1 super Yang-Mills theory,
arising as an exactly marginal deformation of N = 4 super Yang-Mills.Comment: 14 pages, no figure
Recommended from our members
Hybrid spectrum access with relay assisting both primary and secondary networks under imperfect spectrum sensing
This paper proposes a novel hybrid interweave-underlay spectrum access for a cognitive amplify-and-forward relay network where the relay forwards the signals of both the primary and secondary networks. In particular, the secondary network (SN) opportunistically operates in interweave spectrum access mode when the primary network (PN) is sensed to be inactive and switches to underlay spectrum access mode if the SN detects that the PN is active. A continuous-time Markov chain approach is utilized to model the state transitions of the system. This enables us to obtain the probability of each state in the Markov chain. Based on these probabilities and taking into account the impact of imperfect spectrum sensing of the SN, the probability of each operation mode of the hybrid scheme is obtained. To assess the performance of the PN and SN, we derive analytical expressions for the outage probability, outage capacity, and symbol error rate over Nakagami-m fading channels. Furthermore, we present comparisons between the performance of underlay cognitive cooperative radio networks (CCRNs) and the performance of the considered hybrid interweave-underlay CCRN in order to reveal the advantages of the proposed hybrid spectrum access scheme. Eventually, with the assistance of the secondary relay, performance improvements for the PN are illustrated by means of selected numerical results
The Stokes Phenomenon and Quantum Tunneling for de Sitter Radiation in Nonstationary Coordinates
We study quantum tunneling for the de Sitter radiation in the planar
coordinates and global coordinates, which are nonstationary coordinates and
describe the expanding geometry. Using the phase-integral approximation for the
Hamilton-Jacobi action in the complex plane of time, we obtain the
particle-production rate in both coordinates and derive the additional
sinusoidal factor depending on the dimensionality of spacetime and the quantum
number for spherical harmonics in the global coordinates. This approach
resolves the factor of two problem in the tunneling method.Comment: LaTex 10 pages, no figur
On a new class of summation formulas involving the generalized hypergeometric F 2 2 polynomial
A note on the Virasoro blocks at order 1/c
We derive an explicit expression for the contribution to the Virasoro
blocks in 2D CFT in the limit of large with fixed values of the operators'
dimensions. We follow the direct approach of orthonormalising, at order ,
the space of the Virasoro descendants to obtain the blocks as a series
expansion around . For generic conformal weights this expansion can be
summed in terms of hypergeometric functions and their first derivatives with
respect to one parameter. For integer conformal weights we provide an
equivalent expression written in terms of a finite sum of undifferentiated
hypergeometric functions. These results make the monodromies of the blocks
around manifest.Comment: 13 pages; v2: added references to previous wor
- âŠ