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In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree. §1 Basic notionsIn the study of deterministic dynamical systems, there are several invariants related to the asymptotic growth of complexity of the orbit structure. One of the most important things is the topological entropy, which reflects the growth of the number of orbits distinguishable with limit precision. We can also describe the growth in topological complexity of families of orbits from the homotopical and homological points of view (see [1] and Chapter 8 of [2] for details). In fact there are close relations between them. In [3], Manning showed that for a continuous map f on a compact connected manifold M the topological entropy h(f ) is no less than the growth rate of the action f *

Hierarchically porous activated coke is widely applied in pollutant removal due to its excellent molecule adsorption and transportation ability. Catalytic activation with the participation of alkali/alkaline earth metal salt has been reported to be effective for constructing hierarchical pore configuration; however, the technical condition remains to be explored for providing guidance to practical preparation process. Herein, the relationship between the porous structure of Zhundong coal-based activated coke and the technical condition during catalytic activation is systematically discussed. Based on comparisons of porous structures obtained under different carbonization−activation conditions, one-step catalytic activation is demonstrated to be more favorable for pore development than traditional carbonization−activation process. Physicochemical structural analyses of the precursor and the prepared activated coke reveal that pore development during catalytic activation is also related to the surface chemistry of the precursor and particle size. Amplified preparation experiments in rotary kiln further verify the potential of one-step catalytic activation in industrial production. As a proof of application, selective catalytic reduction tests show that the prepared hierarchically porous activated coke via one-step catalytic activation exhibits high efficiency in NO removal. This work highlights the promoting role of one-step catalytic activation in pore development, providing guidance for preparing high-performance activated coke under practical industrial conditions.

Allele-specific amplification on the basis of polymerase chain reaction (PCR) has been widely used for singlenucleotide polymorphism (SNP) genotyping. However, the extraction of PCR-compatible genomic DNA from whole blood is usually required. This process is complicated and tedious, and is prone to cause crosscontamination between samples. To facilitate direct PCR amplification from whole blood without the extraction of genomic DNA, we optimized the pH value of PCR solution and the concentrations of magnesium ions and facilitator glycerol. Then, we developed multiplex allele-specific amplifications from whole blood and applied them to a case-control study. In this study, we successfully established triplex, five-plex, and eight-plex allelespecific amplifications from whole blood for determining the distribution of genotypes and alleles of 14 polymorphisms in 97 gastric cancer patients and 141 healthy controls. Statistical analysis results showed significant association of SNPs rs9344, rs1799931, and rs1800629 with the risk of gastric cancer. This method is accurate, time-saving, cost-effective, and easy-to-do, especially suitable for clinical prediction of disease susceptibility.