Cohomology in one-dimensional substitution tiling spaces

Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which ``forces its border.' One can then represent the tiling space as an inverse limit of an inflation and substitution map on a cellular complex formed from the collared tiles; the cohomology of the tiling space is computed as the direct limit of the homomorphism induced by inflation and substitution on the cohomology of the complex. For one-dimensional substitution tiling spaces, we describe a modification of the Anderson-Putnam complex on collared tiles that allows for easier computation and provides a means of identifying certain special features of the tiling space with particular elements of the cohomology.

     

Unusual [3+2]-cycloaddition of acrylic acid derivatives to 7-formyl-4,5,6,7-tetrahydro-4,5,7-trimethylpyrrolo[3,2-c]pyridine under Michael reaction conditions

8-Substituted tetrahydropyrido[3,2-e]pyrrolizines are formed in the [3+2]-cycloaddition of 2-formyltetrahydropyrrolo[3,2-c]pyridine and acrolein, acrylonitrile, and methyl acrylate in the presence of trilon B. Russian International Friendship University, 117923 Moscow. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1670–1675, December, 1998.     

Controlling the variation of axial water exchange rates in macrocyclic lanthanide(III) complexes

The rate of axial water exchange in well-defined series of lanthanide complexes depends on the extent of second sphere hydration which is determined by complex hydrophobicity and the nature of the lanthanide ion and its counter-ion.     

Bifurcations and Attractor-Repeller Splittings of Non-Saddle Sets

This paper is devoted to the study of some aspects of the stability theory of flows. In particular, we study Morse decompositions induced by non-saddle sets, including their corresponding Morse equations, attractor-repeller splittings of non-saddle sets and bifurcations originated by implosions of the basin of attraction of asymptotically stable fixed points. We also characterize the non-saddle sets of the plane in terms of the Euler characteristic of their region of influence.     

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.     

Ultrasound promoted efficient and green synthesis of β-amino carbonyl compounds in aqueous hydrotropic medium

Ultrasound promoted synthesis of β-amino carbonyl compounds in aqueous hydrotropic medium at ambient temperature is reported. The remarkable features of the new procedure are shorter reaction time, excellent yields in aqueous medium, cleaner reaction profile and simple experimental and work-up procedure.     

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.     

Potential drugs and nondrugs: prediction and identification of important structural features

Using decision trees, a model to discriminate between potential drugs and nondrugs has been developed. Compounds from the Available Chemical Directory and the World Drug Index databases were used as training set; the molecular structures were represented using extended atom types. The error rate on an independent validation data set is 17.4%. The number of false negatives can be reduced by penalizing the misclassification of drugs so that 92 out of 100 potential drugs are correctly recognized. At the same time, 34 out of 100 nondrugs are classified as potential drugs. The predictions of the model can be used to guide the purchase or selection of compounds for biological screening or the design of combinatorial libraries. The visualization of the generated models in the form of colored trees allowed us to identify a few, surprisingly simple features that explain the most significant differences between drugs and nondrugs in the training set: Just by testing the presence of hydroxyl, tertiary or secondary amino, carboxyl, phenol, or enol groups, already three quarters of all drugs could be correctly recognized. The nondrugs, on the other hand, are characterized by their aromatic nature with a low content of functional groups besides halogens. The general applicability of the model is shown by the predictions made for several Organon databases.