We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization [1] leads to a formulation in terms of gauge invariant but curvilinear variables. Remainders of the curved space are Jacobians, an effective potential, and sign factors just as for the problem of a particle in a box. Based on this resu...

Let Xi, i ∈ N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a smooth enough mapping from B intoR. An asymptotic evaluation of Zn = E(exp(nΦ( ∑n i=1 Xi/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305–318] and Kusuoka and Liang [Probab. Theory Related Fields 116 (2000) 221–238]. In this paper, a...

The method of largest remainders (Hamilton) is used for allotment of 288 of the seats among the 56 Greek constituencies. This method possesses various paradoxes as was observed through two centuries of application. So we propose a modification where the seats are allocated at a first stage by the lower Hare-Quota and the additional ones using the method of major fractions (Webster) restricted s...

This paper deals with the summation problem of power series of the form Sb a(f ;x) = ∑ a≤k≤b f(k)x k, where 0 ≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) is a differentiable function defined on [a, b). We present a symbolic summation operator with its various expansions, and construct several summation formulas with estimable remainders for Sb a(f ;x), by the ...

A bstract We present the complete set of leading-color two-loop contributions required to obtain next-to-next-to-leading-order (NNLO) QCD corrections three-jet production at hadron colliders. analytic expressions for a generating finite remainders, valid in physical region production. The continuation known Euclidean-region results is determined from small numerical evaluations amplitudes. that...

Motivated by several conjectures posed in the paper "F. Qi and A.-Q. Liu, Completely monotonic degrees for a difference between logarithmic psi functions, J. Comput. Appl. Math., vol. 361, pp. 366--371 (2019); available online at https://doi.org/10.1016/j.cam.2019.05.001", authors compute completely of remainders asymptotic expansions logarithm gamma function digamma function.

A bstract We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up two loops in QCD. reconstruct form finite remainders from numerical evaluations over fields including all colour contributions. Compact expressions are found using pentagon function basis. provide a fast and stable implementation for colour- helicity-summed int...