Thermo-XRD-analysis and peptization study of the adsorption of alizarinate by Co-, Ni-, and Cu-montmorillonite

The adsorption of the monovalent anionic dye alizarinate onto Co-, Ni- and Cu-montmorillonite was carried out by adding the dye into aqueous clay suspensions. During the loading of the clay suspension by alizarinate, only some of the added organic anion is adsorbed by the clay forming d-coordination chelate complexes on the clay surface. Maximum adsorption of Co-, Ni- and Cu-clay were 13, 13 and 25 mmol dye per 100 g clay. Since the capacity of the clay for these transition metal cations is 38 mmol per 100 g clay, these saturations indicate that only part of the transition metal cations form positively charged d-coordination chelate complexes with metal:ligand ratio of 1. The complex cations can be located inside the interlayer spaces or on the broken bonds surfaces. Thermo-XRD-analysis and peptization studies of the solids and the clay water systems respectively were used here to identify the sorption sites. The Co and Ni complexes were obtained on the broken bonds surfaces whereas the Cu complexes were obtained in the interlayer space. Co²⁺, Ni²⁺ and Cu²⁺ were extracted from the clay into suspensions containing excess alizarinate.     

An algorithm for selecting a good value for the parameter c in radial basis function interpolation

The accuracy of many schemes for interpolating scattered data with radial basis functions depends on a shape parameter c of the radial basis function. In this paper we study the effect of c on the quality of fit of the multiquadric, inverse multiquadric and Gaussian interpolants. We show, numerically, that the value of the optimal c (the value of c that minimizes the interpolation error) depends on the number and distribution of data points, on the data vector, and on the precision of the computation. We present an algorithm for selecting a good value for c that implicitly takes all the above considerations into account. The algorithm selects c by minimizing a cost function that imitates the error between the radial interpolant and the (unknown) function from which the data vector was sampled. The cost function is defined by taking some norm of the error vector E = (E ₁, ... , E_N)^T where E _k = E_k = f_k - S^k x_k) and S _k is the interpolant to a reduced data set obtained by removing the point x _k and the corresponding data value f _k from the original data set. The cost function can be defined for any radial basis function and any dimension. We present the results of many numerical experiments involving interpolation of two dimensional data sets by the multiquadric, inverse multiquadric and Gaussian interpolants and we show that our algorithm consistently produces good values for the parameter c. This revised version was published online in June 2006 with corrections to the Cover Date.     

Nonlinear bipartite matching

We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex objectives, approximative algorithms for norm minimization and maximization, and a randomized algorithm for optimizing arbitrary objectives.     

On test sets for nonlinear integer maximization

A finite test set for an integer optimization problem enables us to verify whether a feasible point attains the global optimum. In this paper, we establish several general results that apply to integer optimization problems with nonlinear objective functions.     

The correlation dimension of rat hearts in an experimentally controlled environment

The electric response of several isolated rat hearts in a controlled environment was studied experimentally. The correlation dimension D(2) was estimated and was found to be between 4 and 6.5 when the response was nearly periodic. The variation of D(2) with the concentration of calcium was studied and a general trend of its increase with increasing concentration was found. Two types of ventricular fibrillation (VF) were observed, one that corresponds to a stochastic signal where D(2) is unbounded and the other to a low dimensional dynamical system with 3.5相似文献   

Delocalization in the anderson model due to a local measurement

We study a one-dimensional Anderson model in which one site interacts with a detector monitoring the occupation of that site. We demonstrate that such an interaction, no matter how weak, leads to total delocalization of the Anderson model, and we discuss the experimental consequences.