Abstract Small-amplitude, traveling, space periodic solutions –called Stokes waves– of the 2 dimensional gravity water waves equations in deep are linearly unstable with respect to long-wave perturbations, as predicted by Benjamin and Feir 1967. We completely describe behavior four eigenvalues close zero linearized at wave, Floquet exponent is turned on. prove particular conjecture that a pair ...

In this paper, we propose a method using continuous wavelets to study the multivariate fractional Brownian motion through deviations of transformed random process find an efficient estimate Hurst exponent eigenvalue regression covariance matrix. The results simulations experiments shown that performance proposed estimator was in bias but variance get increase as signal change from short long me...

We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and ...

Indentation is a new method for estimating residual stress. The plastic behavior of the materials under study can affect indentation parameters and, thus, influences the results of residual stress measurement. In this paper, the effect of yield stress and work-hardening exponent on the accuracy of residual stress measurements in steels and aluminums was studied. Results showed that, for m...

Let us consider a homogeneous Markov chain with discrete time and with a finite set of states are nonrecurrent. The goal of this work is to study frequencies of trajectories in this chain, i.e., " words " composed of symbols E 1 ,. .. , E n ending with the " space " E 0. Let us order words according to their probabilities ; denote by p(t) the probability of the tth word in this list. In this pa...

The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. Th...

We consider generalized linear stochastic dynamical systems with secondorder state transition matrices. The entries of the matrix are assumed to be either independent and exponentially distributed or equal to zero. We give an overview of new results on evaluation of asymptotic growth rate of the system state vector, which is called the Lyapunov exponent of the system.

In this note we prove injectivity and relative asphericity for “layered” systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. We also give an elementary geometric proof of a result due to Bogley–Pride and Serre that is used in the proof of the main theorem. AMS Classification 20E22, 20F05; 57M20, 57Q05

In this note we prove injectivity and relative asphericity for “layered” systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. We also give elementary geometric proofs of results due to Bogley–Pride and Serre that are used in the proof of the main theorem. AMS Classification 20E22, 20F05; 57M20, 57Q05