Frames and the Feichtinger conjecture

We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linearly independent sequences. We further show that the two conjectures are implied by the paving conjecture. Finally, we show that Weyl-Heisenberg frames over rational lattices are finite unions of Riesz basic sequences.

     

The structure of liquid water. A low frequency (10–400 cm) Raman study

The recently developed molecular form of the ground state inversion potential method (GIPM) is applied here to the calculation of the total subshell photoionization cross sections of the water molecule in the energy range from threshold to 50 eV. The results show that the ionization can be accurately represented as a superposition of atomic processes.     

Excess partial molar enthalpies,entropies, Gibbs energies,and volumes in aqueous dimethylsulfoxide

The excess partial molar enthalpies, the vapor pressures, and the densities of dimethylsulfoxide (DMSO)–H₂O mixtures were measured and the excess partial molar Gibbs energies and the partial molar volumes were calculated for DMSO and for H₂O. The values of the excess partial molar Gibbs energies for both DMSO and H₂O are negative over the entire composition range. The results for the water-rich region indicated that the presence of DMSO enhances the hydrogen bond network of H₂O. Unlike monohydric alcohols, however, the solute-solute interaction is repulsive in terms of the Gibbs energy. This was a result of the fact that the repulsion among solutes in terms of enthalpy surpassed the attraction in terms of entropy. The data in the DMSO-rich region suggest that DMSO molecules form clusters which protect H₂O molecules from exposure to the nonpolar alkyl groups of DMSO.     

A new dimension in thermal analysis

Summary An enormous development has taken place within the last five years in synchronous teaching over the Internet, i.e. both the teacher and the students are simultaneously in direct communication with each other as in a normal class-room or auditorium. With this concept it is possible to communicate orally, to exchange Power Point Presentations, documents, programmes and live web-camera pictures. It is even possible to use an electronic black board on which both the teacher and the students can work simultaneously. The great advantage with this type of teaching is that it is not restricted to a single class-room/auditorium with limited access, but in a virtual room accessible to everybody in principle all over the world, and which certainly open up new possibilities in teaching. The purpose of this paper is to present and to discuss the concept of virtual class-room teaching, how the system operates in practice, its advantages and, finally, how its inherent limitations can be overcome.     

Stabilisation of a nucleic acid three-way junction by an oligonucleotide containing a single 2'-C to 3'-O-phosphate butylene linkage prepared by a tandem RCM-hydrogenation method

A cyclic dinucleotide with a butylene linker between the upper 2'-C position and the 3'-O-phosphate linkage was synthesised from simple nucleoside building blocks via a tandem ring-closing metathesis and hydrogenation procedure. The major of two phosphorus epimers was incorporated into an oligodeoxynucleotide, as well as into an LNA-DNA mixmer oligonucleotide. These were evaluated as parts in three different secondary structures, a duplex, a bulged duplex and a three-way junction, with both DNA and RNA complements. In the DNA:RNA hybrid molecule, the oligodeoxynucleotide containing this single 2'-C to 3'-O-phosphate butylene linkage was found to stabilise a three-way junction.     

Parallel synthesis of PNA-peptide conjugate libraries

An optimized semi-automatic protocol for parallel synthesis of up to 96 peptide nucleic acids (PNA) or PNA-peptide conjugates using Boc-protection strategy has been developed using a robotic system. The approach is illustrated by synthesizing PNA and PNA-peptide libraries varying between 15 and 27 amino acid units. The peptides (NLS (nuclear localization signal) or Tat-peptide) were attached to N-terminus of the PNA. The method was found to be far superior to that based on the SPOT/Fmoc protocol by which PNA oligomers are synthesized on a modified cellulose membrane. On a 0.5 micromole scale the method typically yielded 2 mg product of 90% purity by HPLC/MALDI-TOF analysis. This approach is suitable for screening of a large number of PNA and/or peptide sequences for biochemical and biological studies.     

All-trans-1-acyloxy-1,3-pentadiene-5 ols as reactive dienes in new intramolecular diels-alder reactions

The high reactivity of the $\text{all-trans}$-1-acyloxy-1,3-pentadiene-5-ols as dienes in intramolecular Diels-Alder reactions with maleic anhydride and fumaric acid ethylester monochloride is discussed.     

Synthesis of N-1-(Indanyloxymethyl) and N-1-(4-Hydroxybut-2-enyloxymethyl) Analogues of the HIV Drugs Emivirine and GCA-186

A series of Emivirine and GCA-186 analogues substituted at N-1 with indan-1-yloxymethyl (6a–6c) and indan-2-yloxymethyl (6d–6f) were synthesized by reaction of the corresponding bis(indanyloxy)methans with uracils having 5-ethyl or 5-isopropyl and 6-benzyl or 6-(3,5-dimethylbenzyl) substituents. A route to the corresponding N-1 substituted 4-hydroxybut-2-enyloxymethyl analogue was also devised. All newly synthesized compounds showed potent activity against wild-type HIV-1, the most active compound being 5-ethyl-1-(indan-1-yloxymethyl)-6-(3,5-dimethylbenzyl)uracil (6b), which was 50-fold more active than Emivirine.