Homological Pisot substitutions and exact regularity

We consider one-dimensional substitution tiling spaces where the dilatation (stretching factor) is a degree d Pisot number, and the first rational Čech cohomology is d-dimensional. We construct examples of such “homological Pisot” substitutions whose tiling flows do not have pure discrete spectra. These examples are not unimodular, and we conjecture that the coincidence rank must always divide a power of the norm of the dilatation. To support this conjecture, we show that homological Pisot substitutions exhibit an Exact Regularity Property (ERP), in which the number of occurrences of a patch for a return length is governed strictly by the length. The ERP puts strong constraints on the measure of any cylinder set in the corresponding tiling space.     

Coibacins A-D, Antileishmanial Marine Cyanobacterial Polyketides with Intriguing Biosynthetic Origins

Four unsaturated polyketide lactone derivatives, coibacins A-D, were isolated from a Panamanian marine cyanobacterium, cf. Oscillatoria sp. The two different types of termini observed in these co-occurring metabolites, either a methyl cyclopropyl ring as seen in curacin A or a methyl vinyl chloride similar to that observed in the jamaicamides, suggest an intriguing flexibility in the "beta branch" forming biosynthetic process. The coibacins possess selective antileishmanial activity as well as potent anti-inflammatory activity.     

Role of the gouy phase in the coherent phase control of the photoionization and photodissociation of vinyl chloride

We demonstrate theoretically and experimentally that the Gouy phase of a focused laser beam may be used to control the photoinduced reactions of a polyatomic molecule. Quantum mechanical interference between one- and three-photon excitation of vinyl chloride produces a small phase lag between the dissociation and ionization channels on the axis of the molecular beam. Away from the axis, the Gouy phase introduces a much larger phase lag that agrees quantitatively with theory without any adjustable parameters.     

Regioselective N‐Alkylation of Ethyl 4‐Benzyloxy‐1,2,3‐triazolecarboxylate: A Useful Tool for the Synthesis of Carboxylic Acid Bioisosteres

Acidic 4‐hydroxy‐1,2,3‐triazole is a proven bioisostere of acidic functions that has recently been used to replace the acidic moieties of biologically active leads. Straightforward chemical strategies for the synthesis of the three possible N‐alkylated 4‐hydroxy‐1,2,3‐triazole regioisomers have been designed and reported herein, by identifying the optimal conditions under which the alkylation of ethyl 4‐benzyloxy‐1,2,3‐triazolecarboxylate (compound 19 ) can be regiodirected to the triazole N(b) position and thus produce the only isomer that cannot be obtained via the cycloaddition reaction. Furthermore, an innovative platform for parallel synthesis, called Arachno and which has been patented by the authors' group, has been used to speed up the process, and an NMR study has been carried out to better understand the reactivity of compound 19 towards the N(b) position. A library of benzyloxy protected 4‐hydroxy‐1,2,3‐triazoles has been prepared using the two strategies: regiodirection for the N(b) and N(c) isomers and cycloaddition for the N(a) isomers; the processes are described herein. The three N‐alkylated regioisomer series have been characterized spectroscopically (NMR and MS). The subsequent catalytic hydrogenation of the 4‐benzyloxy protective group on the N‐alkylated‐4‐benzyloxy‐5‐ethoxycarbonyl‐1,2,3‐triazoles provided the corresponding substituted 4‐hydroxy‐1,2,3‐triazoles.     

The MTXαR method: a semi-empirical version of the multiple scattering Xα scheme with application to Li2

We propose a new method for determining the α parameter for use in the multiple scattering Xα method based on molecular rather than atomic considerations. Such as α value for lithium has been obtained by requiring agreement between the calculated and experimental values of the minimum in the Li₂ potential curve. Use of such a molecular value of α_R yields a potential curve all of whose features are in substantially better agreement with experiment than those obtained with the standard “atomic” α value. The desirable aspects of the original MSXα scheme including the muffin-tin potential approximation are retained in the present MTXα_R version.     

A theoretical investigation of the origins of the green and red spectra of Ca2

The potential energy curves and transition moments of the ground state of Ca₂ and ¹Σ⁺_u states correlating with the ¹S + ¹P and ¹S + ¹D calcium atoms have been calculated. The calculations support the assignment of the observed emission spectra of Ca₂ in the red and in the green to transitions between the ground state and the 1,2¹Σ⁺_u states. Predissociation of the 1¹Σ⁺_u state is also shown to be possible from an interaction with the 1³Π_u state.     

Chemical Design of Non‐Ionic Polymer Brushes as Biointerfaces: Poly(2‐oxazine)s Outperform Both Poly(2‐oxazoline)s and PEG

The era of poly(ethylene glycol) (PEG) brushes as a universal panacea for preventing non‐specific protein adsorption and providing lubrication to surfaces is coming to an end. In the functionalization of medical devices and implants, in addition to preventing non‐specific protein adsorption and cell adhesion, polymer‐brush formulations are often required to generate highly lubricious films. Poly(2‐alkyl‐2‐oxazoline) (PAOXA) brushes meet these requirements, and depending on their side‐group composition, they can form films that match, and in some cases surpass, the bioinert and lubricious properties of PEG analogues. Poly(2‐methyl‐2‐oxazine) (PMOZI) provides an additional enhancement of brush hydration and main‐chain flexibility, leading to complete bioinertness and a further reduction in friction. These data redefine the combination of structural parameters necessary to design polymer‐brush‐based biointerfaces, identifying a novel, superior polymer formulation.     

Central sets and substitutive dynamical systems

In this paper we establish a new connection between central sets and the strong coincidence conjecture   for fixed points of irreducible primitive substitutions of Pisot type. Central sets, first introduced by Furstenberg using notions from topological dynamics, constitute a special class of subsets of N$\mathbb{N}$ possessing strong combinatorial properties: Each central set contains arbitrarily long arithmetic progressions, and solutions to all partition regular systems of homogeneous linear equations. We give an equivalent reformulation of the strong coincidence condition in terms of central sets and minimal idempotent ultrafilters in the Stone–?ech compactification βN$\beta \mathbb{N}$. This provides a new arithmetical approach to an outstanding conjecture in tiling theory, the Pisot substitution conjecture  . The results in this paper rely on interactions between different areas of mathematics, some of which had not previously been directly linked: They include the general theory of combinatorics on words, abstract numeration systems, tilings, topological dynamics and the algebraic/topological properties of Stone–?ech compactification of N$\mathbb{N}$.