Locally graded minimal non CC-groups arep-groups

The research of the two last authors has been supported by DGICYT (Spain) PS88-0085.     

Finite groups with a given absolute central factor group

Let G be a group and L(G) be the absolute center of G, that is, the set of all elements of G fixed by all automorphisms of G. In this paper, we classify all finite groups G whose absolute central factors are isomorphic to a cyclic group, \({\mathbb{Z}_p \times \mathbb{Z}_p}\) , D ₈, Q ₈, or a non-abelian group of order pq for some distinct primes p and q.     

A functional central limit theorem for diffusions on periodic submanifolds of ℝ N

We prove a functional central limit theorem for diffusions on periodic sub- manifolds of ℝ^N. The proof is an adaptation of a method presented in [BenLioPap] and [Bha] for proving functional central limit theorems for diffusions with periodic drift vectorfields. We then apply the central limit theorem in order to obtain a recurrence and a transience criterion for periodic diffusions. Other fields of applications could be heat-kernel estimates, similar to the ones obtained in [Lot].Mathematics Subject Classification (2000): 35B27, 60F05, 58J65The author wants to express his gratitude toward the National Cheng Kung University in Tainan (Taiwan) for its kind hospitality.     

二次周期系数微分方程的周期解

给出利用Schauder不动点定理求一类二次周期系数微分方程的周期解的一种方法,得到较好结果.     

Global dynamics of the periodic logistic system with periodic impulsive perturbations

This paper studies the global behaviors of the periodic logistic system with periodic impulsive perturbations. The results of D.D. Bainov and P.S. Simeonov (1993) are extended and dynamics different from the corresponding continuous system are found. It is shown that the system may have a unique positive periodic solution which is globally asymptotically stable, or go extinct when the two periods are rational dependent. When they are rational independent, the system has no periodic solutions, however, still has a global attractor or go extinct under some conditions.     

Groups with many periodic factor-groups

Groups, all proper factor-groups of which are hyperfmite, are studied in this article.     

Dirichlet series with periodic coefficients

In this paper we shall unify the results obtained so far in various scattered literature, for Dirichlet characters and the associated Dirichlet L-functions, under the paradigm of periodic arithmetic functions and the associated Dirichlet series. Notably we shall determine the Laurent coefficients of the series in question to cover Funakura’s result and proceed on to prove the Ayoub-Berndt-Carlitz-Chowla-Müller-Redmond theorem.     

Groups with periodic defining relations

In the paper, the solvability of the word problem and the conjugacy problem is proved for a wide class of finitely presented groups defined by periodic defining relations of a sufficiently large odd degree. In the proof, we use a certain simplified version of the classification of periodic words and transformations of these words, which was presented in detail in the author’s monograph devoted to the well-known Burnside problem. The result is completed by the proof of an interesting result of Sarkisyan on the existence of a group, given by defining relations of the form E _i ² = 1, for which the word problem is unsolvable. This result was first published in abstracts of papers of the 13th All-Union Algebra Symposium in Gomel in 1975.     

New periodic recurrences with applications

We develop two methods for constructing several new and explicit m-periodic difference equations. Then we apply our results to two different problems. Firstly we show that two simple natural conditions appearing in the literature are not necessary conditions for the global periodicity of the difference equations. Secondly we present the first explicit non-linear analytic potential differential system having a global isochronous center.     

Bank-Laine functions with periodic zero-sequences

A Bank-Laine function is an entire function E such that E(z) = 0 implies that E’(z) = ±1. Such functions arise as the product of linearly independent solutions of a second order linear differential equation ω″ + A(z)ω = 0 with A entire. Suppose that $$E(z)=R(z)e^{g(z)}\prod_{j=1}^m \prod_{k=1}^{q_j}(e^{\alpha_jz}-\beta_{j,k}),$$ where R is a rational function, g is a polynomial, and the α_j and β_j,k are non-zero complex numbers, and that E’(z) = ±1 at all but finally many zeros z of E. Then the quotients α_j/α_j′ are all rational numbers and E is a Bank-Laine function and reduces to the form E(z) = P₀ (e^αz) e^Q ₀(z) with α a non-zero complex number and P₀ and Q₀ polynomials.     

Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays

A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution.     

Existence of positive periodic solutions of an SEIR model with periodic coefficients

An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.