different discrete models of population dynamics of certain insects have been investigated under various feasible conditions within the framework of nonlinear dynamics. evolutionary phenomena are discussed through bifurcation analysis leading to chaos. some tools of nonlinear dynamics, such as lyapunov characteristic exponents (lce), lyapunov numbers, correlation dimension, etc. are calculated ...

‎given an integer $n$‎, ‎we denote by $mathfrak b_n$ and $mathfrak c_n$ the classes of all groups $g$ for which the map $phi_{n}:gmapsto g^n$ is a monomorphism and an epimorphism of $g$‎, ‎respectively‎. ‎in this paper we give a characterization for groups in $mathfrak b_n$ and for groups in $mathfrak c_n$‎. ‎we also obtain an arithmetic description of the set of all integers $n$ such that a gr...

We find a bound for the exponent of the Schur multiplier of a finite p-group in terms of the exponent and Engel length of the given group. It is also proved that if G is a 3-Engel group of finite exponent, then the exponent of H2(G) divides exp G. When G is a 4-Engel group of exponent e, the exponent of H2(G) divides 10e.

We consider the discrete memoryless asymmetric broadcast channels. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this exponent function. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.

We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here we let both q and m vary and our estimate is explicit and does not depend on the elliptic curve.

A sufficient condition on concavity of the auxiliary function which appears in the random coding exponent as the lower bound of the quantum reliability function for general quantum states is noted. The validity of its sufficient condition is shown by some numerical computations.

We prove bounds on the diiusion constant for the Rubinstein-Duke-model by means of a variational formula. The leading term decreases quadratically with the length of the polymer chain. The coeecient of proportionality agrees with the one for the model with periodic boundary conditions. The next leading term is anomalous. Upper and lower bounds on the corresponding scaling exponent are given.

We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here, we let both q and m vary; our estimate is explicit and does not depend on the elliptic curve.

We analyse the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities – the lower spectral radius and the largest Lyapunov exponent – are not algorithmically approximable.