Interior C 1, γ-Regularity for Weak Solutions of Nonlinear Second Order Parabolic Systems

The interior C ^{γ, γ/2}-regularity for the first gradient with respect to the space variables of a weak solution to a class of nonlinear second order parabolic systems is proven under the assumption that oscillations of coefficients are controlled by the ellipticity constant.     

On random permutations without cycles of some lenghts

We deal with random permutations of the symmetric group S_Nendowed with the Haar probability measure. The main purpose of the remark is to obtain uniform lower estimates for the probability of a permutation without cycles having lengths in some J ⊂ {1, . . . . N} . ThesetJcan itself depend on N. The only information used is a bound for the sum of reciprocals of elements in J.     

Lyndon factorization of sturmian words

We express any general characteristic sturmian word as a unique infinite non-increasing product of Lyndon words. Using this identity, we give a new ω-division for characteristic sturmian words. We also give a short proof of a result by Berstel and de Luca (Sturmian words, Lyndon words and trees, Theoret. Comput. Sci., 178 (1997) 171–203.); more precisely, we show that the set of factors of sturmian words that qualify as Lyndon words is the set of primitive Christoffel words.     

A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series

The object of this research in the sphere of queueing theory is the law of the iterated logarithm under the conditions of heavy traffic in queues in series. In this paper, the laws of the iterated logarithm are proved for the values of important probabilistic characteristics of the queueing system, like the sojourn time of a customer, and maximum of the sojourn time of a customer. Also, we prove that the sojourn time of a customer can be approximated by some recurrent functional. We also provide the results of statistical simulations for various system parameters and distributions.