We analyze a routing scheme for a broad class of networks which converges (in the Cesaro sense) with probability one to the set of approximate Cesaro–Wardrop equilibria, an extension of the notion of a Wardrop equilibrium. The network model allows for wireline networks where delays are caused by flows on links, as well as wireless networks, a primary motivation for us, where delays are caused b...

On the OrliczCesaro sequence spaces ( ces ) which are defined by using Orlicz function , we show that the space ces equipped with both Amemiya and Luxemburg norms possesses uniform Opial property and uniform Kadec-Klee property if satisfy the 52 -condition.

The Zhao-Woodroofe condition has been introduced in [19] and it is a necessary and sufficient condition for the existence of a martingale approximation of a causal stationary process. Here, a nonadapted version is given and the convergence of Cesaro averages is replaced by a convergence of a subsequence. The nonadapted version is of a different form than in other cases, e.g. of Wu-Woodroofe or ...

A local limit theorem is proved for partial sums of a hidden Markov chain, assuming global asymptotic normality for a related sum, a fairly weak mixing condition, and a non-lattice condition. The proof proceeds by a study of the conditional characteristic functions, the analysis of which relies heavily on a theorem from Breiman (1968). The paper concludes with a Cesaro type limit theorem for th...

Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for Macdonald function Kiτ(x). The results can be applied, instance, to study summability of divergent Kontorovich-Lebedev integrals in sense Jones. Namely, we answer affirmatively a question (cf. [Ehrenmark U. Summability experiments class inverse transforms. Comput Math Appl. 2018;76(1):141–154.]...

A general theorem concerning many absolute summability methods is proved. 2000 Mathematics Subject Classification. 40F05, 40G05, 40D15, 40D25.

Pagano, L., Cornely, O.A., Busca, A., Caira, M., Cesaro, S., Gasbarrino, C., Girmenia, C., Heinz, W.J., Herbrecht, R., Lass-Flörl, C., Nosari, A., Potenza, L., Racil, Z., Rickerts, V., Sheppard, D.C., Simon, A., Ullmann, A.J., Valentini, C.G., Vehreschild, J.J., Candoni, A., Vehreschild, M.J.G.T. Combined antifungal approach for the treatment of invasive mucormycosis in patients with hematologi...

An entangled ergodic theorem was introduced in [1] in connection with the quantum central limit theorem, and clearly formulated in [6]. Namely, let U be a unitary operator on the Hilbert space H, and for m ≥ k, α : {1, . . . , m} 7→ {1, . . . , k} a partition of the set {1, . . . , m} in k parts. The entangled ergodic theorem concerns the convergence in the strong, or merely weak (s–limit, or w...