Light Mesons elm Form Factor and Running Coupling Effects

The pion and kaon electromagnetic form factors $F_{M}(Q^2)$ are calculated at the leading order of pQCD using the running coupling constant method. In computations dependence of the meson distribution amplitudes on the hard scale $Q^2$ is taken into account. The Borel transform and resummed expression for $F_{M}(Q^2)$ are found. The effect of the next-to-leading order term in expansion of $\alpha_{S}(\lambda Q^2)$ in terms of $\alpha_{S}(Q^2)$ on the pion form factor $F_{\pi}(Q^2)$ is discussed, comparison is made with the infrared matching scheme's result.Comment: 10 pages, 2 figures. Talk given at the Euroconference QCD98, Montpellier 2-8th July 1998, France; to appear in Proceeding

Power corrections to the π0γ\pi^0\gamma transition form factor and pion distribution amplitudes

Employing the standard hard-scattering approach and the running coupling method we calculate a class of power-suppressed corrections $\sim 1/Q^{2n},n=1,2,3,...$ to the electromagnetic $\pi^0\gamma$ transition form factor (FF) $Q^2F_{\pi\gamma}(Q^2)$ arising from the end-point $x \to 0,1$ integration regions. In the investigations we use a hard-scattering amplitude of the subprocess $\gamma+\gamma^{*} \to q +\bar{q}$, symmetrized under exchange $\mu_R^2 \leftrightarrow \bar{\mu}_R^2$ important for exclusive processes containing two external photons. In the computations the pion model distribution amplitudes (DA's) with one and two non-asymptotic terms are employed. The obtained predictions are compared with the CLEO data and constraints on the DA parameters $b_2(\mu_0^2)$ and $b_4(\mu_0^2)$ at the normalization point $\mu_0^2=1 GeV^2$ are extracted. Further restrictions on the pion DA's are deduced from the experimental data on the electromagnetic FF $F_{\pi}(Q^2)$.Comment: 23 pages, 6 figures; the version published in Phys. Rev. D69, 094010 (2004

Which Digraphs with Ring Structure are Essentially Cyclic?

We say that a digraph is essentially cyclic if its Laplacian spectrum is not completely real. The essential cyclicity implies the presence of directed cycles, but not vice versa. The problem of characterizing essential cyclicity in terms of graph topology is difficult and yet unsolved. Its solution is important for some applications of graph theory, including that in decentralized control. In the present paper, this problem is solved with respect to the class of digraphs with ring structure, which models some typical communication networks. It is shown that the digraphs in this class are essentially cyclic, except for certain specified digraphs. The main technical tool we employ is the Chebyshev polynomials of the second kind. A by-product of this study is a theorem on the zeros of polynomials that differ by one from the products of Chebyshev polynomials of the second kind. We also consider the problem of essential cyclicity for weighted digraphs and enumerate the spanning trees in some digraphs with ring structure.Comment: 19 pages, 8 figures, Advances in Applied Mathematics: accepted for publication (2010) http://dx.doi.org/10.1016/j.aam.2010.01.00

Matrices of forests, analysis of networks, and ranking problems

The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference relations / sports competitions are considered. It is shown that the vertex accessibility measure based on spanning forests has a number of desirable properties. An interpretation for the stochastic matrix of out-forests in terms of information dissemination is given.Comment: 8 pages. This article draws heavily from arXiv:math/0508171. Published in Proceedings of the First International Conference on Information Technology and Quantitative Management (ITQM 2013). This version contains some corrections and addition