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If Φ is a positive definite function on a real linear space E of infinite dimension and Φ enjoys certain symmetry conditions we are able to show that Φ is expressible as a certain Laplace-Stieltjes transform. Conversely, if Φ is given by such a transform we can often show that Φ is positive definite on E. In particular, our results apply to the Lp spaces, 0 < p < ∞, as well as to other Orlicz spaces. We also are able to show that the only positive definite continuous sup-norm symmetric functions on C(T), the space of bounded real continuous functions on T, are constants whenever C(T) contains a sequence of functions with sup-norm one and disjoint support. Finally, we apply these ideas to obtain a result on radial exponentially convex functions on a Hilbert space.
A single–loop fourth-order sigma-delta (ΣΔ) interface circuit for closed-loop micromachined accelerometer is presented in this work. Two additional electronic integrators are cascaded with the micromachind sensing element to form a fourth-order loop filter to eliminate quantization noise. A switched-capacitor (SC) charge integrator and correlated double sampling (CDS) are applied to reduce input-referred electronic noise. Matlab and Hspice simulation results indicate that signal-to-noise-and-distortion ratio (SNDR) is 86.5dB, effective number of bits (ENBO) is 14.08bits when over sampling ratio (OSR) is 128, the sensitivity of the __Roshe1258-Shoes Roshe Trainers Men Dark Blue Green__ system is 0.65V/g, the full measurement range can be achieved from -5g to Light Fluorescent Green Nike Free 5.0 V3 Women +5g.