In this paper we provide an example of a modified antiferromagnetic Potts model which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs. This example runs counter to the notion that the regular tree has the slowest decay of correlation amongst d-regular graphs. Sokal [7] conjectured that uniqueness in the hard-core model on the d-regular tree im...

In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among the...

We introduce a square lattice into the Penna bit-string model for biological ageing and study the evolution of the spatial distribution of the population considering different strategies of childcare. Two of the strategies are related to the movements of a whole family on the lattice: in one case the mother cannot move if she has any child younger than a given age, and in the other case if she ...

Residential block construction of big cities in China began in the 1950s, and four models had far-reaching influence on modern residential block in its development process, including unit compound and residential district in 1950s to 1980s, and gated community and open community in 1990s to now. Based on analysis of the four models’ fabric, the article takes residential blocks in Hangzhou west ...

In this paper, the performance of uplink spectral efficiency in massive multiple input multiple output (MIMO) over spacially correlated Ricean fading channel is presented. The maximum ratio combining (MRC) receiver is employed at the base station (BS) for two different methods of channel estimation. The first method is based on pilot-assisted least minimum mean square error (LMMSE) estimation, ...