Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: Uq(gl(m∣n))U_q(gl(m|n))}

The type-I quantum superalgebras are known to admit non-trivial one-parameter families of inequivalent finite dimensional irreps, even for generic $q$. We apply the recently developed technique to construct new solutions to the quantum Yang-Baxter equation associated with the one-parameter family of irreps of $U_q(gl(m|n))$, thus obtaining R-matrices which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form.Comment: 10 pages, LaTex file (some errors in the Casimirs corrected

On Type-I Quantum Affine Superalgebras

The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple generators (``extra $q$-Serre relations") which need to be imposed to properly define \uqgh and $U_q(osp(2|2n)^{(1)})$. We present a general technique for deriving the spectral parameter dependent R-matrices from quantum affine superalgebras. We determine the R-matrices for the type-I affine superalgebra $U_q(sl(m|n)^{(1)})$ in various representations, thereby deriving new solutions of the spectral-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R-matrices depending on two additional spectral-like parameters, providing generalizations of the free-fermion model.Comment: 23 page

Fundamental limits to imaging resolution for focused ion beams

This article investigates the limitations on the formation of focused ion beam images from secondary electrons. We use the notion of the information content of an image to account for the effects of resolution, contrast, and signal‐to‐noise ratio and show that there is a competition between the rate at which small features are sputtered away by the primary beam and the rate of collection of secondary electrons. We find that for small features, sputtering is the limit to imaging resolution, and that for extended small features (e.g., layered structures), rearrangement, redeposition, and differential sputtering rates may limit the resolution in some cases

EVALUATION OF METHANE GAS PRODUCTION IN A SIMULTANEOUS REGRESSION SYSTEM

Methane gas production is a function of volatile solids activity in anaerobic digesters. Increasing the solids retention time of the swine manure digester system without increasing the hydraulic retention time would theoretically increase the methane gas production efficiency. Coagulation treatments were performed on the effluent of the second digester in a system of two digesters in series . The objective of this paper is to describe mathematically the relationship of the Coagulation treatments in the second digester to biogas production and volatile solids retention. An initial, single equation, ordinary least squares regression produced statistically significant parameter estimates, but failed to accurately describe the treatment activity occurring in the second digester. To assess the treatment activity of the second digester and account for the activity of first digester on the second, data was regressed through a simultaneous equation system. Both two-stage and three-stage least squares regression were examined

Gene doctoring: a method for recombineering in laboratory and pathogenic Escherichia coli strains

Background: Homologous recombination mediated by the lambda-Red genes is a common method for making chromosomal modifications in Escherichia coli. Several protocols have been developed that differ in the mechanisms by which DNA, carrying regions homologous to the chromosome, are delivered into the cell. A common technique is to electroporate linear DNA fragments into cells. Alternatively, DNA fragments are generated in vivo by digestion of a donor plasmid with a nuclease that does not cleave the host genome. In both cases the lambda-Red gene products recombine homologous regions carried on the linear DNA fragments with the chromosome. We have successfully used both techniques to generate chromosomal mutations in E. coli K-12 strains. However, we have had limited success with these lambda-Red based recombination techniques in pathogenic E. coli strains, which has led us to develop an enhanced protocol for recombineering in such strains. \ud \ud Results: Our goal was to develop a high-throughput recombineering system, primarily for the coupling of genes to epitope tags, which could also be used for deletion of genes in both pathogenic and K-12 E. coli strains. To that end we have designed a series of donor plasmids for use with the lambda-Red recombination system, which when cleaved in vivo by the I-SceI meganuclease generate a discrete linear DNA fragment, allowing for C-terminal tagging of chromosomal genes with a 6xHis, 3xFLAG, 4xProteinA or GFP tag or for the deletion of chromosomal regions. We have enhanced existing protocols and technologies by inclusion of a cassette conferring kanamycin resistance and, crucially, by including the sacB gene on the donor plasmid, so that all but true recombinants are counter-selected on kanamycin and sucrose containing media, thus eliminating the need for extensive screening. This method has the added advantage of limiting the exposure of cells to the potential damaging effects of the lambda-Red system, which can lead to unwanted secondary alterations to the chromosome. \ud \ud Conclusion: We have developed a counter-selective recombineering technique for epitope tagging or for deleting genes in E. coli. We have demonstrated the versatility of the technique by modifying the chromosome of the enterohaemorrhagic O157:H7 (EHEC), uropathogenic CFT073 (UPEC), enteroaggregative O42 (EAEC) and enterotoxigenic H10407 (ETEC) E. coli strains as well as in K-12 laboratory strains

Shining a Light on Mental Health

Each profession faces unique situations when it comes to serving those needing support with mental health, and it is important as Christians that we come together with a holistic approach. Posting about care for individuals with mental health crises in the various professions from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation. https://inallthings.org/shining-a-light-on-mental-health

The homotropenylium cation : a system with a pinched π ring current

The homotropenylium cation (1, C8H9+) is a key species in the discussion of homoaromaticity. Constrained optimisations around the minimum structure have been performed, varying the size of the gap spanned by the CH2-bridge and optimising all other geometrical parameters. At each bridging distance, ab initio current-density maps have been calculated and plotted using the ipsocentric approach. Analysis of the maps, including decomposition into localised orbital contributions, gives a clear indication of a global diatropic ring current passing through the gap. The change in p(pi)-p(pi) interaction, from conventional p overlap around the conjugated seven-carbon perimeter to s overlap (p(sigma)-p(sigma)) in the gap, results in a distinctive pinched topology, with two streams of current pinched down into one for part of the circuit. This ring current is diatropic and therefore the species 1 is aromatic on the magnetic criterion