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This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed and the Mackey–Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.

A novel temperature-compensating structure for micromechanical bridge resonators has been developed in this paper. The temperature drift of resonance frequency is compensated by the output voltage of a Si/SiO2 bilayer cantilever temperature sensor, which is integrated in the same chip with the bridge resonator. The mechanism of this kind of temperature sensor resembles that of commercial bimetallic temperature sensors. The deformation of the cantilever measured by a Wheatstone bridge located at the clamped end changes with temperature due to the different thermal expansion coefficients of silicon and silicon dioxide. Both the bridge and the cantilever are of the same thickness and are fabricated simultaneously with the same materials and by an identical process flow. So there are few errors caused by the temperature difference between the temperature sensor and the resonator itself, which occurs during fast temperature changes.

In the study of electrostatic forces of semiconductor microstructures, especially in submicrometer or nanometer orders, it is valuable to analyse the influence of the space-charge layer at the surface of the microstructures. When the distance between microstructures is larger than 1 µm, the influence of space charge is a negligible factor and the metal approximation formula can be used. When the distance is reduced to the order of submicrometers or tens of nanometers, the error introduced by the metal approximation formula increases rapidly, dominated by the distance and the doping concentration. For the commonly used material n-type silicon, whose doping concentration is 1015 cm-3, when the distance is less than 450 nm, the error caused by the metal approximation formula is more than 10%. At this time, the metal approximation formula cannot be used and the influence of the space-charge layer must be taken into account.