φ production in In–In collisions at 158 A GeV

The NA60 experiment has measured muon pair production in In–In collisions at 158 AGeV at the CERN SPS. This paper presents a high statistics measurement of φ→μ μ meson production. Differential spectra, yields, mass and width are measured as a function of centrality and compared to previous measurements in other colliding systems at the same energy. The width of the rapidity distribution is found to be constant as a function of centrality, compatible with previous results. The decay muon polar angle distribution is measured in several reference frames. No evidence of polarization is found as a function of transverse momentum and centrality. The analysis of the p _T spectra shows that the φ has a small radial flow, implying a weak coupling to the medium. The T _eff parameter measured in In–In collisions suggests that the high value observed in Pb–Pb in the kaon channel is difficult to reconcile with radial flow alone. The absolute yield is compared to results in Pb–Pb collisions: though significantly smaller than measured by NA50 in the muon channel, it is found to exceed the NA49 and CERES data in the kaon channel at any centrality. The mass and width are found to be compatible with the PDG values at any centrality and at any p _T : no evidence for in-medium modifications is observed.     

Characterization of a class of graphs related to pairs of disjoint matchings

For a given graph consider a pair of disjoint matchings the union of which contains as many edges as possible. Furthermore, consider the ratio of the cardinalities of a maximum matching and the largest matching in those pairs. It is known that for any graph is the tight upper bound for this ratio. We characterize the class of graphs for which it is precisely . Our characterization implies that these graphs contain a spanning subgraph, every connected component of which is the minimal graph of this class.     

Upper Bounds for α-Domination Parameters

We provide a new upper bound for the α-domination number in terms of a parameter α, 0 < α ≤ 1, and graph vertex degrees. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic construction is used to generalise another well-known upper bound for the classical domination in graphs. Using a different probabilistic construction, we prove similar upper bounds for the α-rate domination number, which combines the concepts of α-domination and k-tuple domination.     

ASYMPTOTIC BEHAVIOR OF THE ECKHOFF APPROXIMATION IN BIVARIATE CASE

The paper considers the Krylov-Lanczos and the Eckhoff approximations for recovering a bivariate function using limited number of its Fourier coefficients. These approximations are based on certain corrections associated with jumps in the partial derivatives of the approximated function. Approximation of the exact jumps is accomplished by solution of systems of linear equations along the idea of Eckhoff. Asymptotic behaviors of the approximate jumps and the Eckhoff approximation are studied. Exact constants of the asymptotic errors are computed. Numerical experiments validate theoretical investigations.     

Noncomplanarity effects in the one-dimensional spin-dependent scattering

The scattering of a spin-polarized quantum wave on a potential barrier is investigated. The vectors of spin-polarization of incident wave and the internal magnetic field (magnetization) of the barrier are not generally located in the same plane and they form a noncomplanar system. The dependences of the polarization vectors of waves scattered forward and backward on the degrees of freedom determining the orientation of the barrier magnetization are investigated.     

One-phase parabolic free boundary problem in a convex ring

This paper studies a free boundary problem for the heat equation in a convex ring. It is proved that the considered problem has unique solution under some conditions on the initial data.     

Asymptotic behavior of the Eckhoff method for convergence acceleration of trigonometric interpolation

Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the jumps are approximated by solution of a system of linear equations. The accuracy of the jump approximation is explored and the corresponding asymptotic error of interpolation is derived. Numerical results validate theoretical estimates.     

On scattering of the spin-non-polarized wave on the two-barrier noncomplanar system

The scattering of a spin-non-polarized wave on a structure the potential profile of which contains two identical barriers with the noncomplanar internal magnetic field inductions is considered. The dependences of the transport characteristics of the structure on the degrees of freedom describing the noncomplanarity of this structure are investigated.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.