The harmonic polylogarithms (hpl’s) are introduced. They are a generalization of Nielsen’s polylogarithms, satisfying a product algebra (the product of two hpl’s is in turn a combination of hpl’s) and forming a set closed under the transformation of the arguments x = 1/z and x = (1−t)/(1+t). The coefficients of their expansions and their Mellin transforms are harmonic sums. AMS(1991) subject cl...

Oneand two-dimensional harmonic polylogarithms, HPLs and GPLs, appear in calculations of multi-loop integrals. We discuss them in the context of analytical solutions for two-loop master integrals in the case of massive Bhabha scattering in QED. For the GPLs we discuss analytical representations, conformal transformations, and also their transformations corresponding to relations between master ...

All coboundary Lie bialgebras and their corresponding Poisson–Lie structures are constructed for the oscillator algebra generated by {N,A+, A−,M}. Quantum oscillator algebras are derived from these bialgebras by using the Lyakhovsky and Mudrov formalism and, for some cases, quantizations at both algebra and group levels are obtained, including their universal R–matrices.

Two dimensions Mathieu equation containing periodic terms as well as the delayed parameters has been investigated in the present work. The present system represents to a generalized form of the one-dimension delay Mathieu equation. The mathematical difficulty for delay the coupled Mathieu equation has been overcome by using the matrices method. Properties of inverse complex matrices enable us t...

*Correspondence: [email protected] 2School of Mathematical Sciences, Soochow University, Suzhou, 215006, China Full list of author information is available at the end of the article Abstract The existence of infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities is shown. This result is a corollary of two theorems. These theorems, one for a weak sub-quadratic...

We present a method of producing single attosecond pulses by high order harmonic generation with multi-cycle nonlinear chirped driver laser pulses. The symmetry of the laser field in several optical cycles near the pulse center is dramatically broken, and then the photons which cover a much broad spectrum burst almost only in one optical cycle. So an ultra-broad continuum spectrum appears in th...

We establish connections between different gauge-theoretical problems in high and low dimensions. In particular we show that higher dimensional asd equations on total spaces of spinor bundles over low dimensional manifolds can be interpreted as Taubes-Pidstrygach’s generalisation of Seiberg-Witten equations. By collapsing each fibre of the spinor bundle to a point, we relate solutions of Taubes...

We show how backreaction of the inflaton potential energy on heavy scalar fields can flatten the inflationary potential, as the heavy fields adjust to their most energetically favorable configuration. This mechanism operates in previous UV-complete examples of axion monodromy inflation – flattening a would-be quadratic potential to one linear in the inflaton field – but occurs more generally, a...

(1.1) Some of the main results described in [Report] are the following (in rough terms; notations and precise references will be given below): (1) A map (f>:{M,g)-+(N,h) between Riemannian manifolds which is continuous and of class L\ is harmonic if and only if it is a critical point of the energy functional. (2) Let (M, g) and (N, h) be compact, and <̂ 0: (M, g) -> (N, h) a map. Then ^0 can be ...