This paper provides an illustration of the principled design of an interactive learning environment. It provides a view of the early stages of this process where design, testing, and redesign are most critical. The long term goals of principled design are twofold: (1) to create a system that can be convincingly demonstrated as an effective and practical learning aid and (2) to provide a replica...

We consider the following stochastic partial differential equation: ∂u ∂t = 1 2 ∆u + κu ˙ F , for x ∈ R d in dimension d ≥ 3, where ˙ F (t, x) is a mean zero Gaussian noise with the singular covariance E ˙ F (t, x) ˙ F (t, y) = δ(t − s) |x − y| 2. Solutions u t (dx) exist as singular measures, under suitable assumptions on the initial conditions and for sufficiently small κ. We investigate vari...

Single-particle dynamics of the Anderson impurity model are studied using both the numerical renormalization group (NRG) method and the local moment approach (LMA). It is shown that a ‘two-self-energy’ description of dynamics inherent to the LMA, as well as a conventional ‘single-self-energy’ description, arise within NRG; each yielding correctly the same local single-particle spectrum. Explici...

In recent years, constructive field techniques and the method of renormalization group around extended singularities have been applied to the weak coupling regime of the Anderson Model. It has allowed to clarify the relationship between this model and the theory of random matrices. We review this situation and the current program to analyze in detail the density of states and Green’s functions ...

The present study deals with the decolorization of CI Acid Red SR (ARAN as a model contaminant from textileindustry using sawdust as an adsorbent. The effects of initial AR88 concentration, adsorbent dosage, pH. c not acttime and ',riming rah: wcrg studied in a batch mode. The variation of pH from 3 to 10 showed no considerablechange in decolorization rate. The desired conditions for decoloriza...

In this paper, we study the consensus problem of multiple agents on a kind of famous graph, Peterson graph. It is an undirected graph with 10 vertices and 15 edges. Each agent randomly walks on this graph and communicates with each other if and only if they coincide on a node at the same time. We conduct numerical study on the consensus problem in this framework and show that global consensus c...