Word maps in finite simple groups

Elements of the free group define interesting maps, known as word maps, on groups. It was previously observed by Lubotzky that every subset of a finite simple group that is closed under endomorphisms occurs as the image of some word map. We improve upon this result by showing that the word in question can be chosen to be in $$v(\mathbf F _n),$$ the verbal subgroup of the free group generated by the word v, provided that v is not a law on the finite simple group in question. In addition, we provide an example of a word w that witnesses the chirality of the Mathieu group $$M_{11}$$. The paper concludes by demonstrating that not every subset of a group closed under endomorphisms occurs as the image of a word map.     

Generation and Reactivity of a One-Electron-Oxidized Manganese(V) Imido Complex with a Tetraamido Macrocyclic Ligand

The synthesis and X-ray structure of a new manganese(V) mesitylimido complex with a tetraamido macrocyclic ligand (TAML), [Mn^V(TAML)(N-Mes)]⁻ ( 1 ), are reported. Compound 1 is oxidized by [(p-BrC₆H₄)₃N ]^+.[SbCl₆]⁻ and the resulting Mn^VI species readily undergoes H-atom transfer and nitrene transfer reactions.     

Analysis of carbenoxolone by ultra‐high‐performance liquid chromatography tandem mass spectrometry in mouse brain and blood after systemic administration

Carbenoxolone is a derivative of glycyrrhetinic acid found in the root of Glycyrrhiza glabra, colloquially known as licorice. It has been used as a treatment for peptic and oral ulcers. In recent years, carbenoxolone has been utilized in basic research for its ability to block gap junctional communication. Better understanding the distribution of carbenoxolone after systemic administration can lead to a better understanding of its potential sites of action. Presented is an ultra high‐performance liquid chromatography tandem mass spectrometer (UHPLC–MS/MS) method for the identification and quantification of carbenoxolone in mouse blood and brain tissue. Twenty mice were injected intraperitoneally with 25 mg/kg carbenoxolone and brain tissue and blood were collected for analysis. Blood concentrations (mean ± SD) at 15, 30, 60 and 120 min were determined to be (n = 5) 5394 ± 778, 2636 ± 836, 1564 ± 541 and 846 ± 252 ng/mL, respectively. Brain concentrations (mean ± SD) at 15, 30, 60 and 120 mins were determined to be (n = 5) 171 ± 62, 102 ± 35, 55 ± 10 and 27 ± 9 ng/g, respectively. The analysis of these specimens at the four different time points resulted in blood and brain half‐lives in mice of ~43 and 41 min, respectively. The UHPLC–MS/MS method was determined to be sensitive and robust for quantification of carbenoxolone.     

Challenge and Solution of Characterizing Glass Transition Temperature for Conjugated Polymers by Differential Scanning Calorimetry

Thermomechanical properties of polymers highly depend on their glass transition temperature (T _g). Differential scanning calorimetry (DSC) is commonly used to measure T _g of polymers. However, many conjugated polymers (CPs), especially donor–acceptor CPs (D–A CPs), do not show a clear glass transition when measured by conventional DSC using simple heat and cool scan. In this work, we discuss the origin of the difficulty for measuring T _g in such type of polymers. The changes in specific heat capacity (Δc _p) at T _g were accurately probed for a series of CPs by DSC. The results showed a significant decrease in Δc _p from flexible polymer (0.28 J g^?1 K^?1 for polystyrene) to rigid CPs (10^?3 J g^?1 K^?1 for a naphthalene diimide‐based D–A CP). When a conjugation breaker unit (flexible unit) is added to the D–A CPs, we observed restoration of the Δc _p at T _g by a factor of 10, confirming that backbone rigidity reduces the Δc _p. Additionally, an increase in the crystalline fraction of the CPs further reduces Δc _p. We conclude that the difficulties of determining T _g for CPs using DSC are mainly due to rigid backbone and semicrystalline nature. We also demonstrate that physical aging can be used on DSC to help locate and confirm the glass transition for D‐A CPs with weak transition signals. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1635–1644     

Euler’s partition theorem for all moduli and new companions to Rogers–Ramanujan–Andrews–Gordon identities

The Ramanujan Journal - We generalise Euler’s partition theorem involving odd parts and distinct parts for all moduli and provide new companions to...     

Automorphism groups of designs with λ=1

If $G$ is a finite group and $k=q>2$ or $k=q+1$ for a prime power $q$ then, for infinitely many integers $v$, there is a 2-$(v,k,1)$-design $\mathbf{D}$ for which $\mathrm{Aut}\mathbf{D}?G$.     

Synthetic,Chemically Defined Polymer‐Coated Microcarriers for the Expansion of Human Mesenchymal Stem Cells

Mesenchymal stem cells (MSC), also called marrow stromal cells, are adult cells that have attracted interest for their potential uses in therapeutic applications. There is a pressing need for scalable culture systems due to the large number of cells needed for clinical treatments. Here, a tailorable thin polymer coating—poly(poly(ethylene glycol) methyl ether methacrylate‐ran‐vinyl dimethyl azlactone‐ran‐glycidyl methacrylate) [P(PEGMEMA‐r‐VDM‐r‐GMA); PVG]—to the surface of commercially available polystyrene and glass microcarriers to create chemically defined surfaces for large‐scale cell expansion is applied. These chemically defined microcarriers create a reproducible surface that does not rely on the adsorption of xenogenic serum proteins to mediate cell adhesion. Specifically, this coating method anchors PVG copolymer through ring opening nucleophilic attack by amine residues on poly‐l ‐lysine that is pre‐adsorbed to the surface of microcarriers. Importantly, this anchoring reaction preserves the monomer VDM reactivity for subsequent functionalization with an integrin‐specific Arg‐Gly‐Asp peptide to enable cell adhesion and expansion via a one‐step reaction in aqueous media. MSCs cultured on PVG‐coated microcarriers achieve sixfold expansion—similar to the expansion achieved on PS microcarriers—and retain their ability to differentiate after harvesting.     

Synthesis of a macrocycle based on Linked Amino Acid Mimetics (LAAM)

We report the synthesis of a macrocycle utilizing a novel framework of standard amino acids in combination with subunits that we have named as Linked Amino Acid Mimetics (LAAMs). Macrocycles based on the LAAM concept provide both a peptide targeting region and two independently variable functional regions. In the prototype structure, the commonly known Arg-Gly-Asp (RGD) sequence was used for the targeting region. The functional regions contain a phenyl group, and the linkage was formed via a Ring-Closing Metathesis (RCM) reaction.