ON RUBIN'S HARMONIC ANALYSIS AND ITS RELATED POSITIVE DEFINITE FUNCTIONS

In this paper,a new formulation of the Rubin’s q-translation is given,which leads to a reliable q-harmonic analysis.Next,related q-positive definite functions are introduced and studied,and a Bochner’s theorem is proved.

Stability Analysis Using the Minimum Function Analysis Approach

This article studies a new kind of stability judgment for dynamic systems, the definiteness Lyapunov derivative function approach based on the minimum function. The new results are described by introducing the normal positivity. The article analyzes the relationship of a general system and a polynomial system, the judgment and measurement of positive definiteness, the polar coordinate approach, and constructing the algorithms for positive definite v·(x). Therefore, a new and systematic theory on stability judgment is clearly described.

Electron densitymap evaluation functions for determining the quality of protein crystal structures

Background Finding methods to judge the quality of X-ray crystallographic information is an active research topic.The quality of electron density maps reconstructed by Fourier transform is always limited by the finite resolution,the amplitude/phase error and the completeness of diffraction data.At present,the R value and effective resolution are common ways of evaluating the quality of electron density maps.Unfortunately,the current evaluation methods are only dependent on diffraction amplitude,without any phase information.Methods Advanced evaluation functions in real space are designed to estimate the electron density map quality.The electron density map definition evaluation function relies on the atomicity of the electron density distribution.We use the power spectrum electron density entropy in protein crystallography for the first time.These two functions include both structure factor amplitudes and phases via the Fourier transform of electron density map.Results We carry out tests on synthetic data sets of known structures,varying the resolution and error,and draw the quality curves of electron density maps with theoretical,noisy and experimental diffraction data by two evaluation functions at different resolutions.The curves reveal the optimum structure and resolution of proteins clearly.Conclusions The work presented here offers new methods to evaluate the qualities of the electron density maps of proteins with slight differences,and brand new indicators to select the optimum diffraction resolution of protein structures.

Predictive Control Based on Ranking Multi-objective Optimization Approaches for a quasi-Z Source Inverter

In power converter control,predictive control has several merits,such as simple concept and fast response.However,the necessity to use the weighting factor inside the cost function makes the control design complex in the case of regulating multivariables where the value of the weighting factor is obtained by a nontrivial process.Also,it primarily depends on the system parameters and operating points of the control system.This paper aims to enhance the model predictive algorithm of the singlestage topology of a quasi-Z Source Inverter(qZSI).The concept of a multi-objective optimization approach is used in addition to the sub-cost function definition to remove the weighting factors.By using the sub-cost function definition,the inductor current is pushed away from the main loop of the predictive algorithm.Thus,no weighting factor is needed to manage the priority of the inductor current.The other two control targets,which are the capacitor voltage and load currents,will be controlled by the multi-objective optimization approach without using any weighting factors.A detailed theoretical analysis of the proposed technique will be given and validated based on simulation results.