Tensor products of strongly graded vertex algebras and their modules

We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We consider a tensor product of strongly graded vertex algebras and its tensor product strongly graded modules. We prove that a tensor product of strongly graded irreducible modules for a tensor product of strongly graded vertex algebras is irreducible, and that such irreducible modules, up to equivalence, exhaust certain naturally defined strongly graded irreducible modules for a tensor product of strongly graded vertex algebras. We also prove that certain naturally defined strongly graded modules for the tensor product strongly graded vertex algebra are completely reducible if and only if every strongly graded module for each of the tensor product factors is completely reducible. These results generalize the corresponding known results for vertex operator algebras and their modules.Comment: 26 pages. For the sake of readability, I quote certain necessary technical definitions from earlier work of Y.-Z. Huang, J. Lepowsky and L. Zhang [arXiv:0710.2687, arXiv:1012.4193, arXiv:math/0609833

A STUDY ON THE ANTITUMOUR EFFECT OF TOTAL FLAVONOIDS FROM PTERIS MULTIFIDA POIR IN H22 TUMOUR-BEARING MICE

The objective of this paper was to investigate the inhibitory effect of total flavonoids from Pteris multifida Poir on growth of transplanted H22 tumour in mice. H22 tumour-bearing mice model was established; the experimental animals were divide/d into the model group, Pteris multifida Poir total flavonoids high-, low-dose groups, and CTX group. Pteris multifida Poir groups were administered continuously for 10d, and CTX group was administered every other day. Tumour inhibition rate, thymus index and spleen index were calculated. Serum levels of TNF-α and IL-2 were determined, as well as total antioxidant capacity (T-AOC) and malondialdehyde (MDA) levels in serum. Compared with the model group, the total flavonoids of Pteris multifida Poir can significantly inhibit tumour growth, with tumour inhibition rates of high- and low-dose groups 49.36% and 33.97%, respectively. They can also evidently increase the spleen and thymus indices of tumour-bearing mice, elevate serum TNF-α and IL-2 levels increase serum T-AOC level and reduce serum MDA level in tumour-bearing mice. The study concluded that total flavonoids from Pteris multifida Poir has an obvious inhibitory effect on transplanted H22 tumours; its mechanism of action may be associated with the improvement of immune function and enhancement of antioxidant capacity in mice

Minimum confinement reinforcement for prestressed concrete piles and a rational seismic design framework

The design of prestressed concrete piles in seismic regions is required to include confinement reinforcement in potential plastic hinge regions. However, the existing requirements for quantifying this reinforcement vary significantly, often resulting in unconstructible details. This paper presents a rational approach for designing minimum confinement reinforcement for prestressed concrete piles in seismic regions. By varying key variables, such as the concrete strength, prestressing force, and axial load, the spiral reinforcement quantified according to the proposed approach provides a minimum curvature ductility capacity of about 18, while the resulting ultimate curvature is 28% greater than an estimated target curvature for seismic design. This paper also presents a new axial load limit for prestressed piles, an integrated framework for seismic design of piles and superstructure, the dependency of pile displacement capacity on surrounding soils, and how further reduction to confinement reinforcement could be achieved, especially in medium to soft soils and in moderate to low seismic regions