scholarly journals Recursion relation for boundary contribution

2015 ◽  
Vol 2015 (6) ◽  
Author(s):  
Qingjun Jin ◽  
Bo Feng
2010 ◽  
Vol 2010 (1) ◽  
Author(s):  
Bo Feng ◽  
Junqi Wang ◽  
Yihong Wang ◽  
Zhibai Zhang

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Congkao Wen ◽  
Shun-Qing Zhang

Abstract We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2, 0) supergravity on AdS3× S3, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.


Author(s):  
Maxim Kazarian

Abstract We derive a quadratic recursion relation for the linear Hodge integrals of the form $\langle \tau _{2}^{n}\lambda _{k}\rangle $ . These numbers are used in a formula for Masur-Veech volumes of moduli spaces of quadratic differentials discovered by Chen, Möller and Sauvaget. Therefore, our recursion provides an efficient way of computing these volumes.


1993 ◽  
Vol 08 (06) ◽  
pp. 1139-1152
Author(s):  
M.A. MARTÍN-DELGADO

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.


2010 ◽  
Vol 19 (12) ◽  
pp. 1571-1595 ◽  
Author(s):  
STAVROS GAROUFALIDIS ◽  
XINYU SUN

The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative A-polynomial of twist knots. Our multivariable creative telescoping method allows us to compute linear recursions for sums of the form [Formula: see text] given a recursion relation for [Formula: see text] and the hypergeometric kernel c(n, k). As an application of our method, we explicitly compute the non-commutative A-polynomial for twist knots with -15 and 15 crossings. The non-commutative A-polynomial of a knot encodes the monic, linear, minimal order q-difference equation satisfied by the sequence of colored Jones polynomials of the knot. Its specialization to q = 1 is conjectured to be the better-known A-polynomial of a knot, which encodes important information about the geometry and topology of the knot complement. Unlike the case of the Jones polynomial, which is easily computable for knots with 50 crossings, the A-polynomial is harder to compute and already unknown for some knots with 12 crossings.


2019 ◽  
Vol 34 (28) ◽  
pp. 1950223 ◽  
Author(s):  
A. D. Alhaidari

We use the Tridiagonal Representation Approach (TRA) to obtain exact bound states solution (energy spectrum and wave function) of the Schrödinger equation for a three-parameter short-range potential with [Formula: see text], [Formula: see text] and [Formula: see text] singularities at the origin. The solution is a finite series of square-integrable functions with expansion coefficients that satisfy a three-term recursion relation. The solution of the recursion is a non-conventional orthogonal polynomial with discrete spectrum. The results of this work could be used to study the binding of an electron to a molecule with an effective electric quadrupole moment which has the same [Formula: see text] singularity.


1992 ◽  
Vol 29 (02) ◽  
pp. 255-267 ◽  
Author(s):  
W. T. Ma ◽  
G. vH. Sandri ◽  
S. Sarkar

The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency: p 0 = e–m ; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n 2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for the z-transform of the distribution is also reported.


1997 ◽  
Vol 09 (01) ◽  
pp. 59-75
Author(s):  
Kenji Mohri

A residue formula which evaluates any correlation function of topological SUn Yang–Mills theory with arbitrary magnetic flux insertion in two-dimensions are obtained. Deformations of the system by two-form operators are investigated in some detail. The method of the diagonalization of a matrix-valued field turns out to be useful to compute various physical quantities. As an application we find the operator that contracts a handle of a Riemann surface and a genus recursion relation.


It is shown that the dipole moment function, μ ( R , Z a , Z b ), for an arbitrary bound electronic state of a one-electron diatomic molecule, with inter-nuclear distance R and atomic numbers Z a , Z b may be expressed exactly in terms of the separation eigenconstant C and the electronic energy eigenvalue W of the Schrödinger equation by means of the Hellmann-Feynman theorem and a new recursion relation. The formula is used to investigate the behaviour of μ in the vicinity of the united atom and when the nuclei are far apart. The generalization required to extend the relation to other expectation values is derived in an appendix.


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