Equality of symmetrized tensors and the coordinate ring of the flag variety

In this note we give a transparent proof of a result of da Cruz and Dias da Silva on the equality of symmetrized decomposable tensors. This will be done by explaining that their result follows from the fact that the coordinate ring of a flag variety is a unique factorization domain.Comment: 5 page

Quantum state transformations and the Schubert calculus

Recent developments in mathematics have provided powerful tools for comparing the eigenvalues of matrices related to each other via a moment map. In this paper we survey some of the more concrete aspects of the approach with a particular focus on applications to quantum information theory. After discussing the connection between Horn's Problem and Nielsen's Theorem, we move on to characterizing the eigenvalues of the partial trace of a matrix.Comment: 40 pages. Accepted for publication in Annals of Physic

A note on the global structure of proper Lie groupoids in low codimensions

We observe that any connected proper Lie groupoid whose orbits have codimension at most two admits a globally effective representation on a smooth vector bundle, i.e., one whose kernel consists only of ineffective arrows. As an application, we deduce that any such groupoid can up to Morita equivalence be presented as an extension of some action groupoid G n X with G compact by some bundle of compact Lie groups.Comment: 12 page

The encapsulation and controlled release of proteins from “meltable” chemically cross-linked hydrogels

\ua9 2024 The Authors. Journal of Applied Polymer Science published by Wiley Periodicals LLC.Chemically crosslinked hydrogels can be used for the controlled delivery of therapeutic proteins, however, cargo loading can be challenging. A common approach involves performing the hydrogel crosslinking step in the presence of the cargo proteins, however, this can require the utilization of selective chemistries to ensure the cargos do not chemically react with the forming hydrogel network. We demonstrate that chemically crosslinked hydrogels based upon the protein polymer Capsular antigen fragment 1 (Caf1) can be used to encapsulate proteins within a chemically crosslinked hydrogel network. This encapsulation exploits the “meltable” feature of Caf1 hydrogels, where upon heating the Caf1 protein unfolds with concomitant depolymerization of the hydrogel network. Protein cargos can be loaded into the “molten” form of the hydrogel which cools with protein refolding and concomitant reformation of the hydrogel network to entrap the cargos, ensuring a more homogenous dispersion of the cargo. Analysis of release profiles indicated lower burst release in comparison to release from identical hydrogels loaded by an absorption method. This work is significant because it suggest that the “meltable” feature of Caf1 hydrogels may present an improved method of loading protein cargos into crosslinked hydrogel networks whilst avoiding the need for crosslinking chemistries

Enhancing the kinetics of hydrazone exchange processes: an experimental and computational study

The capacity of hydrazone bonds to readily undergo component exchange processes sees their extensive utilization in dynamic combinatorial chemistry. The kinetics of hydrazone exchange are optimal at pH ∼4.5, which limits the use of hydrazone-based dynamic combinatorial libraries, particularly for biological targets which are only stable at near-neutral pH values. It would thus be advantageous if hydrazone exchange proceeded with faster rates at pH values closer to neutral. We experimentally and computationally evaluated the hypothesis that hydrazones possessing neighbouring acidic or basic functional groups within the carbonyl-derived moitety of the hydrazone would enhance exchange rates. Our work suggests that judiciously placed N- or O-hydrogen bond acceptors within the carbonyl-derived moiety of the hydrazone stabilize transition states via hydrogen bonding interactions, providing a valuable boost to exchange kinetics at near-neutral pH values. We anticipate these findings will be of interest in dynamic combinatorial chemistry, dynamic covalent polymers/materials, functionalized nanoparticles and interlocked molecules, all of which may benefit from hydrazone exchange processes able to operate at near-neutral pH values

The 24-Cell and Calabi-Yau Threefolds with Hodge Numbers (1,1)

Calabi-Yau threefolds with h^11(X)=h^21(X)=1 are constructed as free quotients of a hypersurface in the ambient toric variety defined by the 24-cell. Their fundamental groups are SL(2,3), a semidirect product of Z_3 and Z_8, and Z_3 x Q_8.Comment: 22 pages, 3 figures, 3 table

Life cycle assessment of biofuels from Jatropha curcas in West Africa: a field study

In recent years, liquid biofuels for transport have benefited from significant political support due to their potential role in curbing climate change and reducing our dependence on fossil fuels. They may also participate to rural development by providing new markets for agricultural production. However, the growth of energy crops has raised concerns due to their high consumption of conventional fuels, fertilizers and pesticides, their impacts on ecosystems and their competition for arable land with food crops. Lowinput species such as Jatropha curcas, a perennial, inedible crop well adapted to semiarid regions, has received much interest as a new alternative for biofuel production, minimizing adverse effects on the environment and food supply. Here, we used life-cycle assessment to quantify the benefits of J. curcas biofuel production inWest Africa in terms of greenhouse gas emissions and fossil energy use, compared with fossil diesel fuel and other biofuels. Biodiesel from J. curcas has a much higher performance than current biofuels, relative to oil-derived diesel fuels. Under West Africa conditions, J. curcas biodiesel allows a 72% saving in greenhouse gas emissions compared with conventional diesel fuel, and its energy yield (the ratio of biodiesel energy output to fossil energy input) is 4.7. J. curcas production studied is eco-compatible for the impacts under consideration and fits into the context of sustainable development

A unified approach on Springer fibers in the hook, two-row and two-column cases

We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordan basis and consider the standard torus relative to this. We deal with the problem to describe the flags fixed by the torus which belong to a given component of the Springer fiber. We solve the problem in the hook, two-row and two-column cases. We provide two main characterizations which are common to the three cases, and which involve dominance relations between Young diagrams and combinatorial algorithms. Then, for these three cases, we deduce topological properties of the components and their intersections.Comment: 42 page