37 research outputs found
On the multiple Borsuk numbers of sets
The Borsuk number of a set S of diameter d >0 in Euclidean n-space is the
smallest value of m such that S can be partitioned into m sets of diameters
less than d. Our aim is to generalize this notion in the following way: The
k-fold Borsuk number of such a set S is the smallest value of m such that there
is a k-fold cover of S with m sets of diameters less than d. In this paper we
characterize the k-fold Borsuk numbers of sets in the Euclidean plane, give
bounds for those of centrally symmetric sets, smooth bodies and convex bodies
of constant width, and examine them for finite point sets in the Euclidean
3-space.Comment: 16 pages, 3 figure
Applications of boroxide ligands in supporting small molecule activation by U(iii) and U(iv) complexes
Mixed Electronic and Ionic Conduction Properties of Lithium Lanthanum Titanate
With the continued increase in Liâmetal anode rate capability, there is an equally important need to develop highârate cathode architectures for solidâstate batteries. A proposed method of improving charge transport in the cathode is introducing a mixed electronic and ionic conductor (MEIC) which can eliminate the need for conductive additives that occlude electrolyteâelectrode interfaces and lower the net additive required in the cathode. This study takes advantage of a reduced perovskite electrolyte, Li0.33La0.57TiO3 (LLTO), to act as a model MEIC. It is found that the ionic conductivity of reduced LLTO is comparable to oxidized LLTO (Ïbulk = 10â3â10â4 S cmâ1, ÏGB = 10â5â10â6 S cmâ1) and the electronic conductivity is 1 mS cmâ1. The ionic transference numbers are 0.9995 and 0.0095 in the oxidized and reduced state, respectively. Furthermore, two methods for controlling the transference numbers are evaluated. It is found that the electronic conductivity cannot easily be controlled by changing O2 overpressures, but increasing the ionic conductivity can be achieved by increasing grain size. This work identifies a possible class of MEIC materials that may improve rate capabilities of cathodes in solidâstate architectures and motivate a deeper understanding of MEICs in the context of solidâstate batteries.Lithium lanthanum titanate can exhibit both high ionic conductivity and high electronic conductivity depending on its oxidation state. While electronic conductivity in solid electrolytes is typically undesirable, the ability to conduct both Liâions and electrons may pose useful for cathode composites. This work investigates the conduction properties of lithium lanthanum titanate and potential methods to control transference number.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154428/1/adfm201909140_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154428/2/adfm201909140-sup-0001-SuppMat.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154428/3/adfm201909140.pd
Effects of Heat Treatment and Additive LiF on the Properties of SolidâState Electrolyte of Li 1.5
Some recent approaches to smaller, faster devices for remote PET radiolabeling
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90295/1/25802601204_ftp.pd