Pointwise Approximation Theorems for Combinations of Bernstein Polynomials With Inner Singularities

We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.Comment: 13 pages, late

Eight-potential-well order-disorder ferroelectric model and effects of random fields

An eight-potential-well order-disorder ferroelectric model was presented and the phase transition was studied under the mean-field approximation. It was shown that the two-body interactions are able to account for the first-order and the second order phase transitions. With increasing the random fields in the system, a first-order phase transition is transformed into a second-order phase transition, and furthermore, a second-order phase transition is inhibited. However, proper random fields can promote the spontaneous appearance of a first-order phase transition by increasing the overcooled temperature. The connections of the model with relaxors were discussed.Comment: 8 pages, 5 figures. Submitted to Applied Physics Letter