Modified Hyaluronan Hydrogels Support the Maintenance of Mouse Embryonic Stem Cells and Human Induced Pluripotent Stem Cells

These studies provide evidence for the ability of a commercially available, defined, hyaluronan‐gelatin hydrogel, HyStem‐C?, to maintain both mouse embryonic stem cells (mESCs) and human induced pluripotent stem cells (hiPSCs) in culture while retaining their growth and pluripotent characteristics. Growth curve and doubling time analysis show that mESCs and hiPSCs grow at similar rates on HyStem‐C? hydrogels and mouse embryonic fibroblasts and Matrigel?, respectively. Immunocytochemistry, flow cytometry, gene expression and karyotyping reveal that both human and murine pluripotent cells retain a high level of pluripotency on the hydrogels after multiple passages. The addition of fibronectin to HyStem‐C? enabled the attachment of hiPSCs in a xeno‐free, fully defined medium.

     

A chromenoquinoline-based fluorescent off-on thiol probe for bioimaging

A new chromenoquinoline-based fluorescent off-on thiol probe 2 is reported. In aqueous buffer solutions at physiological pH, the probe exhibited 223-fold enhancement in fluorescence intensity by a Michael addition of cysteine to the maleimide appended to a chromenoquinoline. Cell permeability and live cell imaging of thiols are also demonstrated.     

AlCl3 induced C-N bond formation followed by Pd/C-Cu mediated coupling-cyclization strategy: synthesis of pyrrolo[2,3-b]quinoxalines as anticancer agents

AlCl₃ facilitated C-N bond forming reaction between 2,3-dichloroquinoxaline and anilines affording a convenient method for the preparation of N-aryl substituted 3-chloroquinoxalin-2-amines. A related N-benzyl derivative, however, was prepared via a conventional method. These N-alkyl/aryl substituted 3-chloroquinoxalin-2-amines on coupling with terminal alkynes in toluene under Pd/C-Cu catalysis afforded a range of 1,2-disubstituted pyrrolo[2,3-b]quinoxalines within 3-5 h in good to excellent yields. Some of the compounds synthesized showed promising anti-proliferative properties when tested in vitro against two cancer cell lines. Docking studies indicated that these molecules interact well with human Akt in silico.     

Vector bundles on toric varieties

Following Sam Payne?s work, we study the existence problem of nontrivial vector bundles on toric varieties. The first result we prove is that every complete fan admits a nontrivial conewise linear multivalued function. Such functions could potentially be the Chern classes of toric vector bundles. Then we use the results of Cortiñas, Haesemeyer, Walker and Weibel to show that the (non-equivariant) Grothendieck group of the toric 3-fold studied by Payne is large, so the variety has a nontrivial vector bundle. Using the same computation, we show that every toric 3-fold X either has a nontrivial line bundle, or there is a finite surjective toric morphism from Y to X, such that Y has a large Grothendieck group.     

Decomposition theorem for the cd-index of Gorenstein<Superscript>*</Superscript> posets

We prove a decomposition theorem for the cd-index of a Gorenstein^* poset analogous to the decomposition theorem for the intersection cohomology of a toric variety. From this we settle a conjecture of Stanley that the cd-index of Gorenstein* lattices is minimized on Boolean algebras.     

State-Feedback Stabilization of Well-Posed Linear Systems

A finite-dimensional linear time-invariant system is output-stabilizable if and only if it satisfies the finite cost condition, i.e., if for each initial state there exists at least one L² input that produces an L² output. It is exponentially stabilizable if and only if for each initial state there exists at least one L² input that produces an L² state trajectory. We extend these results to well-posed linear systems with infinite-dimensional input, state and output spaces. Our main contribution is the fact that the stabilizing state feedback is well posed, i.e., the map from an exogenous input (or disturbance) to the feedback, state and output signals is continuous in L_loc² in both open-loop and closed-loop settings. The state feedback can be chosen in such a way that it also stabilizes the I/O map and induces a (quasi) right coprime factorization of the original transfer function. The solution of the LQR problem has these properties.     

