A Spatial Investigation of ƒÐ-Convergence in China

Using techniques of spatial econometrics, this paper investigates ƒÐ-convergence of provincial real per capita gross domestic product (GDP) in China. The empirical evidence concludes that spatial dependence across regions is strong enough to distort the traditional measure of ƒÐ-convergence. This study focuses on the variation of per capita GDP that is dependent on the development processes of neighboring provinces and cities. This refinement of the conditional ƒÐ-convergence model specification allows for analysis of spatial dependence in the mean and variance. The corrected measure of ƒÐ-convergence in China indicates a lower level of dispersion in the economic development process. This implies a smaller divergence in real per capita GDP, although convergence across regions is still a challenging goal to achieve in the 2000s.ƒÐ-Convergence, Moran's index, spatial dependence, spatial lag

Tighter weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems

We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the $\beta$th ($0\leq\beta\leq1$) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in [Phys. Rev. A 97, 042332 (2018)]

3-(3-Bromo­phen­yl)-N-phenyl­oxirane-2-carboxamide

There are two independent mol­ecules in the asymmetric unit of the title compound, C15H12BrNO2. In both mol­ecules, the two benzene rings adopt a cis configuration with respect to the ep­oxy ring. In one mol­ecule, the ep­oxy ring makes dihedral angles of 60.5 (2) and 77.92 (19)° with the two benzene rings; in the other mol­ecule, the values are 61.0 (2) and 81.43 (19)°. Inter­molecular N—H⋯O and C—H⋯O hydrogen bonding is present in the crystal structure

New discrimination procedure of location model for handling large categorical variables

The location model proposed in the past is a predictive discriminant rule that can classify new observations into one of two predefined groups based on mixtures of continuous and categorical variables. The ability of location model to discriminate new observation correctly is highly dependent on the number of multinomial cells created by the number of categorical variables. This study conducts a preliminary investigation to show the location model that uses maximum likelihood estimation has high misclassification rate up to 45% on average in dealing with more than six categorical variables for all 36 data tested. Such model indicated highly incorrect prediction as this model performed badly for large categorical variables even with large sample size. To alleviate the high rate of misclassification, a new strategy is embedded in the discriminant rule by introducing nonlinear principal component analysis (NPCA) into the classical location model (cLM), mainly to handle the large number of categorical variables. This new strategy is investigated on some simulation and real datasets through the estimation of misclassification rate using leave-one-out method. The results from numerical investigations manifest the feasibility of the proposed model as the misclassification rate is dramatically decreased compared to the cLM for all 18 different data settings. A practical application using real dataset demonstrates a significant improvement and obtains comparable result among the best methods that are compared. The overall findings reveal that the proposed model extended the applicability range of the location model as previously it was limited to only six categorical variables to achieve acceptable performance. This study proved that the proposed model with new discrimination procedure can be used as an alternative to the problems of mixed variables classification, primarily when facing with large categorical variables