[en] Because of the large coupling constant perturbation theory does not work in quantum chromodynamics at low energies. Attempts are made to find an approximation, which in zeroth order results in reasonable statements about the hadronic spectrum. The CPsup(N-1) is of particular interest in this connection. Section 1 is on the classical CPsup(N-1)-model; section 2 on generating functionals and operator product insertions; section 3 on 1/N expansion of the CPsup(N-1)-model and section 4 on the supersymmetric CPsup(N-1)-model. (G.Q.)

[en] The conjecture that ζ(4) satisfies ζ(4)= 36/17 Σ_n=1^∞ ((n!)²/(2n)! 1/n⁴ is proved analytically. (orig.)

[en] We have rigorously derived the perimeter generating function for the mean-squared radius of gyration of convex polygons. This function was first conjectured by Jensen. His nonrigorous result is based on the analysis of the long series expansions.

[en] It is proved that if f and g are complex-valued arithmetical functions such that g(2n + 1) - Af(n) → 0 (n → ∞), A ≠ 0, then either f(n) → 0(n → ∞), or f(n) = n^s, 0 ≤ Res < 1 and A -f(2), g(n) = f(n) for every odd n. In this paper the case when f and g are pairs of multiplicative functions is considered. (author). 3 refs

[en] For a general Franklin system {f_n}_n=0^∞ generated by an admissible sequence T, we obtain necessary and sufficient conditions on T under which the corresponding system is a basis or an unconditional basis in B¹[0,1]

[en] In this work, we set the conditions under which matrix functions are expanded into matrix trigonometric series.

[en] Higher twists are important in large n moments, however, one must be cautious in this region because the perturbative expansion of the twist-two component as well as other expansions are ill behaved, showing an early divergence. Estimates can help in differentiating between different schemes and analyzing their behavior

[en] A reformulation of rational approximants to holomorphic function in Csup(n) is given. A convergence theorem providing the multidegree of convergence for (μ, 1)-approximants under certain restrictions is discussed. (author)

No abstract available

[en] Several decades of parallel developments in the calculation and analysis of series expansions for lattice statistics have led to many new insights into critical phenomena. These studies have centered on the use of the finite lattice method for series expansions in lattice statistics and the use of differential approximants in analysing such series. One of these strands of research ultimately led to the result that a number of unsolved lattice statistics problems cannot be expressed as D-finite functions. Somewhat ironically, given power and success of differential approximants in analysing series, neither the assumed functional form, nor any finite generalisation thereof can fit such cases exactly. (topical review)