Strictly locally order affine complete lattices

We call a latticeL strictly locally order-affine complete if, given a finite subsemilatticeS ofL ⁿ, every functionf: S L which preserves congruences and order, is a polynomial function. The main results are the following: (1) all relatively complemented lattices are strictly locally order-affine complete; (2) a finite modular lattice is strictly locally order-affine complete if and only if it is relatively complemented. These results extend and generalize the earlier results of D. Dorninger [2] and R. Wille [9, 10].     

p-(1H-phenanthro[9,10-d]imidazol-2-yl)- substituted calix[4]arene, a deep cavity for guest inclusion

The reaction of tetra-p-formyltetra-O-propylcalix[4]arene with phenanthrenequinone in the presence of NH(4)OAc affords compound 2, a new class of calixarene with an expanded aromatic cavity, that could be stabilized by hydrogen-bonded bridges and/or ion pairing, thus preventing collapse into fully stacked pinched cone conformations as depicted. Two partially protonated calixarenes interdigitate in the solid state to give rise to a self-assembled face-to-face dimer, stabilized by pi-pi stacking interactions.     

A natural extension for the greedy β-transformation with three arbitrary digits

We construct a planar version of the natural extension of the piecewise linear transformation T generating greedy β-expansions with digits in an arbitrary set of real numbers A = {a ₀, a ₁, a ₂}. As a result, we derive in an easy way a closed formula for the density of the unique T-invariant measure µ absolutely continuous with respect to Lebesgue measure. Furthermore, we show that T is exact and weak Bernoulli with respect to µ.     

The transfer of tin and germanium atoms from N-heterocyclic stannylenes and germylenes to diazadienes

New N-heterocyclic stannylenes and germylenes were synthesized by transamination of E[N(SiMe3)2] (E = Ge, Sn) with alpha-amino-aldimines or ethylidene-1,2-diamines and were characterized by spectroscopic methods and in the case of the germylene 10 g by X-ray diffraction. The reactions of several germylenes and stannylenes with diazadienes were studied by using dynamic NMR and computational methods. Experimental and theoretical studies confirmed that metathesis with exchange of the Group 14 atom is feasible for both stannylenes and germylenes, with exchange rates being generally higher for stannylenes. The metathesis of the diazadiene 3 b and the stannylene 1 b follows second-order kinetics and exhibits a sizeable negative entropy of activation. The transfer reaction is inhibited by bulky substituents in both reactants and surprisingly coincides with a suppression of the fragmentation of the stannylene into tin and diazadiene. A connection between oxidative addition and ring fragmentation was also observed in the reaction of 1 f with sulfur. Density functional theory (DFT) calculations suggest that all metathesis reactions proceed via transient spirocyclic [1+4] cycloaddition products, the formation of which is generally endothermic and endergonic. The spirostannanes display a distorted Psi-tbp geometry at the tin atom and their cycloreversion requires low or nearly negligible activation energies; spirogermanes exhibit distorted tetrahedral central atoms and sizeable energy barriers with respect to the same reaction. Complementary studies of cycloadditions of diazadienes to triplet germylenes or stannylenes indicate that these reactions are exothermic. The lowest triplet state in the carbene homologues results from promotion of an electron from an n(N) orbital with pi character rather than the n(C)-sigma orbital as in carbenes, and singlet-triplet excitation energies decrease from carbon to tin. Spirostannanes exhibit a triplet ground-state multiplicity that implies that the energy hypersurfaces for the reactions of singlet and triplet stannylenes with diazadienes intersect; for germylenes, the singlet hypersurface is always lower in energy. A reaction mechanism explaining the different thermal stabilities of N-heterocyclic germylenes and stannylenes, and the coincidence between ring metathesis and thermal decomposition of the latter, is proposed based on the different separation of the singlet and triplet energy hypersurfaces.