although explicit and implicit knowledge of language learners are essential to theoretical and pedagogical debates in second language acquisition (sla), little research has addressed the effects of instructional interventions on the two knowledge types (r. ellis, 2005).this study examined the relative effectiveness of explicit and implicit types of form-focused instruction (ffi) on the acquisit...

Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...

A method for the explicit computation of the Lyapunov exponents of certain Markov processes is developed. Its utility is demonstrated by an application to two-dimensional random evolution differential equations. Our approach exploits the relation between the Lyapunov exponent and the p-moment Lyapunov exponents, as was first observed and studied by Arnold [1]. The p-moment Lyapunov exponent is ...

We think of x (t, y) as the position of a particle at time t when its velocity is v (t). The process x (t, y) is the simplest example of a random evolution: one-dimensional motion at a constant but random velocity determined by the state of the Markov chain associated with v(t). We denote by P(y,~i){" }, Y real, v~sA, the probability laws of the joint process (x (t, y), v (t)), where v (0)= v/....

We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of selfsimilar fields. More specifically, we are able to construct any Gaussian field belonging to this class with given Hurst index and exponent. Our construction provides for simulations of texture as well as for detection of anisotropies in an i...