Bottomonium dipion transitions

Dipion transitions of the subthreshold bottomonium levels $\Upsilon (nS)\to \Upsilon (n'S) \pi\pi$ with $n>n', n=2,3,4, n'=1,2$ are studied in the framework of the chiral decay Lagrangian, derived earlier. The channels $B\bar B, B\bar B^*+ c.c, B^* \bar B^*$ are considered in the intermediate state and realistic wave functions of $\Upsilon (n S),B$ and $B^*$ are used in the overlap matrix elements. Imposing the Adler zero requirement on the transition matrix element, one obtains 2d and 1d dipion spectra in reasonable agreement with experiment.Comment: 34 pages, 18 figure

PGGA: A predictable and grouped genetic algorithm for job scheduling

This paper presents a predictable and grouped genetic algorithm (PGGA) for job scheduling. The novelty of the PGGA is twofold: (1) a job workload estimation algorithm is designed to estimate a job workload based on its historical execution records, (2) the divisible load theory (DLT) is employed to predict an optimal fitness value by which the PGGA speeds up the convergence process in searching a large scheduling space. Comparison with traditional scheduling methods such as first-come-first-serve (FCFS) and random scheduling, heuristics such as a typical genetic algorithm, Min-Min and Max-Min indicates that the PGGA is more effective and efficient in finding optimal scheduling solutions

Legendre transformations on the triangular lattice

The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be considered as discrete analogues of relativistic Toda type lattices. Some of obtained equations are new, up to the author knowledge. As an example, one of them is studied in more details, in particular, its higher continuous symmetries and zero curvature representation are found.Comment: 13 pages, late

Elliptic operators in even subspaces

In the paper we consider the theory of elliptic operators acting in subspaces defined by pseudodifferential projections. This theory on closed manifolds is connected with the theory of boundary value problems for operators violating Atiyah-Bott condition. We prove an index formula for elliptic operators in subspaces defined by even projections on odd-dimensional manifolds and for boundary value problems, generalizing the classical result of Atiyah-Bott. Besides a topological contribution of Atiyah-Singer type, the index formulas contain an invariant of subspaces defined by even projections. This homotopy invariant can be expressed in terms of the eta-invariant. The results also shed new light on P.Gilkey's work on eta-invariants of even-order operators.Comment: 39 pages, 2 figure

Coupled-channel model for charmonium levels and an option for X(3872)

The effects of charmed meson loops on the spectrum of charmonium are considered, with special attention paid to the levels above open-charm threshold. It is found that the coupling to charmed mesons generates a structure at the D \bar{D}* threshold in the 1++ partial wave. The implications for the nature of the X(3872) state are discussed.Comment: 27 pages, 7 EPS figure

Lower-modular elements of the lattice of semigroup varieties. III

We completely determine all lower-modular elements of the lattice of all semigroup varieties. As a corollary, we show that a lower-modular element of this lattice is modular.Comment: 10 pages, 1 figur

Rapidity distribution of particle multiplicity in DIS at small x

Analytical study of the rapidity distribution of the final state particles in deep inelastic scattering at small x is presented. We separate and analyse three sources of particle production: fragmentation of the quark-antiquark pair, accompanying coherent soft gluon radiation due to octet color exchange in the t-channel, and fragmentation of gluons that form parton distribution functions. Connection to Catani-Ciafaloni-Fiorani-Marchesini (CCFM) equations and the role of gluon reggezation are also discussed.Comment: 14 pages, 6 Figures. Abstract extended, minor misprints corrected, derivations improved and explanations are streamlined. Published in Physics Letters, B