The essential structure of the mixed–integer programming formulation for chance–constrained program (CCP) with stochastic right–hand side is the intersection of multiple mixing sets with a 0− 1 knapsack. To improve our computational capacity on CCP, an underlying substructure, the (single) mixing set with a 0 − 1 knapsack, has received substantial attentions recently. In this study, we first pr...

We investigate what can be learnt about the η -η mixing by means of dispersive representation of axial anomaly. We show that our method leads to the strong bounds for the η − η mixing angle: θ = −15.3◦ ± 1. Moreover, our result manifests also a dramatic dependence of the width Γη→2γ on the mixing angle θ. This property explains how the relatively small mixing strongly effects the decay width.

<p><strong>Abstract: </strong>This study aims to determine: (1) The type of code-switching and code-mixing used, (2) function used by teachers students, (3) reason students use code-mixing. This research was conducted using a qualitative descriptive method. Data collection in this carried out observation, questionnaire, interview then analyzed describing the results. results s...

holds. This is the assertion of the Second Borel-Cantelli Lemma. If the assumption of independence is dropped, (1) fails in general. However, (1) remains true if independence is replaced by pairwise independence (Durrett (1991), Theorem (6.6) ch. 1) or by uniform mixing (Iosifescu and Theodorescu (1969) Lemma 1.1.2’). Rieders (1993) showed by an example that strong mixing without any further as...

We consider a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions. Continuing our previous work [2] for the law of large numbers, we prove here that the fluctuations are gaussian when the environment is Gibbsian satisfying the “strong mixing condition” of Dobrushin and Shlosman and the mixing rate is large enough...

Let (Σ, σ) be a Zd subshift of finite type. Under a strong irreducibility condition (strong specification), we show that Aut(Σ) contains any finite group. For Zd–subshifts of finite type without strong specification, examples show that topological mixing is not sufficient to give any finite group in the automorphism group in general: in particular, End(Σ) may be an abelian semigroup. For an exa...