Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings $\varphi: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume has nontrivial Under certain assumptions on $\Re$, we prove $\varphi$ is of the form $\psi + \tau$, where $\psi$ either an isomorphism or negative anti-isomorphism onto $\tau$ additive mapping into centre which maps commutat...

We present methods to detect the transitions from quasiperiodic to chaotic motion via strange nonchaotic attractors (SNAs). These procedures are based on the time needed by the system to recur to a previously visited state and a quantification of the synchronization of trajectories on SNAs. The applicability of these techniques is demonstrated by detecting the transition to SNAs or the transiti...

In spite of the analogies between Q p and F p ((t)) which became evident through the work of Ax and Kochen, an adaptation of the complete recursive axiom system given by them for Q p to the case of F p ((t)) does not render a complete axiom system. We show the independence of elementary properties which express the action of additive polynomials as maps on F p ((t)). We formulate an elementary ...

We study a 1D ring of diffusively coupled logistic maps in the vicinity of an unstable, spatially homogeneous fixed point. The failure of linear controllers due to additive noise is discussed with the aim of clarifying the failure mechanism. A criterion is suggested for estimating the noise level that can be tolerated by the given controller. The criterion implies the loss of control for surpri...

In this work, a chaotification technique is proposed for increasing the complexity of chaotic maps. The consists adding remainder multiple scalings map’s value next iteration, so that most- and least-significant digits are combined. By appropriate parameter tuning, resulting map can achieve higher Lyapunov exponent value, result was first proven theoretically then showcased through numerical si...

Let R be a 2-torsion free σ-prime ring. It is shown here that if U 6⊂ Z(R) is a σ-Lie ideal of R and a, b in R such that aUb = σ(a)Ub = 0, then either a = 0 or b = 0. This result is then applied to study the relationship between the structure of R and certain automorphisms on R. To end this paper, we describe additive maps d : R −→ R such that d(u) = 2ud(u) where u ∈ U, a nonzero σ-square close...

Let R be a semiprime ring and let F, f : R → R be (not necessarily additive) maps satisfying F (xy) = F (x)y + xf(y) for all x, y ∈ R. Suppose that there are integers m and n such that F (uv) = mF (u)F (v) + nF (v)F (u) for all u, v in some nonzero ideal I of R. Under some mild assumptions on R, we prove that there exists c ∈ C(I) such that c = (m + n)c2, nc[I, I] = 0 and F (x) = cx for all x ∈...

The spatial variability of three indicators of learning and developmental disability (LDD) was assessed for Cape Cod, Massachusetts. Maternal reports of receiving special education services, attention deficit hyperactivity disorder, and educational attainment were available for a birth cohort from 1969-1983. Using generalized additive models and residential history, maps of the odds of LDD were...

7 High-order epistasis has been observed in many genotype-phenotype maps. These multi-way inter8 actions could have profound implications for evolution and may be useful for dissecting complex 9 traits. Previous analyses have assumed a linear genotype-phenotype map, and then applied a linear 10 high-order epistasis model to dissect epistasis. The assumption of linearity has not been tested 11 i...

Figure 1: Principle of habitat modelling: sampling of species distribution data (here: presence-absence data) and selected predictor variables; estimating an empirical, predictive model (in this case: by logistic regression a generalised linear model for binary response variables, other, more flexible approaches are generalised additive models, classification and regression trees, artificial ne...