M-body Pure State Entanglement

The simple entanglement of N-body N-particle pure states is extended to the more general M-body or M-body N-particle states where $N\neq M$. Some new features of the M-body N-particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose-Einstien condensate model is demonstrated.Comment: 9 pages, 2 figure

High performance millimeter-wave microstrip circulators and isolators

Millimeter wave systems, phased array antennas, and high performance components all require wideband circulators (and isolators) to perform diplexing and switching, to improve isolation and Voltage Standing Wave Ratio (VSWR), and to construct IMPATT diode reflection amplifiers. Presently, most of the millimeter-wave circulators and isolators are available in the configurations of waveguide or stripline, both of which suffer from the shortcomings of bulky size/weight, narrow bandwidth, and poor compatibility with monolithic millimeter-wave integrated circuits (MMIC). MMW microstrip circulators/isolators can eliminate or improve these shortcomings. Stub-tuned microstrip circulator configuration were developed utilizing the electromagnetic fields perturbation technique, the adhesion problems of microstrip metallization on new ferrite substrate were overcome, the fabrication, assembly, packaging techniques were improved, and then successfully designed, fabricated a Ka band circulator which has isolation and return loss of greater than 16dB, insertion loss less than 0.7dB. To assess the steady and reliable performance of the circulator, a temperature cycling test was done over the range of -20 to +50 C for 3 continuous cycles and found no significant impact or variation of circulator performance

Estimation and tests for power-transformed and threshold GARCH models

Consider a class of power transformed and threshold GARCH(p,q) (PTTGRACH(p,q)) model, which is a natural generalization of power-transformed and threshold GARCH(1,1) model in Hwang and Basawa (2004) and includes the standard GARCH model and many other models as special cases. We ¯rst establish the asymptotic normality for quasi-maximum likelihood estimators (QMLE) of the parameters under the condition that the error distribution has ¯nite fourth moment. For the case of heavy-tailed errors, we propose a least absolute deviations estimation (LADE) for PTTGARCH(p,q) model, and prove that the LADE is asymptotically normally distributed under very weak moment conditions. This paves the way for a statistical inference based on asymptotic normality for heavy-tailed PTTGARCH(p,q) models. As a consequence, we can construct the Wald test for GARCH structure and discuss the order selection problem in heavy-tailed cases. Numerical results show that LADE is more accurate than QMLE for heavy tailed errors. Furthermore the theory is applied to the daily returns of the Hong Kong Hang Seng Index, which suggests that asymmetry and nonlinearity could be present in the ¯nancial time series and the PTTGARCH model is capable of capturing these characteristics. As for the probabilistic structure of PTTGARCH(p,q), we give in the appendix a necessary and su±cient condition for the existence of a strictly stationary solution of the model, the existence of the moments and the tail behavior of the strictly stationary solution