In this paper we deal with C*-algebras of real rank zero that can be represented as inductive limits A = lim −→(An, νn+1,n) of direct sums of homogeneous C*-algebras of the form An = ⊕ i=1 Pn,iM[n,i](C(Xn,i))Pn,i, where Xn,i are finite CW complexes and Pn,i are selfadjoint projections. Following [3] we called these C*-algebras approximately homogeneous. Our main result asserts that any approxim...

Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents. We consider linear system of differential equations with time-periodic coefficient matrix. Assuming that the matrix depends analytically on small parameter, derive full expansion its Based this, prove only constant order exponents multiplicity higher than one will be perturbed linearly. The requ...

We study the string-property of being periodic and having periodicity smaller than a given bound. Let Σ be a fixed alphabet and let p, n be integers such that p ≤ n2 . A length-n string over Σ, α = (α1, . . . , αn), has the property Period(p) if for every i, j ∈ {1, . . . , n}, αi = αj whenever i ≡ j (mod p). For an integer function g = g(n) ≤ n2 , the property Period(≤ g) is the property of al...

Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons as described by the Kerr nonlinear Maxwell system. Using a model of the nonlinear polarization, which does not generate higher harmonics, we obtain a closed...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

A generalized Lotka-Volterra model for a pair of interacting populations of predators and prey is studied. The model accounts for the prey's interspecies competition and therefore is asymptotically stable, whereas its oscillatory behavior is induced by temporal variations in environmental conditions simulated by those in the prey's reproduction rate. Two models of the variations are considered,...