PRESENTATIONS: FROM KAC-MOODY GROUPS TO PROFINITE AND BACK

We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on both.     

Energetically important C-H···F-C pseudohydrogen bonding in water: evidence and application to rational design of oligonucleotides with high binding affinity

It is controversial whether organic fluorine can form energetically important hydrogen bonds in aqueous environments. We previously showed by NMR and molecular modeling that the unexpectedly high binding affinity of 2'F-ANA is largely due to a C-H···F-C pseudohydrogen bond at pyrimidine-purine steps. Comparisons of the melting of duplexes with identical sequence composition but a rearranged sequence confirm that energetically important fluorine-mediated pseudohydrogen bonding is in operation in these sequences. The effect is of particular importance when the H-bond donor (purine H8) is activated by the presence of fluorine at its own 2'-position. These results provide a rational method to increase the binding affinity of antisense oligonucleotides by placement of 2'F-ANA modifications at pyrimidine-purine steps.     

Embeddings of SL(2; ?) into the cremona group

Geometric and dynamic properties of embeddings of SL(2; ℤ) into the Cremona group are studied. Infinitely many nonconjugate embeddings that preserve the type (i.e., that send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many nonconjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2; ℤ), preserves an elliptic curve and all its elements of infinite order are hyperbolic.     

Distinct columnar and lamellar liquid crystalline phases formed by new bolaamphiphiles with linear and branched lateral hydrocarbon chains

A universal building block for the convergent synthesis of a wide variety of different T-shaped ternary amphiphiles was developed and used for the synthesis of a series of new liquid-crystalline materials composed of a rigid biphenyl core with polar glycerol groups at both ends and linear or branched alkyl chains in a lateral position. In addition, compounds with bulky achiral (2,4,6-trimethylphenoxy, adamantane-1-carboxylate, benzoate) or chiral (menthyl or cholesteryl) substituents attached to the end of the lateral alkyl chain were also investigated. In all cases the lateral chains were connected to the aromatic core by an ether linkage. The effect of the ether linking unit on mesophase stability and mesophase type is discussed with respect to conformational effects. The liquid-crystalline phases were investigated by polarizing microscopy, calorimetry, and X-ray diffraction of surface aligned samples. Upon enlarging the lateral chains a series of different polygonal cylinder phases was observed, which were replaced by lamellar phases and a non-cylinder hexagonal columnar phase by further increasing the size of these substituents. Remarkably, only pentagonal, hexagonal, and giant hexagonal cylinder phases could be observed, whereas mesophases composed of cylinders with a smaller number of sides are missing. No distinct chirality effects were observed for the menthyl- and cholesteryl-substituted compounds. However, the rodlike shape of the polycyclic cholesteryl core leads to a unique phase structure combining an organization of the alicyclic cholesteryl cores perpendicular to the layer planes and the aromatic biphenyl cores parallel to the layer planes.