Jump inversions of algebraic structures and Σ-definability

© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim It is proved that for every countable structure A and a computable successor ordinal α there is a countable structure A−α which is (Formula presented.) -least among all countable structures C such that A is Σ-definable in the αth jump C(α). We also show that this result does not hold for the limit ordinal α = ω. Moreover, we prove that there is no countable structure A with the degree spectrum (Formula presented.) for (Formula presented.)

A Novel Approach for Real Mass Transformation from V2O5 Particles to Nanorods

A solid-state, mass-quantity transformation from V2O5 powders to nanorods has been realized via a two-step approach. The nanorods were formed through a controlled nanoscale growth from the nanocrystalline V2O5 phase created by a ball milling treatment. The nanorods grow along the [010] direction and are dominated by {001} surfaces. Surface energy minimization and surface diffusion play important roles in their growth mechanism. Real large quantity production can be achieved when the annealing process is conducted in a fluidized bed which can treat large quantities of the milled materials at once. The crystal orientation of nanorods provides an improved cycling stability for lithium intercalation

Growth of V2O5 nanorods from ball-milled powders and their performance in cathodes and anodes of lithium-ion batteries

The two-stage procedure of ball milling and annealing in air represents a prospective method of preparing nanorods of V2O5 with electrochemical properties suitable for the application in lithium-ion batteries. Commercially purchased V2O5 powder is milled in a ball mill as the first step of the synthesis. The as-milled precursor is subsequently annealed in air to produce the morphology of nanorods via solid-state recrystallization. We have recently investigated intermediate stages of the formation of nanorods, and this paper summarizes the synthesis method including the description of the current understanding of the growth mechanism. The obtained V2O5 nanorods have been assessed as an electrode material for both anodes and cathodes of lithium-ion batteries. When used in cathodes, the nanorods demonstrate a better retention of capacity upon cycling than that of the commercially available powder of V2O5. When used in anodes, the performances of nanorods and the reference V2O5 powder are similar to a large extent, which is related to a different operating mechanism of V2O5 in anodes. The experimentally observed capacity of V2O5 nanorods in an anode has stabilized at the level of about 450 mAh/g after few cycles