Let Q(S) be the moduli space of area one holomorphic quadratic differentials for an oriented surface S of genus g ≥ 0 with m ≥ 0 punctures and 3g − 3 + m ≥ 2. We show that for every compact subset K of Q(S) the as-ymptotic growth rate δ(K) of the number of periodic orbits of the Teichmüller flow Φ t which are contained in K is not bigger than h = 6g − 6 + 2m, and sup K δ(K) = h. Similarly, h is...

In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when the initial value thumbs the finite set in the increasing order. We are able to predict, using closed formulas, the number of gop for the set FN of all the fu...

agriculture as one of the major economic sectors of iran, has an important role in gross domestic production by providing about 14% of gdp. this study attempts to forecast the value of the agriculture gdp using periodic autoregressive model (par), as the new seasonal time series techniques. to address this aim, the quarterly data were collected from march 1988 to july 1989. the collected data w...

We derive new bounds on the periodic (cyclic) total squared correlation (PTSC) of binary antipodal signature sets for any number of signatures K and any signature length L. Optimal designs that achieve the new bounds are then developed for several (K,L) cases. As an example, it is seen that complete (K = L + 2) Gold sets are PTSC optimal, but not, necessarily, Gold subsets of K < L + 2 signatur...

We study fixed point theorems for maps which satisfy a property of stretching a suitably oriented topological space Z along the paths connecting two disjoint subsets Z− l and Z− r of Z . Our results reconsider and extend previous theorems in [56, 59, 60] where the case of two-dimensional cells (that is topological spaces homeomorphic to a rectangle of the plane) was analyzed. Applications are g...

We introduce a topology T on the space U of uniformly discrete subsets of the Euclidean space. Assume that S in U admits a unique autocorrelation measure. The diffraction measure of S is purely atomic if and only if S is almost periodic in (U,T ). This result relates idealized quasicrystals to almost periodicity. In the context of ergodic point processes, the autocorrelation measure is known to...

Let 9 be an automorphism of finite order of a free group X. We characterise the action of 9 on X by showing that X has a free basis which is the disjoint union of finite subsets Sj, where if S,, ~ {uq, «,,..., uk) then u¡9 ~ ul+x (0 < 1 < k) and uk9 = AjUqBj for some A}, B¡ in X and e = ±1. As an application of this result, we obtain a list of the conjugacy classes of periodic automorphisms of ...

A nonempty subset A ⊆ {1, 2 . . . , n} is relatively prime if gcd(A) = 1. Let f(n) denote the number of relatively prime subsets of {1, 2 . . . , n}. The sequence given by the values of f(n) is sequence A085945 in Sloane’s On-Line Encyclopedia of Integer Sequences. In this article we show that f(n) is never a square if n ≥ 2. Moreover, we show that reducing the terms of this sequence modulo any...

Abstract Background: Identity disturbance is one of the DSM-IV criteria for borderline personality disorder, but there has been little attention to its nature. Four subsets of identity disturbance (role absorption, painful incoherence, inconsistency and lack of commitment) have been assessed. This study aimed to assess the role of these subsets in patients with borderline person...