Scale-invariant occupancy of phase space and additivity of nonextensive entropy <Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>

Phase space can be constructed for N equal and distinguishable binary subsystems which are correlated in a scale-invariant manner. In the paper, correlation coefficient and reduced probability are introduced to characterize the scale-invariant correlated binary subsystems. Probabilistic sets for the correlated binary subsystems satisfy Leibnitz triangle rule in the sense that the marginal probabilities of N-system are equal to the joint probabilities of the (N −1)-system. For entropic index q ≠ 1, nonextensive entropy S _q is shown to be additive in the scale-invariant occupation of phase space.     

Study on Oxidation Activity of CuCeZrO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> Doped with K for Diesel Engine Particles in NO/O<Subscript>2</Subscript>

CuCeZrO_x and KCuCeZrO_x catalysts were synthesized and coated on the blank diesel particulate filter (DPF) substrate and a particulate matter (PM) loading apparatus was used for soot loading. The catalytic performances of soot oxidation were evaluated by temperature programmed combustion (TPC) test and characterization tests were conducted to investigate the physicochemical properties of the catalysts. The reaction mechanism in the oxidation process was analyzed with diffuse reflectance infrared Fourier transform spectroscopy. The results demonstrated that CuCeZrO_x catalyst exhibited high activities of soot oxidation at low temperature and the best results have been attained with Cu_0.9Ce_0.05Zr_0.05O_x over which the maximum soot oxidation rate decreased to 410 °C. Characterization tests have shown that catalysts containing 90% Cu have uniformly distributed grains and small particle sizes, which provide excellent oxidation activity by providing more active sites and forming a good bond between the catalyst and the soot. The low-temperature oxidation activity of soot could be further optimized due to the excellent elevated NO’s conversion rate by partially substituting Cu with K. The maximum particle oxidation rate can be easily realized at such a low temperature as 347°C.     

On codes with <Emphasis Type="Italic">w</Emphasis>-identifiable parent property

A code is said to be a w-identifiable parent property code (or w-IPP code for short) if whenever d is a descendant of w (or fewer) codewords, and one can always identify at least one of the parents of d. Let C be an (N, w + 1, q)-code and C* an (w + 1)-color graph for C. If a graph G is a subgraph of C* and consists of w + 1 edges with different colors, then G is called a (w + 1)-pattern of C*. In this paper, we proved that C is a w-IPP code if and only if there exists at most one vertex with color degree more than 1 in any (w + 1)-pattern of C*. Foundation item: the National Natural Science Foundation of China (No. 10471093)     

Improved algorithm for calculating contributions to <Emphasis Type="Italic">D</Emphasis>-statistic

D-statistic contribution analysis has been frequently used in practice for fault diagnosis. Existing algorithms for computing contributions to D-statistic tend to distribute cross-term contribution equally between two correlated variables. This leads to increased variance in contribution estimation and hence poor separability of faulty and normal variables. A new method for contribution calculation to D-statistic is proposed here which introduces a weighting scheme capable of distinguishing the contributions of two correlated variables. Simulation examples show that the proposed approach achieves improved resolution for distinguishing faulty and normal conditions.     

Performance analysis of AF relaying based on water-filling power allocation over Nakagami-<Emphasis Type="Italic">m</Emphasis> fading

This paper investigates exact performance of an amplify-and-forward (AF) relay system based on water-filling power allocation in Nakagami-m fading environment, where m is a nonnegative integer plus one half. We first offer the cumulative distribution function (CDF) and probability density function (PDF) of the received signal-to-noise ratio (SNR) at a destination. Then outage probability, moments of SNR, higher-order statistics of the capacity are explicitly conducted. Especially, average symbol error rate (SER) under an additive white generalized Gaussian noise (AWGGN) is developed for water-filling power allocation scheme. While the average SER subjected by an additive white Gaussian noise (AWGN) can be regarded as a special case. Finally, all theoretical formulas are truly attested by various simulation results.     

Five-axis interpolation of continuous short linear trajectories for 3[PP]S-<Emphasis Type="Italic">XY</Emphasis> hybrid mechanism by dual Bezier blending

A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two sub-paths. One sub-path describes the movement of 3[PP]S parallel kinematic mechanism module, and the other one describes the movement of XY platform. A pair of cubic Bezier curves is employed to smooth the corners in those two sub-paths. Based on the homogenous Jacobian matrix of 3[PP]S mechanism, a relationship between the position errors of every driving joint in hybrid mechanism and the position deviation of the tool tip center point at the moving platform is established. This relationship is used to estimate the approximation error for the corners smoothing according to the accuracy requirement of tool tip center in interpolation. Due to the high computational efficiency of this corner smoothing method, it is integrated into the look-ahead module of computer numerical control (CNC) system to perform online tool path smoothing. By performing the speed planning based on a floating window scheme, a jerk limited S-shape speed profile can be generated efficiently. On this basis, a realtime look-ahead scheme, which is comprised of path-smoothing and feedrate scheduling, is developed to acquire a speed profile with smooth acceleration. A monotonic cubic spline is employed for synchronization between those two smoothed sub-paths in tool path interpolation. This interpolation algorithm has been integrated into our own developed CNC system to control a 3PRS-XY experimental instrument (P, R and S standing for prismatic, revolute and spherical, respectively). A club shaped trajectory is adopted to verify the smoothness and efficiency of the five-axis interpolator for hybrid mechanism control.