Birman-Wenzl-Murakami Algebra and the Topological Basis

In this paper, we use entangled states to construct 9x9-matrix representations of Temperley-Lieb algebra (TLA), then a family of 9x9-matrix representations of Birman-Wenzl-Murakami algebra (BWMA) have been presented. Based on which, three topological basis states have been found. And we apply topological basis states to recast nine-dimensional BWMA into its three-dimensional counterpart. Finally, we find the topological basis states are spin singlet states in special case.Comment: 11pages, 1 figur

Synthetic strategies to nanostructured photocatalysts for CO2 reduction to solar fuels and chemicals

Artificial photosynthesis represents one of the great scientific challenges of the 21st century, offering the possibility of clean energy through water photolysis and renewable chemicals through CO2 utilisation as a sustainable feedstock. Catalysis will undoubtedly play a key role in delivering technologies able to meet these goals, mediating solar energy via excited generate charge carriers to selectively activate molecular bonds under ambient conditions. This review describes recent synthetic approaches adopted to engineer nanostructured photocatalytic materials for efficient light harnessing, charge separation and the photoreduction of CO2 to higher hydrocarbons such as methane, methanol and even olefins

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Dynamic Absorptive Capability and Innovation Performance: Evidence from Chinese Cities

Absorptive capability is the capability of actors to acquire, assimilate and exploit external knowledge. In this paper, we consider absorptive capability to be multi-dimensional and to have three dimensions. Although a sufficient amount of work in the literature discusses dynamic absorptive capability, empirical studies are relatively rare. At the urban or regional levels, related empirical studies are even fewer. In this paper, we build a framework of the dynamic absorptive capability at the urban level by using 339 Chinese cities at the prefecture level and above as our sample. In order to take the geographical distance into consideration, we use a Spatial Durbin Model to measure the effects of the acquirement, assimilation, and exploitation of absorptive capability. The results show that all of the core variables (acquirement, assimilation, and exploitation) have significant positive impacts on innovation performance. Additionally, the two control variables (R&D personnel and R&D investment) have significant positive impacts on innovation performance. In this way, the role performed by multidimensional absorptive capability in fostering innovation performance is highlighted, and some policy recommendations are provided