Hypercyclic Abelian Semigroups of Matrices on Rn

We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on R^{n}. For finitely generated semigroups, this characterization is explicit and it is used to determine the minimal number of matrices in normal form over R which form a hypercyclic abelian semigroup on R^{n}. In particular, we show that no abelian semigroup generated by [(n+1)/2] matrices on Rn can be hyper-cyclic. ([ ] denotes the integer part).Comment: 19 page

A geometric control proof of linear Franks' lemma for geodesic flows

We provide an elementary proof of the Franks lemma for geodesic flows that uses basic tools of geometric control theory.Comment: 14 pages, 2 figure

Asymptotic Properties of Random Matrices of Long-Range Percolation Model

We study the spectral properties of matrices of long-range percolation model. These are N\times N random real symmetric matrices H=\{H(i,j)\}_{i,j} whose elements are independent random variables taking zero value with probability 1-\psi((i-j)/b), b\in \mathbb{R}^{+}, where $\psi$ is an even positive function with \psi(t)\le{1} and vanishing at infinity. We study the resolvent G(z)=(H-z)^{-1}, Imz\neq{0} in the limit N,b\to\infty, b=O(N^{\alpha}), 1/3<\alpha<1 and obtain the explicit expression T(z_{1},z_{2}) for the leading term of the correlation function of the normalized trace of resolvent g_{N,b}(z)=N^{-1}Tr G(z). We show that in the scaling limit of local correlations, this term leads to the expression (Nb)^{-1}T(\lambda+r_{1}/N+i0,\lambda+r_{2}/N-i0)= b^{-1}\sqrt{N}|r_{1}-r_{2}|^{-3/2}(1+o(1)) found earlier by other authors for band random matrix ensembles. This shows that the ratio $b^{2}/N$ is the correct scale for the eigenvalue density correlation function and that the ensemble we study and that of band random matrices belong to the same class of spectral universality.Comment: No comment

Topological generators of abelian Lie groups and hypercyclic finitely generated abelian semigroups of matrices

In this paper we bring together results about the density of subsemigroups of abelian Lie groups, the minimal number of topological generators of abelian Lie groups and a result about actions of algebraic groups. We find the minimal number of generators of a finitely generated abelian semigroup or group of matrices with a dense or a somewhere dense orbit by computing the minimal number of generators of a dense subsemigroup (or subgroup) of the connected component of the identity of its Zariski closure.Comment: 14 page

Value creation in mobile banking

The convergence of the Internet and mobile networks creates new opportunities and applications. Treating mobile business as simply an extension to the traditional web could result in missing out unique differentiated qualities for new value-added possibilities. Mobile Banking is considered to be one of the most value-added and important mobile service available. The current research examined technological changes in mobile networks and innovative attributes of Mobile Internet. It has advanced the theoretical framework of innovation in service to develop a customer centric analysis of mBanking value proposition. The article goes on to discuss critical factors in the diffusion of mBanking and explores reasons of failure and further prospects of success.Mobile Banking

The Lorenz model for single-mode homogeneously broadened laser: analytical determination of the unpredictible zone

We have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rates is smaller than 0.11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate "2CP" [4], close to the second laser threshold "2C2th" (threshold of instability). When the pumping parameter "2C" increases, the laser undergoes a period-doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and the fifth order harmonics for the laser-field expansion [4, 14]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations.Comment: 20 pages, 4 figures, 1 anne